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Financial Decision Analysis

Board of Studies

Prof. H. N. Verma Prof. M. K. GhadoliyaVice- Chancellor Director, Jaipur National University, Jaipur School of Distance Education and Learning Jaipur National University, JaipurDr. Rajendra Takale Prof. and Head AcademicsSBPIM, Pune

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Subject Expert Panel

Dr. S. U. Gawade Somrita MitraHead Research, SIOM Subject Matter ExpertPune

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Content Review Panel

Shreya Saraf Shweta MutttalmaniSubject Matter Expert Subject Matter Expert

___________________________________________________________________________________________Copyright ©

This book contains the course content for Financial Decision Analysis.

First Edition 2013

Printed byUniversal Training Solutions Private Limited

Address05th Floor, I-Space, Bavdhan, Pune 411021.

All rights reserved. This book or any portion thereof may not, in any form or by any means including electronic or mechanical or photocopying or recording, be reproduced or distributed or transmitted or stored in a retrieval system or be broadcasted or transmitted.

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A

Index

Content ........................................................................... II

List of Figures ............................................................. VII

List of Tables ..............................................................VIII

Abbreviations ...............................................................IX

Case Study .................................................................. 123

Bibliography ............................................................... 128

Self Assessment Answers ........................................... 131

II

Contents

Chapter I ....................................................................................................................................................... 1Introduction to Financial Statement Analysis ........................................................................................... 1Aim ................................................................................................................................................................ 1Objectives ...................................................................................................................................................... 1Learning outcome .......................................................................................................................................... 11.1 Introduction .............................................................................................................................................. 21.2 Meaning of Finance ................................................................................................................................. 2 1.2.1 Definition of Finance ............................................................................................................... 21.3 Introduction to Financial Statement ......................................................................................................... 21.4 Meaning and Definition of Financial Statement ...................................................................................... 2 1.4.1 Income Statement .................................................................................................................... 3 1.4.2 Position Statement ................................................................................................................... 3 1.4.3 Statement of Changes in Owner’s Equity ................................................................................ 3 1.4.4 Statement of Changes in Financial Position ............................................................................ 41.5 Types of Financial Statement Analysis .................................................................................................... 41.6 Techniques of Financial Statement Analysis ........................................................................................... 5 1.6.1 Comparative Statement Analysis ............................................................................................. 6 1.6.2 Comparative Balance Sheet Analysis ...................................................................................... 6 1.6.3 Comparative Profit and Loss Account Analysis ...................................................................... 6 1.6.4 Trend Analysis ......................................................................................................................... 6 1.6.5 Common Size Analysis ............................................................................................................ 61.7 Funds Flow Statement.............................................................................................................................. 61.8 Cash Flow Statement ............................................................................................................................... 61.9 Ratio Analysis .......................................................................................................................................... 7 1.9.1 Liquidity Ratio ......................................................................................................................... 7 1.9.2 Activity Ratio ........................................................................................................................... 8 1.9.3 Solvency Ratio ......................................................................................................................... 8 1.9.4 Profitability Ratio .................................................................................................................... 9Summary ..................................................................................................................................................... 10References ................................................................................................................................................... 10Recommended Reading ............................................................................................................................. 10Self Assessment ............................................................................................................................................11

Chapter II ................................................................................................................................................... 13Basic Concept of Time Value of Money ................................................................................................... 13Aim .............................................................................................................................................................. 13Objectives .................................................................................................................................................... 13Learning outcome ........................................................................................................................................ 132.1 Introduction ............................................................................................................................................ 142.2 Reasons for Time Value of Money ......................................................................................................... 142.3 Timelines and Notation .......................................................................................................................... 152.4 Valuation Concepts ................................................................................................................................ 162.5 Techniques of Time Value of Money ..................................................................................................... 16 2.5.1 Compounding Techniques/Future Value Technique .............................................................. 16 2.5.2 Future Value of a Single Amount (Lumpsum) ....................................................................... 172.6 Multiple Compounding Periods ............................................................................................................. 182.7 Future Value of Multiple Cash Flows .................................................................................................... 192.8 Effective Rate of Interest In Case of Multi-Period Compounding ........................................................ 19 2.8.1 Growth Rate ........................................................................................................................... 222.9 Discounting or Present Value Concept................................................................................................... 222.10 Simple and Compound Interest ............................................................................................................ 22 2.10.1 Compound Interest ............................................................................................................... 23 2.10.2 Compound Growth Rate ...................................................................................................... 24

A

Summary ..................................................................................................................................................... 25References ................................................................................................................................................... 25Recommended Reading ............................................................................................................................. 25Self Assessment ........................................................................................................................................... 26

Chapter III .................................................................................................................................................. 28Valuing Bonds ............................................................................................................................................. 28Aim .............................................................................................................................................................. 28Objectives .................................................................................................................................................... 28Learning outcome ........................................................................................................................................ 283.1 Introduction ............................................................................................................................................ 293.2 Bond Prices and Interest Rates .............................................................................................................. 29 3.2.1 The Present Value Relationship ............................................................................................. 29 3.2.2 A Measure of Interest Rate Risk in Bonds ............................................................................. 30 3.2.3 A More Formal Measure of Interest Rate Risk - Duration .................................................... 303.3 Determinants of Interest Rates ............................................................................................................... 31 3.3.1 Level of Interest Rates ........................................................................................................... 31 3.3.2 Maturity Premium .................................................................................................................. 35 3.3.3 Default Premium .................................................................................................................... 383.4 Special Feature in Bonds and Pricing Effects ........................................................................................ 39 3.4.1 Convertibility ......................................................................................................................... 39 3.4.2 Callability ............................................................................................................................... 40 3.4.3 Pre-payment Option ............................................................................................................... 43 3.4.4 Interest Rate Caps and Floors ................................................................................................ 44 3.4.5 Other Features ........................................................................................................................ 46Summary ..................................................................................................................................................... 48References ................................................................................................................................................... 48Recommended Reading ............................................................................................................................. 49Self Assessment ........................................................................................................................................... 50

Chapter IV .................................................................................................................................................. 52Risk and Return ......................................................................................................................................... 52Aim .............................................................................................................................................................. 52Objectives .................................................................................................................................................... 52Learning outcome ........................................................................................................................................ 524.1 Introduction ............................................................................................................................................ 534.2 Return ..................................................................................................................................................... 53 4.2.1 Stock Returns ......................................................................................................................... 53 4.2.2 Portfolio Return ..................................................................................................................... 54 4.2.3 Portfolio Proportions .............................................................................................................. 54 4.2.4 Mean Return .......................................................................................................................... 554.3 Variance and Covariance ........................................................................................................................ 55 4.3.1 Sample Variance..................................................................................................................... 56 4.3.2 Sample Covariance ................................................................................................................ 574.4 Population Return and Variance ............................................................................................................. 58 4.4.1 Expectations ........................................................................................................................... 59 4.4.2 Expected Return ..................................................................................................................... 60 4.4.3 Population Variance ............................................................................................................... 60 4.4.4 Population Covariance ........................................................................................................... 614.5 Portfolio Variance .................................................................................................................................. 61 4.5.1 Two Assets ............................................................................................................................. 62 4.5.2 Correlation Coefficient .......................................................................................................... 62 4.5.3 General Formula .................................................................................................................... 63 4.5.4 Effect of Diversification ........................................................................................................ 63

IV

Summary ..................................................................................................................................................... 65References ................................................................................................................................................... 65Recommended Reading ............................................................................................................................. 65Self Assessment ........................................................................................................................................... 66

Chapter V .................................................................................................................................................... 68Cost of Capital ............................................................................................................................................ 68Aim .............................................................................................................................................................. 68Objectives .................................................................................................................................................... 68Learning outcome ........................................................................................................................................ 685.1 Introduction ............................................................................................................................................ 695.2 Meaning of Cost of Capital .................................................................................................................... 69 5.2.1 Definitions ............................................................................................................................. 695.3 Assumption of Cost of Capital ............................................................................................................... 695.4 Classification of Cost of Capital ............................................................................................................ 70 5.4.1 Explicit and Implicit Cost ...................................................................................................... 70 5.4.2 Average and Marginal Cost .................................................................................................... 70 5.4.3 Historical and Future Cost ..................................................................................................... 705.5 Importance of Cost of Capital ................................................................................................................ 715.6 Computation of Cost of Capital ............................................................................................................. 71 5.6.1 Cost of Equity ........................................................................................................................ 71 5.6.2 Dividend Price Approach ....................................................................................................... 72 5.6.3 Dividend Price plus Growth Approach .................................................................................. 72 5.6.4 Earning Price Approach ......................................................................................................... 73 5.6.5 Realised Yield Approach ........................................................................................................ 74 5.6.6 Cost of Debt ........................................................................................................................... 74 5.6.7 Debt Issued at Par .................................................................................................................. 74 5.6.8 Debt Issued at Premium or Discount ..................................................................................... 74 5.6.9 Cost of Perpetual Debt and Redeemable Debt ....................................................................... 75 5.6.10 Cost of Preference Share Capital ......................................................................................... 75 5.6.11 Cost of Retained Earnings ................................................................................................... 76 5.6.12 Measurement of Overall Cost of Capital ............................................................................. 77Summary ..................................................................................................................................................... 79References ................................................................................................................................................... 79Recommended Reading ............................................................................................................................. 79Self Assessment ........................................................................................................................................... 80

Chapter VI .................................................................................................................................................. 82Capital Budgeting ...................................................................................................................................... 82Aim .............................................................................................................................................................. 82Objectives .................................................................................................................................................... 82Learning outcome ........................................................................................................................................ 826.1 Introduction ............................................................................................................................................ 836.2 Definitions .............................................................................................................................................. 836.3 Need and Importance of Capital Budgeting ........................................................................................... 836.4 Capital Budgeting Process ..................................................................................................................... 846.5 Kinds of Capital Budgeting Decisions ................................................................................................... 856.6 Methods of Capital Budgeting of Evaluation ........................................................................................ 85 6.6.1 Pay-back Period ..................................................................................................................... 86 6.6.2 Post Pay-back Profitability Method ....................................................................................... 87 6.6.3 Accounting Rate of Return or Average Rate of Return .......................................................... 87 6.6.4 Net Present Value ................................................................................................................... 88 6.6.5 Internal Rate of Return .......................................................................................................... 88 6.6.6 Capital Rationing ................................................................................................................... 896.7 Risk and Uncertainly in Capital Budgeting ........................................................................................... 90

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6.7.1 Construction of Decision Tree ............................................................................................... 91Summary ..................................................................................................................................................... 92References ................................................................................................................................................... 92Recommended Reading ............................................................................................................................. 92Self Assessment ........................................................................................................................................... 93

Chapter VII ................................................................................................................................................ 95Capitalisation and Capital Structure ....................................................................................................... 95Aim .............................................................................................................................................................. 95Objectives .................................................................................................................................................... 95Learning outcome ........................................................................................................................................ 957.1 Introduction ............................................................................................................................................ 967.2 Meaning of Capital ................................................................................................................................ 96 7.2.1 Fixed Capital .......................................................................................................................... 96 7.2.2 Working Capital ..................................................................................................................... 967.3 Capitalisation ......................................................................................................................................... 977.4 Types of Capitalisation ........................................................................................................................... 97 7.4.1 Over Capitalisation ................................................................................................................ 97 7.4.2 Under Capitalisation .............................................................................................................. 98 7.4.3 Watered Capitalisation ........................................................................................................... 997.5 Capital Structure .................................................................................................................................... 99 7.5.1 Meaning of Capital Structure ................................................................................................. 99 7.5.2 Definition of Capital Structure ............................................................................................ 1007.6 Financial Structure ............................................................................................................................... 1007.7 Optimum Capital Structure .................................................................................................................. 100 7.7.1 Objectives of Capital Structure ............................................................................................ 101 7.7.2 Forms of Capital Structure ................................................................................................... 1017.8 Factors Determining Capital Structure ................................................................................................ 1017.9 Capital Structure Theories ................................................................................................................... 101 7.9.1 Traditional Approach ........................................................................................................... 102 7.9.2 Net Income (NI) Approach .................................................................................................. 102 7.9.3 Net Operating Income (NOI) Approach .............................................................................. 103 7.9.4 Modigliani and Miller Approach ......................................................................................... 104Summary ................................................................................................................................................... 105References ................................................................................................................................................. 105Recommended Reading ........................................................................................................................... 105Self Assessment ......................................................................................................................................... 106

Chapter VIII ............................................................................................................................................. 108Leverage and Dividend Decisions ........................................................................................................... 108Aim ............................................................................................................................................................ 108Objectives .................................................................................................................................................. 108Learning outcome ...................................................................................................................................... 1088.1 Introduction .......................................................................................................................................... 1098.2 Meaning of Leverage ........................................................................................................................... 109 8.2.1 Definition of Leverage ......................................................................................................... 109 8.2.2 Types of Leverages .............................................................................................................. 1098.3 Operating Leverage .............................................................................................................................. 109 8.3.1 Degree of Operating Leverage ..............................................................................................110 8.3.2 Uses of Operating Leverage .................................................................................................1108.4 Financial Leverage ................................................................................................................................110 8.4.1 Degree of Financial Leverage ...............................................................................................111 8.4.2 Alternative Definition of Financial Leverage .......................................................................111 8.4.3 Uses of Financial Leverage ...................................................................................................111 8.4.4 Financial BEP .......................................................................................................................112

VI

8.4.5 Indifference Point..................................................................................................................1128.5 Combined Leverage ..............................................................................................................................112 8.5.1 Degree of Combined Leverage .............................................................................................1138.6 Working Capital Leverage ....................................................................................................................1138.7 Dividend Decisions ...............................................................................................................................114 8.7.1 Meaning of Dividend ............................................................................................................1148.8 Types of Dividend .................................................................................................................................114 8.8.1 Cash Dividend .......................................................................................................................114 8.8.2 Stock Dividend .....................................................................................................................114 8.8.3 Bond Dividend ......................................................................................................................114 8.8.4 Property Dividend .................................................................................................................1148.9 Dividend Decision ................................................................................................................................115 8.9.1 Irrelevance of Dividend ........................................................................................................115 8.9.2 Modigliani and Miller’s Approach........................................................................................1158.10 Relevance of Dividend ........................................................................................................................116 8.10.1 Walter’s Model ....................................................................................................................116 8.10.2 Gordon’s Model ..................................................................................................................1178.11 Factors Determining Dividend Policy .................................................................................................1188.12 Types of Dividend Policy ....................................................................................................................118Summary ................................................................................................................................................... 120References ................................................................................................................................................. 120Recommended Reading ........................................................................................................................... 120Self Assessment ......................................................................................................................................... 121

A

List of Figures

Fig. 1.1 Financial statement ........................................................................................................................... 3Fig. 1.2 Types of financial statement analysis ............................................................................................... 4Fig. 1.3 Techniques of financial statement analysis ....................................................................................... 5Fig. 1.4 Classification of ratio ........................................................................................................................ 7Fig. 2.1 Timeline .......................................................................................................................................... 15Fig. 2.2 Techniques of time value of money ................................................................................... 16Fig. 3.1 Building blocks for interest rates .................................................................................................... 31Fig. 3.2 Yield curves - January 2001 and June 2001 ................................................................................... 35Fig. 3.3 Payoffs on call feature on bond to seller of bond ........................................................................... 41Fig. 3.4 Callable bond prices and interest rates ........................................................................................... 42Fig. 3.5 Effects of caps on floating rate loans .............................................................................................. 44Fig. 3.6 Effects of caps on floating rate loans .............................................................................................. 45Fig. 3.7 Effects of caps on floating rate loans .............................................................................................. 46Fig. 4.1 Graph of return ............................................................................................................................... 56Fig. 5.1 Classification of cost of capital ...................................................................................................... 70Fig. 6.1 Capital budgeting process ............................................................................................................... 84Fig. 6.2 Capital Budgeting Methods ............................................................................................................ 86Fig. 7.1 Position of capital ........................................................................................................................... 97Fig. 7.2 Capital structure theories .............................................................................................................. 102Fig. 7.3 Modigliani and miller approach ................................................................................................... 104Fig. 8.1 Types of leverages ........................................................................................................................ 109Fig. 8.2 Types of dividends .........................................................................................................................114Fig. 8.3 Dividend theories ...........................................................................................................................115

VIII

List of Tables

Table 1.1 Classification of financial statement analysis based on material used ........................................... 5Table 1.2 Classification of financial statement analysis based on method of operation ................................ 5Table 1.3 Difference between funds flow and cash flow statement ............................................................... 7Table 1.4 Liquidity ratios ............................................................................................................................... 7Table 1.5 Activity ratios ................................................................................................................................. 8Table 1.6 Solvency ratios ............................................................................................................................... 8Table 1.7 Profitability ratios .......................................................................................................................... 9

Table 2.1 Value of for various combinations of r and n ............................................................... 17Table 2.2 Compound value .......................................................................................................................... 19Table 2.3 Compounding and interest rate .................................................................................................... 19Table 2.4 Compounding and interest rate .................................................................................................... 20Table 2.5 Compounding and interest rate and EIR ...................................................................................... 21Table 2.6 Growth rate .................................................................................................................................. 22Table 2.7 Value of Rs 1,000 invested at 10% simple and compound interest ............................................. 23Table 2.8 Dividend data ............................................................................................................................... 24Table 4.1 Return on general motors stock 1993-2003 ................................................................................. 56Table 4.2 Stock, returns in 2006 and returns in 2007 .................................................................................. 57Table 7.1 Difference between the financial structure and capital structure ............................................... 100Table 7.2 Format for calculating value of the firm on the basis of NI approach ....................................... 103Table 8.1 Difference between operating leverage and financial leverage ..................................................112

IX

Abbreviations

AS-3 - Accounting StandardCA - Current AssetsCL - Combined LeverageCPM - Critical Path MethodD/P - Dividend PriceDFL - Degree of Financial LeverageDOL - Degree of Operating LeverageE/P - Earning PriceEAIT - Earnings After Interest and TaxEBIT - Earnings Before Interest & TaxEIR - Effective Interest RateEPS - Earnings Per ShareFL - Financial LeverageFVIF - Future Value Interest FactorNI - Net IncomeNOI - Net Operating IncomeOL - Operating LeverageOP - OperatingProfitsPBT - ProfitBeforeTaxPERT - Program Evaluation and Review TechniquePV - Present ValueTA - Total AssetsWCL - Working Capital Leverage

1

Chapter I

Introduction to Financial Statement Analysis

Aim

The aim of this chapter is to:

introducethefinancialstatementanalysis•

explainthetypesoffinancialstatementanalysis•

explicatethetechniquesoffinancialstatementanalysis•

Objectives

The objectives of this chapter are to:

explicatethefundsflowstatement•

elucidatecashflowstatement•

explain the ratio analysis•

Learning outcome

At the end of this chapter, you will be able to:

identifytheprofitabilityratio•

understand trend analysis•

definefinancialstatements•


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1.1 IntroductionBusinessconcernrequiresfinancetomeettheirneedsintheeconomicworld.Anytypeofbusinessactivitydependsonthefinance.Hence,itiscalledaslifebloodofbusinessfirms.Whether,thebusinessconcernsarebigorsmall,theyrequirefinancetofulfiltheirbusinessactivities.

Inthemodernera,alltheactivitiesareconcernedwiththeeconomicactivitiesandveryparticulartoearningprofitthroughanyventureoractivities.Allthebusinessactivitiesaredirectlyrelatedwithmakingprofit.(Accordingtotheeconomics concept of factors of production, rent given to landlord, wage given to labour, interest given to capital and profitgiventoshareholdersorproprietors),abusinessconcernneedsfinancetomeetalltherequirements.Hence,financemaybecalledascapital, investment, fundetc.,buteach termwillhavedifferentmeaningsanduniquecharacters.Risingtheprofitisthemainaimofanykindofeconomicactivity.

1.2 Meaning of FinanceFinancemaybedefined as the art and scienceofmanagingmoney. It includesfinancial service andfinancialinstruments. Finance also is referred as the provision of money at the time when it is required. Finance function is theprocurementoffundsandtheireffectiveutilisationinbusinessfirms.

Theconceptoffinanceincludesfunds,capital,amount,andmoney.However,eachwordishavinguniquemeaning.Studyingandunderstandingtheconceptoffinancebecomeanimportantpartofthebusinessfirm.

1.2.1 Definition of FinanceAccording to Khan and Jain, “Finance is the art and science of managing money."

AccordingtoOxforddictionary,theword‘finance’connotes‘managementofmoney.’Webster’sNinthNewCollegiateDictionarydefinesfinanceas“thescienceonstudyofthemanagementoffunds’and the management of fund as the system that includes the circulation of money, the granting of credit, the making of investments, and the provision of banking facilities.

1.3 Introduction to Financial StatementAfinancialstatementisanofficialdocumentofthefirm,whichexplorestheentirefinancialinformationofthefirm.Themainaimofthefinancialstatementistoprovideinformationandunderstandthefinancialaspectsofthefirm.Hence,preparationofthefinancialstatementisimportantasmuchasthefinancialdecisions.

1.4 Meaning and Definition of Financial StatementAccordingtoHamptorsJohn,thefinancialstatementisanorganisedcollectionofdataaccordingtologicalandconsistentaccountingprocedures.Itspurposeistoconveyanunderstandingoffinancialaspectsofabusinessfirm.It may show a position at a moment of time as in the case of a balance-sheet or may reveal a service of activities over a given period of time, as in the case of an income statement.

Financial statements are the summary of the accounting process, which provides useful information to both internal andexternalparties.JohnN.Nyeralsodefinesitas:

“Financialstatementsprovideasummaryoftheaccountingofabusinessenterprise,thebalance-sheetreflectingthe assets, liabilities and capital as on a certain data and the income statement showing the results of operations during a certain period.”

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Financial statements generally consist of the following two important statements:

Financial Statement

Income Statement Position Statement

Statement of changesin Owner's Equity

Statement of changesin Financial Position

Fig. 1.1 Financial statement(Source:http://vcmdrp.tums.ac.ir/files/financial/istgahe_mali/moton_english/financial_management_[www.

accfile.com].pdf)

A part from that, the business concern also prepares some of the other parts of statements, which are very useful to the internal purpose such as:

Statement of changes in owner’s equity.•Statementofchangesinfinancialposition.•

1.4.1 Income StatementIncomestatementisalsocalledasprofitandlossaccount,whichreflectstheoperationalpositionofthefirmduringa particular period. Normally, it consists of one accounting year. It determines the entire operational performance of the organisation like total income generated and expenses incurred for earning that income.

Incomestatementhelpstoascertainthegrossprofitandnetprofitoftheconcern.Grossprofitisdeterminedbypreparationoftradingormanufacturinga/candnetprofitisdeterminedbypreparationofprofitandlossaccount.

1.4.2 Position StatementPositionstatementisalsocalledasbalancesheet,whichreflectsthefinancialpositionoftheorganisationattheendofthefinancialyear.

Position statement helps to ascertain and understand the total assets, liabilities and capital of the organisation. One can understand the strength and weakness of the organisation with the help of the position statement.

1.4.3 Statement of Changes in Owner’s EquityIt is also called as statement of retained earnings. This statement provides information about the changes or position of owner’s equity in the company. How the retained earnings are employed in the business concern? Nowadays, preparation of this statement is not so popular and nobody prepares the separate statement of changes in owner’s equity.


4

1.4.4 Statement of Changes in Financial PositionIncomestatementandpositionstatementshowsonlyaboutthepositionofthefinance,henceitcannotmeasuretheactualpositionofthefinancialstatement.Statementofchangesinfinancialpositionhelpstodeterminethechangesinfinancialpositionfromoneperiodtoanotherperiod.

Statementofchangesinfinancialpositioninvolvestwoimportantareassuchasfundflowstatementwhichinvolvesthechangesinworkingcapitalpositionandcashflowstatementwhichinvolvesthechangesincashposition.

1.5 Types of Financial Statement AnalysisAnalysisoffinancialstatementisalsonecessarytounderstandthefinancialpositionsduringaparticularperiod.AccordingtoMyres,“Financialstatementanalysisislargelyastudyoftherelationshipamongthevariousfinancialfactors in a business as disclosed by a single set of statements and a study of the trend of these factors as shown in a series of statements.”

Analysisoffinancialstatementisclassifiedintotwoimportanttypesdependingonthematerialusedandmethodsof operations.

Types of FinancialAnalysis

On the basis of Materials Used

On the basis of Methods of Operations

External Analysis

Internal Analysis

HorizontalAnalysis

VerticalAnalysis

Fig. 1.2 Types of financial statement analysis(Source: http://vcmdrp.tums.ac.ir/files/financial/istgahe_mali/moton_english/financial_management_[www.

accfile.com].pdf)

Based on material usedBasedonthematerialused,financialstatementanalysismaybeclassifiedintotwomajortypessuchasexternalanalysis and internal analysis as illustrated in table below:

External Analysis Internal AnalysisOutsiders of the business concern normally conduct external analyses.However, they are indirectly involved in the business concern such as investors, creditors, government organisations and other credit agencies.

The company itself does disclose some of the valuable information to the business concern in this type of analysis.

External analysis is very much useful to understand thefinancialandoperationalpositionofthebusinessconcern.

Internal analysis is used to understand the operational performances of each and every department and unit of the business concern.

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External analysis mainly depends on the published financialstatementoftheconcern.

Internal analysis helps to take decisions regarding achieving the goals of the business concern.

This analysis provides only limited information about the business concern.

Table 1.1 Classification of financial statement analysis based on material used

Based on method of operationBasedonthemethodsofoperation,financialstatementanalysismaybeclassifiedintotwomajortypes,suchashorizontal analysis and vertical analysis as illustrated in the table below.

Horizontal Analysis Vertical Analysis

Underthehorizontalanalysis,financialstatementsarecomparedwithseveralyearsandbasedonthat,afirmmay take decisions.

Undertheverticalanalysis,financialstatementsmeasure the quantities relationship of the various itemsinthefinancialstatementonaparticularperiod.

Normally,thecurrentyear’sfiguresarecomparedwiththe base year (base year is consider as 100) and how thefinancialinformationischangedfromoneyeartoanother.

It is also called as static analysis, because, this analysis helps to determine the relationship with variousitemsappearedinthefinancialstatement.

This analysis is also called as dynamic analysis. For example, a sale is assumed as 100 and other itemsareconvertedintosalesfigures.

Table 1.2 Classification of financial statement analysis based on method of operation

1.6 Techniques of Financial Statement AnalysisFinancialstatementanalysisisinterpretedmainlytodecidethefinancialandoperationalperformanceofthebusinessfirm.Anumberofmethodsareusedtoevaluatethefinancialstatementofthebusinessconcern.Thefollowingarethe common methods, which are widely used by the business concern.

Techniques

RatioAnalysis

ComparativeStatement

TrendAnalysis

Cash Flow Statement

Funds Flow Statement

CommonSize

Analysis

Fig. 1.3 Techniques of financial statement analysis(Source: http://vcmdrp.tums.ac.ir/files/financial/istgahe_mali/moton_english/financial_management_[www.

accfile.com].pdf)


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1.6.1 Comparative Statement AnalysisComparativestatementanalysisisananalysisoffinancialstatementatdifferentperiodoftime.Thisstatementhelpstounderstandthecomparativepositionoffinancialandoperationalperformanceatdifferentperiodoftime.

Comparativefinancialstatementsagainareclassifiedintotwomajorpartssuchascomparativebalancesheetanalysisandcomparativeprofitandlossaccountanalysis.

1.6.2 Comparative Balance Sheet AnalysisComparative balance sheet analysis concentrates only on the balance sheet of the concerns at different period of time.Underthisanalysisthebalancesheetsarecomparedwithpreviousyear’sfiguresorone-yearbalancesheetfiguresarecomparedwithotheryears.Comparativebalancesheetanalysismaybehorizontalorverticalbasis.Thistypeofanalysishelpstounderstandtherealfinancialpositionofthefirmaswellashowtheassets,liabilitiesandcapitals are placed during a particular period.

1.6.3 Comparative Profit and Loss Account AnalysisAnothercomparativefinancialstatementanalysisiscomparativeprofitandlossaccountanalysis.Underthisanalysis,onlyprofitandlossaccountistakentocomparewithpreviousyear’sfigureorcomparewithinthestatement.Thisanalysis helps to understand the operational performance of the business concern in a given period. It may be analysed on horizontal basis or vertical basis.

1.6.4 Trend AnalysisThefinancial statementsmaybe analysedby computing trendsof series of information. Itmaybeupwardordownward directions which involve the percentage relationship of each and every item of the statement with the common value of 100%. Trend analysis helps to understand the trend relationship with various items, which appear inthefinancialstatements.Thesepercentagesmayalsobetakenasindexnumbersshowingrelativechangesinthefinancialinformationresultingwiththevariousperiodsoftime.Inthisanalysis,onlymajoritemsareconsideredfor calculating the trend percentage.

1.6.5 Common Size AnalysisOther importantfinancial statement analysis technique is common size analysis inwhichfigures reported areconvertedintopercentagetosomecommonbase.Inthebalancesheetthetotalassetsfiguresisassumedtobe100andallfiguresareexpressedasapercentageofthistotal.Itisoneofthesimplestmethodsoffinancialstatementanalysis,whichreflectstherelationshipofeachandeveryitemwiththebasevalueof100%.

1.7 Funds Flow StatementFundsflowstatementisoneoftheimportanttools,whichisusedinmanyways.Ithelpstounderstandthechangesinthefinancialpositionofabusinessenterprisebetweenthebeginningandendingfinancialstatementdates.Itisalso called as statement of sources and uses of funds.

InstituteofCostandWorksAccountsofIndia,defines thefundsflowstatementas“astatementprospectiveorretrospective, setting out the sources and application of the funds of an enterprise. The purpose of the statement is toindicateclearlytherequirementoffundsandhowtheyareproposedtoberaisedandtheefficientutilisationandapplication of the same.”

1.8 Cash Flow StatementCashflowstatementisastatementwhichshowsthesourcesofcashinflowandusesofcashout-flowofthebusinessconcernduringaparticularperiodoftime.Itisthestatement,whichinvolvesonlyshort-termfinancialpositionof thebusinessconcern.Cashflowstatementprovidesasummaryofoperating, investmentandfinancingcashflowsandreconcilesthemwithchangesinitscashandcashequivalentssuchasmarketablesecurities.InstituteofCharteredAccountantsofIndiaissuedtheAccountingStandard(AS-3)relatedtothepreparationofcashflowstatement in 1998.

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Followingtablegivesthedifferencebetweenfundsflowstatementandcashflowstatement.

Funds Flow Statement Cash Flow StatementFundsflowstatementisthereportonthemovement•of funds or working capital.

Cashflow statement is the report showing sources•and uses of cash.

Funds flow statement explains how working •capital is raised and used during the particular.

Cashflowstatementexplainstheinflowandoutflow•of cash during the particular period.

Themain objective of fund flow statement is•to show how the resources have been balanced mobilised and used.

Themainobjectiveofthecashflowstatementisto•show the causes of changes in cash between two balance sheet dates.

Funds flow statement, indicates the results of•currentfinancialmanagement.

Cashflowstatementindicatesthefactorscontributing•to the reduction of cash balance in spite of increase in profitandvice-versa.

Inafundsflowstatement,increaseordecreasein•working capital is recorded.

In a cash flow statement only cash receipt and •payments are recorded.

Infundsflowstatementthereisnoopeningand•closing balances.

Cashflowstatementstartswithopeningcashbalance•and ends with closing cash balance.

Table 1.3 Difference between funds flow and cash flow statement

1.9 Ratio AnalysisRatioanalysisisacommonlyusedtooloffinancialstatementanalysis.Ratioisamathematicalrelationshipbetweenonenumbertoanothernumber.Ratioisusedasanindexforevaluatingthefinancialperformanceofthebusinessconcern.Anaccountingratioshowsthemathematicalrelationshipbetweentwofigures,whichhavemeaningfulrelationwitheachother.Ratiocanbeclassifiedintovarioustypes.Classificationofratiofromthepointofviewoffinancialmanagementisasfollows:

Ratio

LiquidityRatio Activity Ratio Solvency Ratio ProfitabilityRatio

Fig. 1.4 Classification of ratio

1.9.1 Liquidity RatioIt is also called as short-term ratio. This ratio helps to understand the liquidity in a business which is the potential ability to meet current obligations. This ratio expresses the relationship between current assets and current assets of the business concern during a particular period. The following are the major liquidity ratios:

Sr. No. Ratio Formula Significant Ratio

1. Current Ratio = 2:1

2. Quick Ratio 1:1

Table 1.4 Liquidity ratios


8

1.9.2 Activity RatioItisalsocalledasturnoverratio.Thisratiomeasurestheefficiencyofthecurrentassetsandliabilitiesinthebusinessconcern during a particular period. This ratio is helpful to understand the performance of the business concern. Some of the activity ratios are given below:

Sr. No. Ratio Formula

1. Stock Turnover Ratio

2. Debtors Turnover Ratio

3. Creditors Turnover Ratio

4. Working Capital Turnover Ratio

Table 1.5 Activity ratios1.9.3 Solvency RatioIt is also called as leverage ratio, which measures the long-term obligation of the business concern. This ratio helps to understand, how the long-term funds are used in the business concern. Some of the solvency ratios are given below:

Sr. No Ratio Formula

1. Debt-Equity Ratio

2. Proprietary Ratio

3. Interest Coverage Ratio

Table 1.6 Solvency ratios

9

1.9.4 Profitability RatioProfitabilityratiohelpstomeasuretheprofitabilitypositionofthebusinessconcern.Someofthemajorprofitabilityratios are given below.

Sr. No Ratio Formula

1. GrossProfitRatio

2. NetProfitRatio

3. OperatingProfitRatio

4. Return in Investment

Table 1.7 Profitability ratios


10

SummaryBusinessconcernrequiresfinancetomeettheirneedsintheeconomicworld.•Financemaybedefinedastheartandscienceofmanagingmoney.•Afinancialstatementisanofficialdocumentofthefirm,whichexplorestheentirefinancialinformationofthe•firm.Financial statements are the summary of the accounting process, which provides useful information to both •internal and external parties.Incomestatementisalsocalledasprofitandlossaccount,whichreflectstheoperationalpositionofthefirm•during a particular period.Incomestatementandpositionstatementshowsonlyaboutthepositionofthefinance,henceitcan’tmeasure•theactualpositionofthefinancialstatement.Analysis of financial statement is also necessary to understand thefinancial positions during a particular•period.External analysis is verymuchuseful to understand thefinancial andoperational positionof the business•concern.Financialstatementanalysisisinterpretedmainlytodeterminethefinancialandoperationalperformanceof•the business concern.Comparativestatementanalysisisananalysisoffinancialstatementatdifferentperiodoftime.•Comparative balance sheet analysis concentrates only the balance sheet of the concern at different periods of •time.Thefinancialstatementsmaybeanalysedbycomputingtrendsofseriesofinformation.•Fundsflowstatementisoneoftheimportanttools,whichisusedinmanyways.•Ratioanalysisisacommonlyusedtooloffinancialstatementanalysis.•

ReferencesFinancial Statements Analysis - An Introduction. • [Pdf]Available at: <http://download.nos.org/srsec320newE/320EL27.pdf>[Accessed11April2014].Introduction to Financial Statement Analysis. • [Pdf]Availableat:<http://www.swlearning.com/ibc/albrecht9e/pdf/Albrecht9e_c05_202-253_low.pdf>[Accessed11April2014].Debarshi, J., • Financial Statement Analysis: For University of Calcutta. Pearson Education India.Robinson, T. R., Henry, E., Pirie, W. L. & Broihanhn, M. A., 2012. • International Financial Statement Analysis, 3rd ed., John Wiley & Sons, UK.CFA Level I Financial Statement Analysis Introduction Video Lecture by Mr. Arif Irfanullah. • [Videoonline]Availableat:<http://www.youtube.com/watch?v=_2Kltr0SRGU>[Accessed11April2014].Introduction to Financial Statements. • [Video online]Available at: <http://www.youtube.com/watch?v=sAMSQ02X0-o>[Accessed11April2014].

Recommended ReadingGibson, C., 2012. • Financial Reporting and Analysis. Cengage Learning.Foster, G. , 1978. • Financial Statement Analysis, 2/e. Springer. Peterson, P. P. & Fabozzi, F. J., 1999. • Analysis of Financial Statements. John Wiley & Sons.

11

Self AssessmentWhich of the following is called as lifeblood of business organisation?1.

Businessa. Salesb. Financec. Marketingd.

___________maybedefinedastheartandscienceofmanagingmoney.2. Businessa. Salesb. Financec. Marketingd.

Match the following3. 1. Liquidity Ratio A. It is also called as turnover ratio.

2. Activity Ratio B. It is also called as leverage ratio.

3. Solvency Ratio C. It is also called as short-term ratio.

4.ProfitabilityRatio D. Return in Investment.1-D, 2-C, 3-A, 4-Ba. 1-B, 2-D, 3-C, 4-Ab. 1-A, 2-B, 3-D, 4-Cc. 1-C, 2-A, 3-B, 4-Dd.

Theconceptoffinanceincludescapital,funds,money,and__________.4. reportsa. managingb. cashc. amountd.

Which of the following statement is true?5. Finance is the art and science of managing moneya. Business is the art and science of managing moneyb. Marketing is the art and science of investing moneyc. Dependency is the art and science of moneyd.

Whichofthefollowingstatementhelpstoascertainthegrossprofitandnetprofitoftheconcern?6. Income statementa. Position statementb. Equity statementc. Analysis statementd.


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__________statementisalsocalledasbalancesheet,whichreflectsthefinancialpositionofthefirmattheend7. ofthefinancialyear.

Income statementa. Position statementb. Equity statementc. Analysis statementd.

Which of the following statement is false?8. Incomestatementisalsocalledasprofitandlossaccount.a. Positionstatementhelpstoascertainandunderstandthetotalassets,liabilitiesandcapitalofthefirm.b. Internalanalysismainlydependsonthepublishedfinancialstatementoftheconcern.c. Internal analysis helps to take decisions regarding achieving the goals of the business concern.d.

_________analysisisverymuchusefultounderstandthefinancialandoperationalpositionofthebusiness9. concern.

Externala. Internalb. Positivec. Negatived.

Underthe________analysis,financialstatementsarecomparedwithseveralyearsandbasedonthat,afirm10. may take decisions.

verticala. externalb. horizontalc. internald.

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Chapter II

Basic Concept of Time Value of Money

Aim


introduce the basic concept of time value of money•

explain reasons for time value of money•

explicate timelines and notation•

Objectives


explicate valuation concepts•

elucidate the techniques of time value of money•

explain multiple compounding periods•

Learning outcome


identify effective rate of interest in case of multi-period compounding•

understand the discounting or present value concept•

recognise simple and compound interest•


14

2.1 IntroductionMoney has time value. A rupee today is more valuable than a year hence. It is on this concept “the time value of money” isbased.Therecognitionofthetimevalueofmoneyandriskisextremelyvitalinfinancialdecisionmaking.

Mostfinancialdecisions,suchasthepurchaseofassetsorprocurementoffunds,affectthefirm’scashflowsindifferenttimeperiods.Forexample,ifafixedassetispurchased,itwillrequireanimmediatecashoutlayandwillgeneratecashflowsduringmanyfutureperiods.Similarly,ifthefirmborrowsfundsfromabankorfromanyothersource, it receives cash and commits an obligation to pay interest and repay principal in future periods.

Thefirmmayalsoraisefundsbyissuingequityshares.Thefirm’scashbalancewillincreaseatthetimesharesareissued,butasthefirmpaysdividendsinfuture,theoutflowofcashwilloccur.Sounddecision-makingrequiresthatthecashflowswhichafirmisexpectedtogiveupoverperiodshouldbelogicallycomparable.Infact,theabsolutecashflowswhichdifferintimingandriskarenotdirectlycomparable.Cashflowsbecomelogicallycomparablewhenthey are appropriately adjusted for their differences in timing and risk. The recognition of the time value of money andriskisextremelyvitalinfinancialdecision-making.Ifthetimingandriskofcashflowsisnotconsidered,thefirmmaymakedecisionswhichmayallowittomissitsobjectiveofmaximisingtheowner’swelfare.ThewelfareofownerswouldbemaximisedwhenNetPresentValueiscreatedfrommakingafinancialdecision.Itisthus,timevalueconceptwhichisimportantforfinancialdecisions.

Thus,weconcludethattimevalueofmoneyiscentraltotheconceptoffinance.Itrecognisesthatthevalueofmoneyis different at different points of time. As money can be put to productive use, its value is different depending upon when it is received or paid. In simpler terms, the value of a certain amount of money today is more valuable than its value tomorrow. It is not because of the uncertainty involved with time but purely on account of timing. The difference in the value of money today and tomorrow is referred as time value of money.

2.2 Reasons for Time Value of MoneyMoney has time value because of the following reasons:

Risk and uncertainty:Futureisalwaysuncertainandrisky.Outflowofcashisinourcontrolaspaymentstopartiesaremadebyus.Thereisnocertaintyforfuturecashinflows.CashinflowsaredependentoutonourCreditor,Bank,etc.Asanindividualorfirmisnotcertainaboutfuturecashreceipts,itprefersreceivingcashnow.

Inflation:Inaninflationaryeconomy,themoneyreceivedtoday,hasmorepurchasingpowerthanthemoneytobe received in future. In other words, a rupee today represents a greater real purchasing power than a rupee a year hence.

Consumption: Individuals generally prefer current consumption to future consumption.

Investment opportunities:Aninvestorcanprofitablyemployarupeereceivedtoday,togivehimahighervalueto be received tomorrow or after a certain period of time.

Thus, the basic principle behind the concept of time value of money is that, a sum of money received today, is worth more than if the same is received after a certain period of time. For example, consider a simple scenario. If you are offered a choice of having Rs. 15,000 today or having Rs. 15,000 in future, you will usually prefer to have those 15,000 now. Similarly, if the choice is given between paying Rs. 15,000 now or paying the same amount at a later stage,youwillusuallyprefertopayRs.15,000later.Itissimple,inthefirstcasebyacceptingRs.15,000early,youcan simply put that amount in the bank and earn some interest. While, in the second case by delaying the payment, you earn interest by keeping the money in the bank.

Therefore, the time gap allowed helps to make some money. This incremental gain is time value of money. Thus, timevalueofmoneyisavitalconsiderationinmakingfinancialdecision.Letustakefewexamples:

15

Example 1: A project needs an initial investment of Rs 2, 00,000. It is expected to give a return of Rs 40,000 per annumattheendofeachyear,forsixyears.TheprojectthusinvolvesacashoutflowofRs2,00,000inthe‘zeroyear’andcashinflowsofRs40,000peryear,forsixyears.Inordertodecide,whethertoacceptorrejecttheproject,itisnecessarythatthePresentValueofcashinflowsreceivedannuallyforsixyearsisascertainedandcomparedwith the initial investment of Rs 2,00,000.

ThefirmwillaccepttheprojectonlywhenthePresentValueofcashinflowsatthedesiredrateofinterestexceedsthe initial investment or at least equals the initial investment of Rs 2, 00,000.

Example 2: Afirmhastochoosebetweentwoprojects.OneinvolvesanoutlayofRs15lakhswithareturnof14%fromthefirstyearonwards,fortenyears.TheotherrequiresaninvestmentofRs15lakhswithareturnof16%per annum for 15 years commencing with the beginning of the sixth year of the project. In order to make a choice betweenthesetwoprojects,itisnecessarytocomparethecashoutflowsandthecashinflowsresultingfromtheproject. In order to make a meaningful comparison, it is necessary that the two variables are strictly comparable. Itispossibleonlywhenthetimeelementisincorporatedintherelevantcalculations.Thisreflectstheneedforcomparingthecashflowsarisingatdifferentpointsoftimeindecision-making.

2.3 Timelines and NotationWhencashflowsoccuratdifferentpointsintime,itiseasiertodealwithusingatimeline.Atimelineshowsthetimingandtheamountofeachcashflowincashflowstream.Thus,acashflowstreamofRs10,000attheendofeachofthenextfiveyearscanbedepictedonatimelineliketheoneshownbelow.

Fig. 2.1 Timeline(Source: http://www.newagepublishers.com/samplechapter/001945.pdf)

Asshownabove,0referstothepresenttime.Acashflowthatoccursattime0isalreadyinpresentvaluetermsand hence does not require any adjustment for time value of money. You must distinguish between a period of time and a point of .Period1whichisthefirstyearistheportionoftimelinebetweenpoint0andpoint1.Thecashflowoccurringatpoint1isthecashflowthatoccursattheendofperiod1.Finally,thediscountrate,whichis12percentinourexample,isspecifiedforeachperiodonthetimelineanditmaydifferfromperiodtoperiod.Ifthecashflowoccursatthebeginning,ratherthantheendofeachyear,thetimelinewouldbeasshowninPartB.Notethatacashflowoccurringattheendoftheyear1isequivalenttoacashflowoccurringatthebeginningofyear2.Cashflowscanbepositiveornegative.Apositivecashflowiscalledacashinflow;andanegativecashflow,acashoutflow.


16

2.4 Valuation ConceptsThe time value of money establishes that there is a preference of having money at present than a future point of time. It means:

That a person will have to pay in future more, for a rupee received today. For example: Suppose your mother •gave you Rs 100 on your tenth birthday. You deposited this money in a bank at 10% rate of interest for one year. How much future sum would you receive after one year? You would receive Rs 110

Future sum = Principal + Interest = 100 + 0.10 × 100

= Rs 110

What would be the future sum if you deposited Rs 100 for two years?You would now receive interest on interest earned after one year.

Future sum = 100 × 1.102 = Rs 121

We express this procedure of calculating as Compound Value or Future Value of a sum.

A person may accept less today, for a rupee to be received in the future. Thus, the inverse of compounding •processistermedasdiscounting.Herewecanfindthevalueoffuturecashflowasontoday.

2.5 Techniques of Time Value of MoneyThere are two techniques for adjusting time value of money. They are as follows

Techniques of Time Value of Money

Compounding Techniques/Future Value Techniques

Discounting/Present Value Techniques

Fig. 2.2 Techniques of time value of money

The value of money at a future date with a given interest rate is called future value. Similarly, the worth of money today that is receivable or payable at a future date is called Present Value.

2.5.1 Compounding Techniques/Future Value TechniqueIn this concept, the interest earned on the initial principal amount becomes a part of the principal at the end of the compounding period.

Example 3: Suppose you invest Rs 2000 for three years in a saving account that pays 10 per cent interest per year. If you let your interest income be reinvested, your investment will grow as follows:

First year: Principal at the beginning 2,000Interest for the year (Rs 2,000 × 0.10) 200Principal at the end 2,200

Second year: Principal at the beginning 2,200Interest for the year (Rs 2,200 × 0.10) 220Principal at the end 2420

17

Third year: Principal at the beginning 2420Interest for the year (Rs 2420 × 0.10) 242Principal at the end 2662

Thisprocessofcompoundingwillcontinueforanindefinitetimeperiod.

The process of investing money as well as reinvesting interest earned there on is called compounding. But, the way it has gone about calculating the future value will prove to be cumbersome if the future value over long maturity periods of 20 years to 30 years is to be calculated.

A generalised procedure for calculating the future value of a single amount compounded annually is as follows:

Formula:

In this equation is called the future value interest factor (FVIF).

where, =FuturevalueoftheinitialflownyearhencePV=Initialcashflowr = Annual rate of Interestn = number of years

By taking into consideration, the above example, we get the same result:

= PV= 2,000 (1.10)3

= 2662

To solve future value problems, we consult a future value interest factor (FVIF) table. The table shows the future value factor for certain combinations of periods and interest rates. To simplify calculations, this expression has been evaluated for various combinations of ‘r’ and ‘n’. Table 2.1 presents one such table showing the future value factor for certain combinations of periods and interest rates.

n/r 6% 8% 10% 12% 14%2 1.124 1.166 1.210 1.254 1.3004 1.262 1.360 1.464 1.574 1.6896 1.419 1.587 1.772 1.974 2.1958 1.594 1.851 2.144 2.476 1.85310 1.791 2.159 2.594 3.106 3.70712 2.012 2.518 3.138 3.896 4.817

Table 2.1 Value of for various combinations of r and n

2.5.2 Future Value of a Single Amount (Lumpsum)The formula for calculating the Future Value of a single amount is as follows:

Example 4: If you deposit Rs 56,650 in a bank which is paying a 12 per cent rate of interest on a ten-year time deposit, how much would the deposit grow at the end of ten years?

Solution: or

= Rs 56, 650 = Rs 55,650 × 3.106 = Rs 1, 75,954.90


18

2.6 Multiple Compounding PeriodsInterest can be compounded monthly, quarterly and half-yearly. If compounding is quarterly, annual interest rate is to be divided by 4 and the number of years is to be multiplied by 4. Similarly, if monthly compounding is to be made, annual interest rate is to be divided by 12 and number of years is to be multiplied by 12.

The formula to calculate the compound value is:

Where, = Future value after ‘n’ years PV=Cashflowtoday r = Interest rate per annum m = Number of times compounding is done during a year n = Number of years for which compounding is done.

Example 5: Calculate the compound value when Rs 1000 is invested for 3 years and the interest on it is compounded at 10% p.a. semi-annually.

Solution: The formula is

= Rs 1340

ORThe compound value of Re. 1 at 5% interest at the end of 6 years is Rs 1.340. Hence the value of ` 1000 using the

table ( ) will be

= 1000 × 1.340= Rs 1,340

Example 6:Calculate the compound value when Rs 10,000 is invested for 3 years and interest 10% per annum is compounded on quarterly basis.

Solution: The formula is

= 10,000 (1 + 0.025)12 = Rs 13,448.89

Example 7: Mr. Ravi Kishan and Sons invests Rs 500, Rs 1,000, Rs 1,500, Rs 2,000 and Rs 2,500 at the end of each year. Calculate the compound value at the end of the 5th year, compounded annually, when the interest charged is 5% per annum.

19

Solution: Statement of the compound valueEnd of the

YearAmount

DepositedNumber of

Years CompoundedCompounded Interest Factor

(FVIFr, n) from Appendix Future Value

(1) (2) (3) (4) (2) × (4)1 500 4 1,216 608.002 1,000 3 1,158 1,158.003 1,500 2 1,103 1,654.504 2,000 1 1,050 2,100.005 2,500 0 1,000 2,500.00

Amount at the end of 5th year is Future Value = 8020.50

Table 2.2 Compound value

2.7 Future Value of Multiple Cash FlowsTheaboveillustrationisanexampleofmultiplecashflows.Thetransactionsinreallifearenotlimitedtoone.Aninvestor investing money in instalments may wish to know the value of his savings after ‘n’ years. The formula is

Where, = Future value after ‘n’ years PV = Present value of money today r = Interest rate m = Number of times compounding is done in a year.

2.8 Effective Rate of Interest In Case of Multi-Period CompoundingEffective interest rate brings all the different bases of compounding such as yearly, half-yearly, quarterly, and monthlyonasingleplatformforcomparisontoselectthebeneficialbase.Now,thequestioniswhichworksouthighest interest amount? When interest is compounded on half-yearly basis, interest amount works out more than the interest calculated on yearly basis. Quarterly compounding works out more than half-yearly basis. Monthly compounding works out more than even quarterly compounding. So, if compounding is more frequent, then the amount of interest per year works out more. Now, we want to equate them for comparison. Suppose, an option is given as the following:

Basis of Compounding Interest RateYearly 10%

Half-yearly 9.5%Quarterly 9%Monthly 8.5%

Table 2.3 Compounding and interest rate

Now, the question is which basis of compounding is to be accepted to get the highest interest rate. The answer is to calculate ‘Effective Interest Rate’.

The formula to calculate the Effective Interest Rate is

Where, EIR = Effective Rate of Interest r = Nominal Rate of Interest (Yearly Interest Rate) m = Frequency of compounding per year


20

Takenominalinterestrateasthebaseandfind-outthecomparablerateofinterestforhalf-yearly,quarterlyandmonthly basis and select that which is most attractive.

Example 8: A company offers 12% rate of interest on deposits. What is the effective rate of interest if the compounding is done on

Half-yearly �Quarterly �Monthly �

As an alternative, the following rates of interest are offered for choice. Which basis gives the highest rate of •interest that is to be accepted?

Basis of Compounding Interest RateYearly 12%

Half-yearly 11.75%Quarterly 11.50%Monthly 11.25%

Table 2.4 Compounding and interest rate

Solution:The formula for calculation of effective interest is as below:•

When the compounding is done on half-yearly basis: �

= 1.1236 – 1 = 12.36%

When the compounding is done on quarterly basis �

= 0.1255 = 12.55%

When the compounding is done on monthly basis �

= 0.1268 = 12.68%

21

Basis of Compounding Interest Rate EIRYearly 12% 12%

Half-yearly 12% 12.36%Quarterly 12% 12.55%Monthly 12% 12.68%

Table 2.5 Compounding and interest rate and EIR

When the compounding is done on half-yearly basis•

= 0.1209 = 12.09%

When the compounding is done on quarterly basis:

= .1200 = 12%

When the compounding is done on monthly basis

= 0.1184 = 11.84%

Example 9: Find out the effective rate of interest, if nominal rate of interest is 12% and is quarterly compounded.

Solution: EIR =

=[(1+0.03)4–1] = 1.126 – 1 = 0.126 = 12.6% p.a.


22

2.8.1 Growth RateThe compound rate of growth for a given series for a period of time can be calculated by employing the future value interest factor table (FVIF)

Example: 10Years Profit (in Lakhs)

1 952 1053 1404 1605 1656 170

Table 2.6 Growth rate

How is the compound rate of growth for the above series determined?This can be done in two given steps:

Theratioofprofitsforyear6toyear1istobedeterminedi.e.,•

The • table is to be looked at. Look at a value which is close to 1.79 for the row for 5 years. The value close to 1.79 is 1.762 and the interest rate corresponding to this is 12%. Therefore, the compound rate of growth is 12 per cent.

2.9 Discounting or Present Value ConceptPresentvalueistheexactreverseoffuturevalue.Thepresentvalueofafuturecashinfloworoutflowistheamountof current cash that is of equivalent value to the decision maker. The process of determining present value of a future payment or receipts or a series of future payments or receipts is called discounting. The compound interest rateusedfordiscountingcashflowsisalsocalledthediscountrate.

2.10 Simple and Compound InterestIn compound interest, each interest payment is reinvested to earn further interest in future periods. However, if no interest is earned on interest, the investment earns only simple interest. In such a case, the investment grows as follows:

Futurevalue=Presentvalue[1+Numberofyears×Interestrate]For example, if ` 1,000 is invested @ 12% simple interest, in 5 years it will become

1,000[1+5×0.12]=Rs1,600

The following table shows how an investment of Rs 1,200 grows over time under simple interest as well as compound interest when the interest rate is 12 per cent. From this table, we can feel the power of compound interest..

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Year Simple Interest Compound InterestStarting Balance + Interest

= Ending Balance Starting Balance + Interest = Ending Balance

1 1,000 + 100 = 1,100 1,000 + 100 = 1,1005 1,400 + 100 = 1,500 1,464 + 146 = 1,61010 1,900 + 100 = 2,000 2,358 + 236 = 2,59420 2,900 + 100 = 3,000 6,116 + 612 = 6,72850 5,900 + 100 = 6,000 1,06,718 + 10672 = 11,7,390100 10,900 + 100 = 11,000 1,25,27,829 + 12,52,783 = 1,37,80,612

Table 2.7 Value of Rs 1,000 invested at 10% simple and compound interest

Example 11: Mr. Abhijeet has deposited Rs 1, 00,000 in a saving bank account at 6 per cent simple interest and wishes to keep the same, for a period of 5 years. Calculate the accumulated Interest.

Solution: Where, = Simple interest

= Initial amount invested I = Interest rate n = Number of years

= Rs 1, 00,000 × 0.06 × 5 years

= Rs 30,000

If the investor wants to know his total future value at the end of ‘n’ yearsFuture value is the sum of accumulated interest and the principal amount.Symbolically

OR

Example 12: Mr. Abhishek’s annual savings is Rs 1,000 which is invested in a bank saving fund account that pays a 5 per cent simple interest. Abhishek wants to know his total future value or the terminal value at the end of 8 years time period.

Solution: = Rs 1000 + Rs 1000 (0.05) (8) = Rs 14,000

2.10.1 Compound InterestExample 13:SupposeMr.JhadavdepositedRs10,00,000inafinancialinstitutewhichpayshim8percentcompoundinterest annually for a period of 5 years. Show how the deposit would grow.

Solution:

= 10, 00,000 = 10, 00,000 (1.469)

= Rs 14, 69,000


24

Note: See compound value of one rupee Table for 5 years at 8% interest.

Variable compounding periods/semi-annual compounding

Example 14: How much does a deposit of Rs 40,000 grow in 10 years at the rate of 6% interest and compounding is done semi-annually. Determine the amount at the end of 10 years.

Solution:

=Rs. 40,000 = Rs 40,000 (1.806) = Rs. 72,240

Alternatively, see the compound value for one rupee table for year 20 and 3% interest rate.

Example 15:(Quarterlycompounding):SupposeafirmdepositsRs50lakhsattheendofeachyear,for4yearsat the rate of 6 per cent interest and compounding is done on a quarterly basis. What is the compound value at the end of the 4th year?

Solution:

=Rs. 50, 00,000 = Rs 50, 00,000 × 1.267 = Rs 63, 35,000

2.10.2 Compound Growth RateFormula: where, = Growth rate in percentages

= Variable for which the growth rate is needed

= Variable value (amount) at the end of year ‘n’

= Growth rate.

Example 16: From the following dividend data of a company, calculate compound rate of growth for 2003–2008.

Year Dividend per Share (Rs)2003 212004 222005 252006 262007 282008 31

Table 2.8 Dividend data

Solution: = = = 1.476

Alternatively, the compound value one Rupee table for 5 years should be seen till closed value to the compound factorisfound.Afterfindingtheclosestvalue,firstaboveitisseentogetthegrowthrate.

25

SummaryMoney has time value.•Mostfinancialdecisions,suchasthepurchaseofassetsorprocurementoffunds,affectthefirm’scashflows•in different time periods.Thefirmmayalsoraisefundsbyissuingequityshares.•Cashflowsbecomelogicallycomparablewhentheyareappropriatelyadjustedfortheirdifferencesintiming•and risk.Outflowofcashisinourcontrolaspaymentstopartiesaremadebyus.•Whencashflowsoccuratdifferentpointsintime,itiseasiertodealwithusingatimeline.•The time value of money establishes that there is a preference of having money at present than a future point •of time.The value of money at a future date with a given interest rate is called future value.•The process of investing money as well as reinvesting interest earned there on is called Compounding.•The formula for calculating the Future Value of a single amount is •Interest can be compounded monthly, quarterly and half-yearly.•The formula to calculate the Effective Interest Rate is •Present value is the exact opposite of future value.•The process of determining present value of a future payment or receipts or a series of future payments or •receipts is called discounting.In compound interest, each interest payment is reinvested to earn further interest in future periods.•

ReferencesBasic Concept of Time Value of Money. • [Pdf]Available at: <http://www.newagepublishers.com/samplechapter/001945.pdf>[Accessed11April2014].The Time Value of Money. • [Pdf]Availableat:<http://homepages.rpi.edu/~tealj2/arch4.pdf>[Accessed11April2014].Drake, P. P. and Fabozzi, J., 2009 • Foundations and Applications of the Time Value of Money John Wiley & Sons.Lieuallen, G. G., 2009. • Basic Federal Income Tax. Aspen Publishers Online.Time Value of Money Overview. • [Videoonline]Availableat:<http://www.youtube.com/watch?v=rZXuh3ECzlc>[Accessed11April2014].Time Value of Money (concept explained). • [Video online]Available at: <http://www.youtube.com/watch?v=gkoEAPAW7eg>[Accessed11April2014].

Recommended ReadingKeown, • Financial Management: Principles and Applications, 10/e. Pearson Education India.Sheeba, K., • Financial Management. Pearson Education India. Doss, D. A., Sumrall III, W. H. and Jones, D. W., 1999. • Strategic Finance for Criminal Justice Organizations. CRC Press.


26

Self AssessmentTherecognitionofthetimevalueofmoneyand_______isextremelyvitalinfinancialdecisionmaking.1.

riska. businessb. fundsc. investmentd.

_________decision-makingrequiresthatthecashflowswhichafirmisexpectedtogiveupoverperiodshould2. be logically comparable.

Positivea. Directb. Negativec. Soundd.

Match the following3.

1. Present value A.Thecompoundinterestrateusedfordiscountingcashflows.

2. Discounting B. It is the exact opposite of future value.

3. Discount rate C. The process of investing money as well as reinvesting interest earned there on.

4. Compounding D. The process of determining present value of a future payment or receipts or a series of future payments.

1-A, 2- C, 3- D, 4-Ba. 1-C, 2- A, 3- B, 4-Db. 1-B, 2- D, 3- A, 4-Cc. 1-D, 2- B, 3- C, 4-Ad.

Whocanprofitablyemployarupeereceivedtoday,togivehimahighervaluetobereceivedtomorroworafter4. a certain period of time?

The managera. An employerb. An individualc. An investord.

Thewelfareofownerswouldbemaximisedwhen___________iscreatedfrommakingafinancialdecision.5. Itisthus,timevalueconceptwhichisimportantforfinancialdecisions.

Net Present Valuea. Net Post Valueb. Net Time Valuec. Net Average Valued.

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Which of the following is a generalised procedure for calculating the future value of a single amount compounded 6. annually?

a.

b. c. d.

What is the formula to calculate the compound value?7.

a. b.

c. d.

Which of the following statement is true?8. The employee may also drop funds by issuing equity shares.a. Thefirmmayalsoraisefundsbyissuingequityshares.b. The employee may also raise funds by issuing equity shares.c. Thefirmmayalsodropfundsbyissuingequityshares.d.

In an ___________ economy, the money received today, has more purchasing power than the money to be 9. received in future.

uncertaina. individualb. alternativec. alternatived.

Which of the following statement is false?10. A rupee today is more valuable than a year hence.a. Money has time value.b. Individuals generally don’t prefer current consumption to future consumption.c. Atimelineshowsthetimingandtheamountofeachcashflowincashflowstream.d.


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Chapter III

Valuing Bonds

Aim


introduce value of a bond•

explain bond prices and interest rates•

explicate the determinants of interest rates•

Objectives


enlist• the empirical evidence on maturity premia

elucidate default premium•

explain special feature in bonds and pricing effects•

Learning outcome


identify determinants of value•

understand the liquidity preference•

definethematuritypremium•

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3.1 IntroductionThevalueofabondisthepresentvalueoftheexpectedcashflowsonthebond,discountedataninterestratethatisappropriatetotheriskinessofthatbond.Asthecashflowsonastraightbondarefixedatissue;thevalueofabondis inversely related to the interest rate that investors demand for that bond. The interest rate charged on a bond is determinedbyboththegenerallevelofinterestrates,whichappliestoallbondsandfinancialinvestments,andthedefaultpremiumspecifictotheentityissuingthebond.

This chapter examines the determinants of both the general level of interest rates and the magnitude of the default premiaonspecificbonds.Thegenerallevelofinterestratesincorporatesexpectedinflationandameasureofrealreturnandreflectsthetermstructure,withbondsofdifferentmaturitiescarryingdifferentinterestrates.Thedefaultpremia varies across time, depending in large part on the health of the economy and investors’ risk preferences.

Bonds often have special features embedded in them that have to be factored into the value. Some of these features are options - to convert into stock (convertible bonds), to call the bond back if interest rates go down (callable bonds)andtoputthebondbacktotheissueratafixedpriceunderspecificcircumstances(putablebonds).Otherbondcharacteristics,suchasinterestratecapsandfloors,haveoptionfeatures.Someoftheseoptionsresidewiththe issuer of the bond, some with the buyer of the bond, but they all have to be priced. Option pricing models can be usedtovaluethesespecialfeaturesandpricecomplexfixedincomesecurities.Somespecialfeaturesinbonds,suchas sinking funds, subordination of further debt and the type of collateral may affect the prices of bonds, as well.

3.2 Bond Prices and Interest RatesThe value of a straight bond is determined by the level of and changes in interest rates. As interest rates rise, the price of a bond will decrease and vice versa. This inverse relationship between bond prices and interest rates arises directly from the present value relationship that governs bond prices.

3.2.1 The Present Value RelationshipThevalueofabond,likeallfinancialinvestments,isderivedfromthepresentvalueoftheexpectedcashflowsonthatbond,discountedataninterestratethatreflectsthedefaultriskassociatedwiththecashflows.Therearetwofeatures that set bonds apart from equity investments.

First,thecashflowsonabond,i.e.,thecouponpaymentsandthefacevalueofthebond,areusuallysetatissue•anddonotchangeduringthelifeofthebond.Evenwhentheydochange,asinfloatingratebonds,thechangesare generally linked to changes in interest rates. Second, bondsusually havefixed lifetimes, unlike stocks, sincemost bonds specify amaturity date.As a•consequence,thepresentvalueofa‘straightbond’withfixedcouponsandspecifiedmaturityisdeterminedentirely by changes in the discount rate, which incorporates both the general level of interest rates and the specificdefaultriskofthebondbeingvalued.

The present value of a bond, expected to mature in N time periods, with coupons every period can be calculated.

PV of Bond =

where, = Coupon expected in period t

Face Value = Face value of the bondr=Discountrateforthecashflows

The discount rate used to calculate the present value of the bond will vary from bond to bond depending upon default risk, with higher rates used for riskier bonds and lower rates for safer ones. If the bond is traded, and a market price is therefore available for it, the internal rate of return can be computed for the bond, i.e., the discount rate at which the present value of the coupons and the face value is equal to the market price. This internal rate of return is called the yield to maturity on the bond.


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Thereareseveraldetails,relatingtoboththemagnitudeandtimingofcashflowsthatcanaffectthevalueofabondand its yield to maturity. First, the coupon payment on a bond may be semi-annual, in which case the discounting hastoallowforthesemi-annualcashflows.(Thefirstcouponwillbediscountedbackhalfayear,thesecondoneyear, the third a year and a half and so on.) Second, once a bond has been issued, it accrues coupon interest between coupon payments and this accrued interest has to be added on to the price of the bond, when valuing the bond.

3.2.2 A Measure of Interest Rate Risk in BondsWhenthefact that thecashflowsonabondarefixedat issue iscombinedwith thepresentvaluerelationshipgoverning bond prices, there is a clear rationale for why interest changes affect bond prices so directly. Any increase in interest rates, either at the economy wide level or because of an increase in the default risk of the company issuing thebond,willlowerthepresentvalueofthestreamofexpectedcashflowsandhencethevalueofthebond.Anydecrease in interest rates will have the opposite impact.

The effect of interest rate changes on bond prices will vary from bond to bond and will depend upon the following characteristics of the bond.

The maturity of the bond: Holding coupon rates and default risk constant, increasing the maturity of a straight •bondwillincreaseitssensitivitytointerestratechanges.Thepresentvalueofcashflowschangesmuchmoreforcashflowsfurtherinthefuture,asinterestrateschange,thanforcashflowswhicharenearerintime.Thelonger term bonds are much more sensitive to interest rate changes than the shorter term bonds. For instance, anincreaseininterestratesfrom8%to10%resultsinadeclineinvalueof7.61%forthefive-yearbondandof19.83%forthefifty-yearbonds.The coupon rate of the bond: Holding maturity and default risk constant, increasing the coupon rate of a straight •bondwilldecreaseitssensitivitytointerestratechanges.Ashighercouponsresultinmorecashflowsearlierin the bond’s life, the present value will change less as interest rates change. At the extreme, if the bond is a ‘zero-coupon’bond,theonlycashflowisthefacevalueatmaturity,andthepresentvalueislikelytovarymuchmore as a function of interest rates. The bonds with the lower coupons are much more sensitive, in percentage terms, to interest rate changes than those with higher coupons.

While the maturity and the coupon rate are the key determinants of how sensitive the price of a bond is to interest rate changes, a number of other factors impinge on this sensitivity. Any special features that the bond has, including convertibilityandcallability,makethematurityofthebondlessdefiniteandcanthereforeaffectthebondprice’ssensitivity to interest rate changes. If there is any relationship between the level of interest rates and the default premia on bonds, the default risk of a bond can affect its price sensitivity.

3.2.3 A More Formal Measure of Interest Rate Risk - DurationAstheinterestrateriskofabondisasignificantcomponentofitstotalrisk,amoreformalmeasureofinterestriskis needed, which consolidates the effects of maturity, coupon rates and the bond’s special features. To arrive at this measure, consider the present value relationship developed earlier in this chapter:

PV of Bond =

Differentiating the bond price with respect to interest rate should provide a formal measure of bond price sensitivity to interest rate changes.

Duration of Bond =

The bond price differential, , is called the duration of the bond and measures the interest rate sensitivity of the bond.

Thedurationofabondisaweightedmaturityofallthecashflowsonthebondincludingthecoupons,wheretheweightsarebaseduponboththetimingandthemagnitudeofthecashflows.Largerandearliercashflowsareweightedmorethansmallerandlatercashflows.Byincorporatingthemagnitudeandtimingofallthecashflows

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on the bond, duration encompassed all the variables that affect bond price sensitivity in one measure. The higher the duration of a bond, the more sensitive it is to changes in interest rates.

The duration of a bond will always be less than the maturity for a coupon bond and equal to the maturity for a zero-coupon bond, with no special features. In general, the duration of a bond will decrease as the coupon rate on the bond increases.

The measure of duration described here is called ‘Macaulay duration’ and it is the simplest version, based upon yieldstomaturity.Itisbasedupontheassumptionofaflattermstructureandmodifiedversionsofduration,whicharemoreflexibleintheirassumptionsaboutthetermstructureanditsshiftsovertime

3.3 Determinants of Interest RatesThediscountrateusedtodiscountcashflowsonabondisdeterminedbyanumberofvariables-thegenerallevelof interest rates in the economy, the term structure of interest rates and the default risk of the bond. Fig. 3.1 provides the building blocks for arriving at the interest rate on a straight corporate bond.

Default Premium

Maturity Premium

Instantaneous (Short-term Default Instantaneous (Short-term -free Rate)

Fig. 3.1 Building blocks for interest rates

Thefirstblockisthelevelofshort-termdefaultfreeinterestratesanditcapturestheoveralllevelofratesintheeconomy.Thesecondblockisamaturitypremium,whichreflectsthedifferencebetweenlonger-termdefaultfreerates and short-term default free rates, and is generally positive. The third block is a default premium, which is related to the default risk of the bond is question. This section takes a closer look at these blocks.

3.3.1 Level of Interest RatesTheshort-termdefaultfreeratecanbedecomposedintotwocomponents–anexpectedinflationrateduringtheperiod and an expected real rate of return.

Short-termdefaultfreerate=ExpectedInflation+ExpectedRealRateofReturn

This identity is known as the Fisher equation and essentially implies that changes in short-term rates can be traced tochangesineitherexpectedinflationortheexpectedrealrateofreturn.ThemorepreciseversionoftheFisherequation allows for the compounding effect.

(1+r) = (1+I) (1+R)where,

r = Nominal interest rateI=ExpectedInflationR = Expected real rate of return

It should be emphasised that the Fisher equation is an identity and there is no question of it being proved or disproved.The realquestions that arise from theequationare the specificassumptionsabout the real rateandexpectedinflation.

Expected inflationExpectedinflationisclearlythedominantvariabledetermininginterestrates.Generallyspeaking,aforecasterwhocanpredictchangesininflationwellshouldalsopostagoodtrackrecordinpredictinginterestratechanges.Thefirststepinforecastinginflationistheunderstandingofitsdeterminants.


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The determinants of inflationThereisconsensusonthedeterminantsofinflation,thoughthereislittleagreementabouttheconsequencesofspecificactionsoninflation.Tounderstandboththedeterminantsofinflationandthesourcesofdisagreementbetweenthedifferentschoolsofthoughtoninflation,consideranotheridentity:

Where:P = Price levelM = Money supply in the economyV = Velocity of money circulation in the economyY = Real Output in the economy

Thevelocityofmoneymeasureshowoftenthecurrency,usedtodefinethemoneysupply‘M’,circulatesintheeconomy and how much is created in terms of transactions for every unit of currency created. Thus, if a $1 in additional currency created $3 in transactions, the velocity of money is 3. While the money supply used in the equation can bedefinedinanumberofdifferentways,rangingfromjustcurrencytobroaderaggregates,thevelocityhastobedefinedconsistently.

This identity can be stated in terms of changes as follows:

Thelefthandsideofthisidentityistheinflationrateandtherighthandsideprovidesthethreedeterminantsoftheinflationrate:

The change in the money supply (dM): If the money supply increases, with no concurrent change in real output •andmoneyvelocity,theinflationratewillincrease.Thisisthebasisfortheargumentbymanymonetarists,who believe that there is no linkage between real output and money supply and that money velocity is stable overlongperiods,thatloosemonetarypolicy(increasingmoneysupply)isthereasonforhighinflation.Whilesome monetarists will concede that monetary policy can have short term effects on real output, most argue that it cannot impact real output in the long-term. They also argue that while money velocity may change over time, thatthesechangesoccurovertheverylong-termandareunlikelytohaveamajorimpactoninflation.The change in money velocity (dV): If the money velocity increases, with no concurrent change in money supply •andrealoutput,theinflationratewillincrease.Economistshavelongdebatedwhymoneyvelocitychangesovertime. One determinant is technology, since changes in the way people save (from checking accounts to money market accounts) and in the way they spend (from cash transactions to credit card transactions) affect the money velocity.Anotheristhefaiththepublichasinthecurrency.Inhyper-inflationaryenvironments,individualsaremuch less willing to hold currency (because it depreciates in value so quickly) and therefore attempt to convert the currency into real goods. This unwillingness to hold currency translates into higher money velocity. Thus, if the central bank is viewed as having eased the reins on money supply, there is often a concurrent increase in moneyvelocity,leadingtoasurgeininflation.The change in real output: If the real output increases, with no concurrent change in money supply and money •velocity,theinflationratewilldecrease.ThisisoftenthebasisoftheargumentusedbyKeynesiansforeasingmonetary policy during economic downturns. Increasing the money supply, they argue, results in a concomitant increaseinrealoutput,sincethereisexcesscapacity,andtheeffectsoninflationarethereforemutedornon-existent.

Measuring InflationAtruemeasureofinflationwouldconsiderchangesinthepricesofallgoodsandservicesusedinaneconomy,weightedbytheirusagevalues.Thereportedmeasuresofinflation,eitherattheconsumerortheproducerlevel,attempttodoso,butoftenlagchangesintrueinflationbecauseofanumberofreasons.Thefirstisthatnotallgoodsand services are traded in a market place, where prices are easily available and goods are fairly standardised. Thus,

33

itiseasytogaugetheinflationinmedicalprescriptionprices,butmuchmoredifficulttogaugetheinflationinthepricesofmedicalservices.Thesecondisthatallinflationindicesarebaseduponsamplingsofpricesofgoods,rather than the universe of all goods traded. Even if the sample is not biased, there is the possibility of sampling error that enters into the numbers. The third is the issue of weighting on the basis of usage value. Due to practical considerationsoftimeandresources,theweightsarenotadjustedeverytimetheinflationindexiscomputedtoallow for changes in usage.

Instead indexweightsareadjusted infrequently, leading tobiased in themeasured inflation.Thus, the inflationindices which kept the usage of gasoline by households constant in the late seventies while oil prices were climbing (andpeoplewerecuttingbackontheuseofgasoline)tendedtooverstatetheinflationrateduringthatperiod.Thefinalconsiderationisaboutthelevelatwhichinflationistobemeasured,sincecountinggoodsateveryleveloftheprocess (from commodity to manufactured good to retailed good) would result in double or even triple counting the samegood.Differentinflationindicesexamineinflationatdifferentstagesintheprocessandcanleadtodifferentconclusionsaboutwhetherinflationisincreasing,decreasingorstayingunchanged.

Forecasting InflationAschangesininflationsignalchangesininterestrates,economistsandanalystshaveexpendedconsiderabletimeandresourcesforecastinginflation,withmixedresults.Theforecastingmodelsusedrangefromthenaivetothesophisticated and are based upon everything from gut feeling to elaborate mathematics. The output from these models canbecontrastedwithpredictionsbasedpurelyuponpastinflation–eithertheinflationinthelasttimeperiodortime-seriesmodelsthatexaminetrendsandshiftsinpastinflation–andtheresultsforthemostpartaremixed.Elaborate forecasting models do no better than time series models in the short term, but may better capture changes ininflationinthelong-termbecausetheyconsiderinformationbeyondwhat’savailableinpastinflationrates.

Theintroductionofinflation-adjustedtreasurybondsafewyearsagohasprovidedaninterestingalternativeforthosewhowouldratherrelyonmarketsfortheirinflationestimatesthaneconomists.Inparticular,ifweviewthemarketinterestrateonaninflationindexedtreasurybondasarisklessrealrateandthemarketinterestrateonanominaltreasurybondofequalmaturityasanominalrate,theexpectedinflationratecanbeestimatedasfollows:

Forinstance,ifthenominalrateis5.1%andtherealrateis2.7%,youcanestimatetheexpectedinflationrateasfollows:

ExpectedInflationRate=1.051/1.027=.0233or2.33%

Testing the Fisher EquationAs mentioned earlier, the Fisher equation is an identity that cannot be proved or disproved. There have, however, been numerous attempts to impose additional constraints on the model, to test the usefulness of the model in explaining changesininterestratesovertime.ThesestudiesgobacktoFisher’sownworkoninterestratesandinflation,wherehefoundthatthecorrelationbetweentherateofinflationandthecommercialpaperratewaslowinbothhissampleperiods–1890to1914and1915to1927.Thecorrelationbetweeninflationandthecommercialpaperratedidnotimproveasvariousleadsandlagsoninflationweretried.

Fama (1976) made the assumption that real rates do not change much over time and that changes in interest rates shouldthereforealmostentirelybecausedbychangesininflation.Hetestedthispropositionbyregressinginterestratesagainstexpectedinflation:

Where, = Nominal interest rate during period t=Expectedinflationduringperiodt


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He argued that if his initial assumption about constant real rates was true, this regression would yield the following:

The intercept would be equal to the constant real rate over the period.•The slope of the regression would be one, since all changes in interest rates would be a consequence of changes •ininflation.

Lackinganadequatemeasureofexpectedinflation,heusedtheone-monthtreasurybillrateatthestartofeachmonthasameasureofexpectedinflationduringthemonthandtheoneandthree-monthtreasurybillratesasmeasuresofnominal rates. His results, for the period 1953 to 1971, were as follows:

CPI regressed against one-month T.Bills = 0.0007 — 0.98 = 0.29 (0.0003) (0.10)CPI regressed against three-month T.Bills = 0.0023 — 0.92 = 0.48 (0.0011) (0.11)

Based upon this regression, he concluded that the hypothesis of constant real rates was supported and that the slope was statistically indistinguishable from one, suggesting that there was a one-to-one relationship between changes ininterestratesandexpectedinflation.

The studies that followed up have generally not been as encouraging. Wood, for instance, updates Fama’s regression, afteraddingalaggedmeasureofinflationandcontraststheresultsfortwoperiods–1953to1971and1974to1981.

Period Regression 1953-71 = 0.0006 - 0.84 + 0.09 -1 0.309 (0.0003) (0.111) (0.064)1974-81 = 0.0023 - 0.25 + 0.47 -1 0.371 (0.0008) (0.12) (0.11)

Thecoefficientonnominalinterestrates(Rt) which was close to one for the 1953-71 time period, used by Fama in his study, drops to 0.25 for the 1974-81 time period.

Thereasonforthesurprisinglygoodresultsfrom1953to1971maybetraceabletothefactthatinflationwasverystableduringthisperiodandthatchangesininflationtendedtobesmall.Thus,itseemslikelythatthehypothesisofstablerealratesandaone-to-onerelationshipbetweeninterestratesandinflationwillberejectedinanyperiodoranyeconomywherethereisvolatilityininterestratesandinflation.Astheimportanceofforecastingincreaseswiththevolatilityofinterestratesandinflation,thecautionarynotesonforecastingshort-terminterestratesbasedonlyuponexpectedinflationshouldbetakentoheart.

Expected real rate of returnThe other component of the Fisher equation is the expected real rate of return. On an intuitive level, the expected real rate of return is the rate at which individuals are willing to trade off current consumption for future consumption. Given the human preference for present consumption, the expected real rate of return should be positive, but can vary widely across time and across economies. If individuals in a society have a strong desire for current consumption, the expected real rate of return will have to be high to induce them to defer consumption.

Realised Real Rates of ReturnAstheexpectedrealrateofreturnisbaseduponthepreferencefunctionsof individuals,whicharedifficult toobserve,wearereducedtoobservingrealisedrealratesofreturn,whichcanbedefinedtobe:

Realised Real Rate of Return = -

35

Where, = Nominal interest rate at the beginning of period t

=ActualInflationduringperiodt

While the expected real rate of return should be positive, the realised real rate of return can be positive or negative, depending upon the period under observation. During the 1970s, for instance, bond investors in the United States earnednegativerealratesofreturnasactualinflationoutstrippedexpectedinflation.

Expected Real Return and Expected Real GrowthUltimately, the real return to investors in an economy comes from real growth in the economy. One way to approach the estimation of expected real return is to estimate the expected real growth rate in the economy. Thus, the expected real return in an economy growing in the long term at 2.5% a year should be approximately 2.5%. If the expected real return increases above the long term growth rate in the economy, the imbalance will lead to a depletion of savings and a shortfall in investments. Alternatively, if the real return decreases below the long term growth rate, the imbalance will lead to an accumulation of savings and over-investment.

3.3.2 Maturity PremiumThe maturity premium refers to the difference in interest rates between a short term (or instantaneous) default-free bondandalonger-maturitydefault-freebond.Inthefollowingsection,thematuritypremiumisclarifiedfurtheranda number of different theories designed to explain the magnitude of the maturity premium are examined.

The yield curveThe relationship between maturity and interest rates is usually captured by a yield curve, which graphs yields on bonds against bond maturities. Fig. 3.2 summarises the treasury yield curve in January and June 2001.

3 month 6 month 1 year 2 year 5 year 10 year 30 year

Jan-01Jun-01

0.00%

1.00%

2.00%

3.00%

4.00%

5.00%

6.00%

Maturity

Fig. 3.2 Yield curves - January 2001 and June 2001(Source: http://people.stern.nyu.edu/adamodar/pdfiles/valn2ed/ch33.pdf)


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In January 2001, the yield curve was slightly downward sloping. But by June 2001, the yield curve had reverted – short term rates dropped while long-term rates increased slightly. While the yield curve has generally been upward sloping over much of this century, there have been periods where the yield curve has been downward sloping.

Spot and forward ratesThe spot rate on a multi-period bond is an average rate that applies over the periods. The forward rate is a one-period rate for a future period and can be extracted from the spot rates. For instance, if is the two-period spot rate and

is the oneperiod spot rate, the forward rate for the second period, , can be obtained.

The forward rate for period three can be extracted using the spot rates for periods 2 and 3.In general, the forward rate for period n can be written as:

If the yield curve for spot rates is upward sloping, the yield curve using forward rates will be even more so. Alternatively, if the spot rate yield curve is downward sloping, the forward rate yield curve will be even more so. The following illustration builds on the previous one and extracts forward rates from spot rates.

Determinants of the maturity premiumThemagnitudeofthematuritypremiumisdeterminedbyanumberoffactorsincludingexpectationsaboutinflation,investorpreferencesforliquidityanddemandsfromspecificmarketsegments.Eachofthesefactorsisexaminedin more detail in the following section.

Expected inflationExpectationsaboutfutureinflationareakeydeterminantoflongertermrates.Ingeneral,ifinflationisexpectedtogoupinfutureperiods,longertermrateswillbehigherthanshortertermrates.Alternatively,ifinflationisexpectedto go down in future period, longer term rates will be lower than short term rates.

An extreme version of this story is the ‘pure expectations hypothesis’, where the term structure is driven entirely bytheexpectationsoninflation.Underthishypothesis,theyieldcurvewillbeupwardslopingifinvestorsexpectinflation to rise in future periods,flat if investors expect inflation to remainunchanged in future periods, anddownwardslopingifinvestorsexpectinflationtodeclineinfutureperiods.

The pure expectations hypothesis can also be stated in terms of forward rates and expected spot rates. If the hypothesis is correct, the forward rate for period n should be the best predictor of the expected spot rate in that period.

n-1Fn = Exp(n-1Sn)Where,

n-1Fn = Forward rate for period nExp(n-1Sn)= Expected one-period spot rate in period n

While the pure expectations hypothesis may be extreme in assuming that forward rates are determined entirely by expectedspotrates,itdoeshighlighttheimportanceofexpectedinflationindeterminingthematuritypremium.

Liquidity preferenceThe liquidity preference theory is not an alternative to the expectations theory. It builds on expectations by taking into account uncertainty and risk aversion. In the form in which it was originally developed by Hicks (1946), the uncertainty was seen as accruing to the lender who concurrently charged a liquidity premium for lending for longer time periods. This uncertainty can also be stated in terms of bond prices, with long-term bonds being viewed as more volatilethanshort-termbonds,asinterestrateschange.Underthistheory,holdingexpectationsofinflationconstant,longer term rates will be higher than shorter term rates. Stated in terms of forward rates and expected spot rates,

n-1Fn = Exp(n-1Sn) + Lt

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Where,Lt = Liquidity premium corresponding to a bond maturity of t periods

While the traditional theory assumes a positive liquidity premium (Lt), the assumption that all lenders prefer to lend short term over long-term may not be always appropriate.

Forinstance,alenderwithfixedliabilitiestwentyyearsfromnowmayviewatwentyyearzero-couponbondaslessriskythanatreasurybillofsixmonths,becauseitmatchescashinflowstocashoutflows.Thequestionthereforebecomes an empirical one – Does the average lender prefer to lend short or long term?

McCulloch (1975) attempted to estimate term premia for different time periods, and arrived at the following estimates.Maturity 6 month 1 year 5 year 10-year 20-year 30-yearEstimate 0.41% 0.43% 0.43% 0.43% 0.43% 0.43%Standard Error 0.06% 0.07% 0.07% 0.07% 0.07% 0.07%

Therearetwokeyfindingsthatemergefromthisstudy.Thepositivetermpremiasuggestthat,onaverageatleast,lenders prefer lending short to long term. The term premia also do not seem sensitive to bond maturity. The second resulthasbeenchallenged in anumberof studies.VanHorne (1965)finds termpremia increasing, albeit at adecreasing rate, with bond maturity.

Demands from specific market segmentsThe price of bonds, like any other security, is determined by demand and supply. If the market is segmented, and therearesizablegroupsofinvestorswhosedemandisforaspecificmaturity,thetermstructurewillbeaffectedbythesegroups.Again,consideringtheextremecase,whereinvestorswilllendandborrowonlyforspecificmaturities,the interest rate at each maturity will be determined by demand and supply at that maturity. Under this scenario, the term structure can take any shape, depending upon the demand and supply at each maturity.

Theassumptionthatinvestorswilllendorborrowonlyforspecificmaturitiesandnotsubstituteothermaturitieseven when it is extremely favourable for them to do so is an extreme one. In reality, market segments do exist and do affect the term structure but only at the margin and for one or two maturities. For instance, the demand from Japanese investors in the late eighties for the just-issued thirty year bonds resulted in a slight kink in the term structure, where the thirty-year bond rates were slightly lower than twenty-nine year bond rates, even though the rest of the yield curve was upward sloping.

The empirical evidence on maturity premiaEmpirical studies of the term structure have examined several questions including the relative frequency of upward and downward sloping term structures, the magnitude of liquidity premia and the presence of market segments. The evidence can be summarised as follows:

The yield curve, at least in this century, has been more likely to be upward sloping than downward sloping. •Examining yield curves at the beginning of each year from 1900 to 2000, the yield curve has been downward sloping in only 29 of the 100 years. This is inconsistent2 with a pure expectations hypothesis, where downward slopingyieldcurvesshouldbejustaslikelyasflatorupwardslopingyieldcurves.Itis,however,consistentwith a combination of the expectation and liquidity preference hypotheses, where positive liquidity premia are demandedoverandaboveexpectedinflation.The term structure is much more likely to be downward sloping when the level of interest rates is high, relative •to historical rates. The table below summarises the frequency of downward-sloping yield curves as a function of the level of interest rates.

1-year Corporate Bond Rate Slope of Yield Curve Positive Flat Negative Above 4.40% 0 0 201900-70 3.25% - 4.40% 10 10 5


38

Below 3.25% 26 0 01971-00 Above 8.00% 4 2 3 Below 8.00% 13 6 0

This evidence is consistent with the expectations and liquidity preference hypotheses, but it is also consistent with a hypothesis that interest rates move within a normal range. When they approach the upper end (lower-end) of the normal range, the yield curve is more likely to be downward sloping (upward sloping).

Studies have generally found that expectations about future interest rates are important in shaping the term •structure. Meiselman computed high positive correlations between forecasting errors and changes in various forward rates, and stable term premia. In contrast, there are many researchers who argue that the volatility in interest rates is much too great to be explained by just expectations about future rates and constant term premia. Shiller (1979) concludes that the greater the volatility in interest rates, the larger the term premium.Attempts by the government to alter the shape of the yield curve by adjusting the maturity of issues have largely •been unsuccessful in the long-term. For instance, “Operation Twist” in 1962 was designed to make the yield curveflatter4byloweringlong-termratesandraisingshorttermrates,byissuingshort-termdebttofinancedeficits.Thoughtheyieldcurvedidflatten,long-termyieldsdidnotdecline.Thiscanbeviewedasevidenceofthe weakness of the market segmentation hypothesis.There is evidence that the shape of the term structure has strong predictive power for future changes in the real •economy. Harvey (1991) examined the G-7 countries (Canada, France, Germany, Italy, Japan, U.K., and U.S.A.) and concluded that 54% of world economic growth could be explained the term structure.

3.3.3 Default PremiumWhile there is no possibility of default for bond issues made by the United States Treasury, corporate bonds or state/local bonds can default on interest or principal payments. If there is any possibility of default on a bond, there will be a default premium in addition to the maturity premium on the bond. The default premium will increase with the perceiveddefaultriskofthebondandisgenerallyalsoafunctionofthematurityandtermsofthespecificbond.Reviewing that, we concluded that:

The most direct measure of default risk is the default rate which measures defaulted issues as a percentage of •theparvalueofdebtoutstanding.Hickmaninvestigatedthedefaultexperienceoffixed-incomecorporatebondsbetween 1900 and 1943, as a function of the bond rating.

RatingsSize of Issue I II III IV V-IX No Rating> $ 5 millions 5.9% 6.0% 13.4% 19.1% 42.4% 28.6%≤$5millions10.2%15.5%9.9%25.2%32.6%27.0%

Hickman’s study has been extended by several researchers and data availability has made this easier to do. Altman computes default rates for high yield bonds from 1970 to the present, on an annual basis and relates them to bond ratings.

Default spreads on bonds tend to increase during economic downturns and decrease during economic booms.•Default spreads are generally larger for longer term bonds than they are for shorter term bonds, for any given •levelofdefaultrisk.Theremaybespecificcircumstances,though,wherethereverseistrue.Johnsondefinesa“crisis-atmaturity”scenario,usuallyinthemidstofarecessionoradepression,whereafirmisperceivedtohaveinsufficientfundstomeetitsimmediatedebtservicingneeds,thoughitisexpectedtoreverttohealthin the long term. In this scenario, the default premia will be lower for longer maturity bonds than for shorter maturity bonds. Johnson found evidence of inverted default premia term structures during 1934, in the midst of the depression.

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3.4 Special Feature in Bonds and Pricing EffectsIn the last section, we examined the question of how to price a government or a corporate bond based upon the expected coupons and the appropriate interest rate for the bond. Most bonds though have other features added on, some of which make the bonds more valuable and some less valuable. In this section, we consider how best to value these special features.

3.4.1 ConvertibilityA convertible bond is a bond that can be converted into a pre-determined number of shares, at the option of the bondholder. While it generally does not pay to convert at the time of the bond issue, conversion becomes a more attractive option as stock prices increase. Firms generally add conversions options to bonds to lower the interest rate paid on the bonds.

The conversion optionInatypicalconvertiblebond,thebondholderisgiventheoptiontoconvertthebondintoaspecifiednumberofsharesof stock. The conversion ratio measures the number of shares of stock for which each bond may be exchanged. Stated differently, the market conversion value is the current value of the shares for which the bonds can be exchanged. The conversion premium is the excess of the bond value over the conversion value of the bond.

Thus a convertible bond with a par value of $1,000, which is convertible into 50 shares of stock, has a conversion ratio of 50. The conversion ratio can also be used to compute a conversion price - the par value divided by the conversion ratio, yielding a conversion price of $20. If the current stock price is $25, the market conversion value is $1,250 (50 * $25). If the convertible bond is trading at $1,300, the conversion premium is $50.

Determinants of valueThe conversion option is a call option on the underlying stock and its value is therefore determined by the variables that affect call option values – the underlying stock price, the conversion ratio (which determines the strike price), the life of the convertible bond, the variance in the stock price and the level of interest rates. Like a call option, the value of the conversion option will increase with the price of the underlying stock, the variance of the stock and the life of the conversion option and decrease with the exercise price (determined by the conversion option).

Theeffectsofincreasedriskinthefirmcancutbothwaysinaconvertiblebond-itwilldecreasethevalueofthestraight bond portion while increasing the value of the conversion option. These offsetting effects will generally mean thatconvertiblebondswillbelessexposedtochangesinthefirm’sriskthanareothertypesofsecurities.Optionpricing models can be used to value the conversion option with three caveats – conversion options are long term, making the assumptions about constant variance and constant dividend yields much shakier, conversion options result in stock dilution, and conversion options are often exercised before expiration, making it dangerous to use European option pricing models. These problems can be partially alleviated by using a binomial option pricing model, allowing for shifts in variance and early exercise and factoring in the dilution effect. The following illustration provides an example of the use of option pricing models in valuing a conversion option in a convertible bond.

The value of a convertible bond is also affected by a feature shared by most convertible bonds that allow for the adjustmentoftheconversionratio(andprice)ifthefirmissuesnewstockbelowtheconversionpriceorhasastocksplit or dividend. In some cases, the conversion price has to be lowered to the price at which new stock is issued.Thisisdesignedtoprotecttheconvertiblebondholderfrommisappropriationbythefirm.

The two components of the convertible bond can be valued as follows:Straight Bond Component•If this bond had been a straight bond, with a coupon rate of 5.75% and a yield to maturity of 9.00% (based upon the bond rating), the value of this straight bond can be calculated:

PV of Bond = = $834.79


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This is based upon semi-annual coupon payments (of $28.75 for semi-annual periods).

Valuing the Conversion Option•The value of the conversion option is estimated using the Black-Scholes model, with the following parameters for the conversion option.

Type of Option = Call Number of Calls/Bond = 25.32 Stock Price = $32.50 Strike Price = $1000/25.32 = $39.49Time to Expiration = 7.5 years Standard Deviation in Stock Prices (ln) = 0.5Riskless rate = 7.75% (Rate on 7.5 year Treasury Bond)Dividend yield on Stock = 3.00%

Allow for the dilution inherent in the exercise (See chapter 5 on warrant pricing for details on the valuation correction).Value of one Call = $ 12.85Value of the Conversion Option = $ 12.85 * 25.32 = $325.43

Value of Convertible Bond•The value of the convertible bond is the sum of the straight bond and conversion option components.

Value of Convertible Bond = Value of Straight Bond + Value of Conversion Option = $ 832.73 + $325.43 = $1158.16

This valuation is based upon the assumption that the conversion option is unconstrained and that the bonds are not callable. The effects of introducing these changes into the analysis will be examined in the following sections.

The effect of forced conversionCompanies that issue convertible bonds sometimes have the right to force conversion, if the stock price rises to a specifiedlevel.Thisrighttoforceconversioncapstheprofitthatcanbemadeontheconversionoption,andhenceaffects its value.

The value of a capped call, with an exercise price of K1 and a cap of K2 can be calculated as follows.Value of capped call (K1, K2) = Value of Call (K1) - Value of Call (K2)

ThisisbecausethecashflowsonacappedcallcanbereplicatedbybuyingthecallwithastrikepriceofK1 and selling the call with a strike price of K2.

3.4.2 CallabilityTheissuerofacallablebondpreservestherighttocallbackthebondandpayafixedprice(generallyatapremiumovertheparvalue)forit.Thus,ifinterestratesdecline(bondpricesrise)aftertheinitialissue,thefirmcanrefundthebondsatthefixedpriceinsteadofthemarketvalue.Addingthecalloptiontoabondshouldmakeitlessattractiveto buyers, since it reduces the potential upside on the bond. As interest rates go down, and the bond price increases, the bonds are more likely to be called back.

There are several common features shared by most callable bonds. Most callable bonds come with an initial period of call protection, during which the bonds cannot be called back. Such bonds are called deferred callable bonds. The call price on most callable bonds is set at an initial level above par value plus one annual coupon payment, but declines as time passes and approaches the par value.

Valuing the callability optionThe issuer’s right to call back a bond if interest rates drop (or bond prices rise) to an attractive level is a call option on the bond and can be valued as such. The payoffs on a callable bond are shown in Fig. 3.3.

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Value of Underlying Asset

Payoffs on Call Option

Strike Price

Value of Bond

Payoffs on Call Feature on Bond

Call Price

Payoffs onCall

Payoffs onCallFeature

Fig. 3.3 Payoffs on call feature on bond to seller of bond(Source: http://people.stern.nyu.edu/adamodar/pdfiles/valn2ed/ch33.pdf)

The value of the callable feature on a callable bond will increase as interest rates decline, and as the volatility of interest rates increases. Since the callable feature is held by the issuer of the bond, the value of a callable bond can be written as follows:

Value of Callable Bond = Value of Straight Bond - Value of Call Feature in BondA callable bond should therefore sell for less than an otherwise similar straight bond.

Traditional analysisThe traditional approach to analysing callable bonds is to estimate yields to call as well as yields to maturity. The formerisbasedupontheassumptionthatthebondwillbecalledatthefirstcalldatewhilethelatterassumesholdingthe bond until maturity. The two yields are compared and the investor chooses the lower of the two as a measure of his expected return on the bond. This approach can also be extended to calculate the yield to all possible call dates and picking the lowest of these yields as the expected yield on the callable bond. This yield is called the yield to worst.

While this approach may give the investor some sense of the potential downside from the callability of the bond, it suffers from all the standard problems of the ‘yield to maturity’ calculation. First, it assumes that the investor can reinvest all coupons until the bond is called at the yield to call, which is not a realistic assumption since calls are much more likely if interest rates go down. Second, it does not examine the rate at which the proceeds from the called bond can be reinvested by the investor. Third, it assumes that the bond will be called on the call date, which takes away the option characteristics of the call feature.

Price/yield relationship for a callable bondThe price/yield relationship on a callable bond is different because the potential that the bond will be called back puts an upper limit on the price. This makes the relationship between price and yield convex, for some range of the yields. The difference is illustrated in Fig. 3.4.


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Non-callable bonda-a'

Callable bonda-b

Coupon rate Yield

Pric

e

y*

a'

b

a

Fig. 3.4 Callable bond prices and interest rates(Source: http://people.stern.nyu.edu/adamodar/pdfiles/valn2ed/ch33.pdf)

The section of the price/yield relationship on the callable bond when the yield falls below y* has negative convexity - i.e., the price appreciation on this bond will be less than the price depreciation for a given change (down or up) in interest rates.

Determinants of value-option pricing approachThe call feature in a callable bond can be valued using option pricing models. It is a series of call options on the underlyingbondanditsvalueisdeterminedbythelevelandvolatilityofinterestrates.Therearesomemodificationsthat need to be made to the standard option pricing models before they can be applied in this context.

Once the call feature is valued as a series of option, the yield on a callable bond can be adjusted for the option features and the difference between this adjusted yield and treasuries of equivalent maturity is called the option adjusted spread. This approach is a more realistic way of considering the effects of the call feature on expected yields than the traditional yield to call approach.

Effective duration and effective convexityIntheprevioussection,wedefineddurationtobeameasureofabond’ssensitivitytointerestratechanges.Whiledoing so, itwas assumed that cashflowsdid not change as interest rates changed.This assumption is clearlyviolatedforcallablebonds,wherethecashflowsonthebondareinfluencedbythelevelofrates-ifinterestratesdrop enough, the bond will be called. For bonds such as these, there is a different measure of duration that is more appropriate called the effective duration. The duration of any bond can be approximated as follows, for a small change in interest rates.

Duration =

Where, = Price of the bond if yield drop by x basis points

= Price of the bond if yield increases by x basis points

= Price of the bond initially y+ = Initial yield + x basis points y- = Initial yield - x basis points

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This approach can be used to estimate the effective duration of callable bonds for any segment of the yield curve. It can also be used for any other bonds with embedded options, such as putable bonds, or mortgage backed securities, which have the prepayment option embedded in them. A similar adjustment can be made to the standard convexity measuretoarriveattheeffectiveconvexityofanybondwithembeddedoptions.[NOTE:Therewasnoequationforconvexity.]

Effective Convexity =

Valuing a callable-convertible bondMany convertible bonds have embedded call features. The presence of two options in the bond, one possessed by the buyer of the bond and the other possessed by the seller of the bond, and the interaction between the two options, implies that the two options have to be valued together. Brennan and Schwartz (1977, 1980) provide an analysis of convertible bonds with call features, default risk and stock price dilution. The simplest approach for illustrating the interaction between the various options is a binomial option pricing model.

Empirical evidence on call featureWhen a convertible bond is callable, holders of the convertible bond lose the opportunity to make further returns on the bond as stock prices increase. Companies can establish a variety of call policies such as calling the instant the market value of the convertible rises above the call price or waiting until the market value is well in excess of the call price. Ingersoll (1977) argues that a bond should be called when its conversion value equals its call price. Giventhatathirty-daynoticehastobegiventobondholdersofacall,firmsmayprefertobuildacushiontoprotectagainst risk during this period.

Theempiricalevidencehoweversuggeststhatfirmsdonotusuallyfollowtheoptimalpolicy.Ingersoll,forinstance,findsthatbetween1968and1975,theaverageconversionvaluewas43.9%abovethecallpriceforbondsand38.5%forpreferredstocks.Thecallpolicychosenbyafirmandcommunicatedtofinancialmarketsimplicitlythroughitsactions, has an effect on the value of the convertible bond.

3.4.3 Pre-payment OptionMortgage backed securities, which came of age in the eighties, securitised residential mortgages, by packaging themandissuingmarketablesecuritiesofvarioustypesonthem–eitherasflowthroughinvestmentswhereholdersreceiveashareofthetotalcashflowsonthepoolofmortgagesorasderivativeproducts,whereholdersreceivecustomisedpackagesofcashflowsdependingupontheirpreferences.Thelatter,calledcollateralisedmortgageobligations,initssimplestform,dividecashflowsonthemortgagepoolintofourtranches,withcashflowsoneachtranchestartingasthecashflowsonthepriortranchearecompleted.

Inrecentyears,CMOshavebeenrefinedfurtherandevenmorespecialisedproductshavebeencreatedincludingstrippedmortgage-backedsecurities(wherecashflowsaredividedonthebasisofprincipalandinterest),floatingrateclassesandinversefloaters(wheretheinterestrateonthesecurityincreasesastheindexratedecreases).Mortgagescan be pre-paid by borrowers, if interest rates decline. This prepayment option that resides with borrowers affects thecashflows,andthereforethevalue,ofallmortgage-backedsecurities.

The prepayment optionThe homeowner may prepay a loan for any number of reasons, but the level of interest rates is a critical variable. If interestratesdeclinesufficiently,thepotentialgainfrompre-paymentmayexceedthecostofpre-payment.Ifthelevel of interest rates were the only determinant of prepayment and homeowners were rational about prepayment decisions, the prepayment option could be valued very similarly to the call option in a callable bond (as a function of the level and volatility of interest rates).

There are, however, other variables besides the level of interest rates that determine whether homeowners prepay. For instance, there is a correlation between prepayment and the age of a mortgage, irrespective of interest rates. Furthermore, some homeowners may never prepay their mortgages no matter how much interest rates drop. There are also seasonal factors that affect prepayment. Consequently, option pricing models alone fall short in pricing prepayment options in mortgage backed securities.


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A number of researchers have attempted to develop models that explain prepayment, as a basis for pricing the prepaymentoption,withcharacteristicssuchasageandcouponrateasinputs,inadditiontospecificcharacteristicsoftheborrowersinthepool.Incaseswhereaspecificratherthanagenericpoolofmortgagesisbeingpriced,thehistoricalpaymentrecordofthespecificpoolisusefulandisoftenthebasisforestimatingprepayments.

Valuing the prepayment optionThe effect of the prepayment option on value will vary with the type of mortgage backed security. Consider, for instance, the price behaviour of interest-only and principal only securities, as interest rates changes. As interest rates increase, the interest payments on the interest-only securities goes up, leading to a higher value for the security, at least initially, though the present value effects (which are negative) start to dominate beyond a certain point. As interest rates decrease, the prepayments lead to lower interest payments and a lower value for the security. The principal-only securities behave more like conventional bonds, increasing in value as interest rates decline and decreasing in value as they increase.

3.4.4 Interest Rate Caps and FloorsAfloatingratebondisabondwhichhasaninterestratelinkeduptoanindex-eitheragovernmentbondrate(treasury bond or bill) or to the LIBOR. The rationale for issuing such bonds is to reduce the interest rate risk for boththeissuerandthebuyerofthebond.Mostfloatingratebondissuers,however,captheirfloatingrateobligationstoensurethatinterestratesdonotriseaboveapre-specifiedrate(thecap).Somefloatingratebondsofferbuyerssomecompensationbyprovidingafloor,belowwhichinterestrateswillnotdecline.Ifafloatingratebondhasacapandafloor,acollariscreated.

Caps, floors and collarsThepresenceofacaponafloatingratebondcanbeillustratedbestbycontrastingabondwithacapagainstafloatingratebondwithoutone,asshowninFig.3.5.

EffectiveInterestRate(%)

Index Rate(for Cap)

Floating RateBond

Cap

Floating Rate+Cap

K(c)

Fig. 3.5 Effects of caps on floating rate loans(Source: http://people.stern.nyu.edu/adamodar/pdfiles/valn2ed/ch33.pdf)

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ThecaponafloatingratebondhasthesameeffectasacalloptiononinterestrateswithastrikepriceofKc, with the issuer of the bond holding the option. A call option on interest rates translates6 into a put option on the underlying bond.Thepriceofafloatingratebondwithacapcanthenbewrittenas:

Priceoffloatingratebondwithcap=Priceoffloatingratebondwithoutcap - Value of put on bond

Thepresenceofaflooroninterestratescanalsobeillustratedusingasimilarcomparisonofabondwithaflooragainst a bond without one in Fig. 3.6.

EffectiveInterestRate (%)

Floating RateBond

Floor

Cap

K(f)

Floating Rate+ Floor


TheflooronafloatingratebondhasthesameeffectasaddingaputoptiononinterestrateswithastrikepriceofKf, with the buyer of the bond holding the put. A put option on interest rates can be translated into a call option on theunderlyingbond.Thepriceofafloatingratebondwithafloorcanthenbewrittenas:

Priceoffloatingratebondwithfloor=Priceoffloatingratebondwithoutcap + Value of call on bond

Finally,thepresenceofbothacapandafloorcanbeillustratedinFig.3.7.


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EffectiveInterestRate (%)

Index Rate(for Cap)

Floating RateBond

Floor

Cap

Collared Bond

K(f) K(c)


Thepresenceofacollaronafloatingratebondcreatestwooptions-acalloptionwithastrikepriceofKc for the issuer of the bond and a put option with a strike price of Kf for the buyer of the bond. These options on interest rates can be stated again in terms on options on the underlying bond.

Priceoffloatingratebondwithcollar=Priceoffloatingratebondwithoutcollar + Value of call on bond - Value of put on bond

Valuing caps and floorsOptionpricingmodelscanbeusedtovaluecaps,floorsandcollarswithsomecaveats.ThekeyassumptionintheBlack Scholes model of constant volatility over the life of the option is likely to be violated for interest rate options, both because of the long-term nature of these options and because the variance in the bond price is likely to change as the bond approaches maturity. There have been attempts to use yield instead of price and assume that it conforms to a normal distribution.

Subrahmanyam (1990) notes that the value of a cap on interest rates can be written as a series of put options on the priceofanequivalentbillorbond.Briys,CrouhyandSchobel(1991)provideaframeworkforpricingcaps,floorsandcollars.Theyarguethatcapsandfloorscanbemodelledasaseriesofindependentoptionsonzerocouponbonds. They allow for the fact that bond prices do not follow the geometric Brownian motion used by Black and Scholes(1973),butadoptadifferentstochasticprocesstopricecaps,floorsandcollars.

3.4.5 Other FeaturesThere are a number of other bond features which affect the value of the bond – a sinking fund provision, where the firmplanstoretireaspecifiedfacevalueofthebondsoutstandingeachyear,provisionsrelatingtothesubordinationof future debt issues and bond covenants on investment and dividend policy.

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Sinking fundsMostindustrialbondissuescomewithsinkingfundprovisions,requiringtheissuertoretireaspecifiedportionofthebondissueeachyear,startingaperiodoftime(fiveortenyears)aftertheinitialissue.Thesinkingfundprovisioncan take one of two forms.

A trustee collects a cash payment from the bond issuer and calls bonds for redemption at the sinking-fund call •price, usually based upon a lottery.Thebondissuercanbuybackbondsintheopenmarketanddeliverthespecifiednumberofbondstothetrustee•intheperiodsspecified.

If the bond issuer has the option to do the latter, bonds will be bought back and delivered if the market price is less than the call price and cash will be delivered to the trustee to make the call if the market price is greater than the call price. Sinking funds usually relate to a single issue, but they can sometimes cover multiple issues (funnel sinking fund). Most sinking funds also allow the bond issuer to accelerate call back, if it is in the issuer’s favour to do so (i.e., interest rates have gone down since the issue).

Asinkingfundhastwoeffects,oneofwhichbenefitstheissuerofthebondandtheotherwhichbenefitsthebuyerof the bond. The issuer of the bond gets a delivery option, because he has an option to either deliver the cash for the call price or to buy the bonds at the market price. The value of this call option (similar to the option in a callable bond) will increase with the volatility of interest rates and decrease with the level of interest rates. The buyer of the bond has less default risk because of the requirement that some of the debt be retired each period. The net effect will determine whether a sinking fund provision adds or detracts from the value of a bond. The empirical evidence on the sinking fund provision is mixed. While some of the earlier studies concluded that a sinking fund provision addedtobondvalue,HoandLee(1985)findthatitsnetvalueisinsignificantoverall,butthatitaddsmorevalueas default risk increases than it does as interest rate volatility increases.

Subordination of further debt and collateralExisting debt holders are negatively affected by the issue of new debt, especially if the new debt has superior claims on the assets of the issuer. Therefore, some bond issues have subordination clauses, which put restrictions on the issue of additional debt.

Additional debt might have to be subordinated to existing debt, i.e., in the event of bankruptcy, subordinated debt will be paid off after existing debt is fully paid. The presence of subordination clauses in a bond agreement should make it less risky and therefore more valuable.

Somebondsareissuedwithspecificcollateralissuedbehindthem,withaspecificassetofthefirmbackingupthepromised payments on the bond. If the collateral is property, the bond is called a mortgage bond, whereas, if it is securities,itisacollateraltrustbond.Otherbondsareissuedwithoutspecificcollateralandarecalledunsecuredbonds. Other things remaining equal, secured bonds should be viewed as less risky and more valuable than equivalent unsecured bonds.

The effect of bond covenantsMost bond issues are accompanied by a set of covenants that restrict the investment and dividend policies of the firm.Thesecovenantsaredesignedtoprotectbondholdersfromstockholders,whomighttrytoexpropriatewealthfrom them by:

investinginmuchriskierprojects,especiallyifthefirmishighlylevered,or•payingsignificantlyhigherdividendsthanexpected.•

Bond covenants should reduce the risk of expropriation on a bond and increase the value of the bond.


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SummaryThevalueofabondisthepresentvalueoftheexpectedcashflowsonthebond,discountedataninterestrate•that is appropriate to the riskiness of that bond.Bonds often have special features embedded in them that have to be factored into the value.•The value of a straight bond is determined by the level of and changes in interest rates.•Any increase in interest rates, either at the economy wide level or because of an increase in the default risk of •thecompanyissuingthebond,willlowerthepresentvalueofthestreamofexpectedcashflowsandhencethevalue of the bond.Holding coupon rates and default risk constant, increasing the maturity of a straight bond will increase its •sensitivity to interest rate changes.The bond price differential, • , is called the duration of the bond and measures the interest rate sensitivity of the bond.Largerandearliercashflowsareweightedmorethansmallerandlatercashflows.•Theshort-termdefaultfreeratecanbedecomposedintotwocomponents–anexpectedinflationrateduring•the period and an expected real rate of return.Expectedinflationisclearlythedominantvariabledetermininginterestrates.•Atruemeasureofinflationwouldconsiderchangesinthepricesofallgoodsandservicesusedinaneconomy,•weighted by their usage values.The other component of the Fisher equation is the expected real rate of return.•The spot rate on a multi-period bond is an average rate that applies over the periods.•The liquidity preference theory is not an alternative to the expectations theory.•The price of bonds, like any other security, is determined by demand and supply.•Inatypicalconvertiblebond,thebondholderisgiventheoptiontoconvertthebondintoaspecifiednumber•of shares of stock.Theissuerofacallablebondpreservestherighttocallbackthebondandpayafixedprice(generallyata•premium over the par value) for it.Many convertible bonds have embedded call features.•The effect of the prepayment option on value will vary with the type of mortgage backed security.•Most bond issues are accompanied by a set of covenants that restrict the investment and dividend policies of •thefirm.

ReferencesIntroduction to Bond Valuation. • [Pdf]Available at:<http://www.arts.uwaterloo.ca/~kvetzal/AFM271/bond.pdf>[Accessed11April2014].Bond Prices and Interest Rates. • [Pdf]Availableat:<http://www-personal.umich.edu/~alandear/courses/102/handouts/BondPrices.pdf>[Accessed11April2014].Johnson, R. S., 2010. • Bond Evaluation, Selection, and Management. John Wiley & Sons.Bond, E. J., 1983. • Reason and Value. CUP Archive.CFA Level I Valuation of Bonds Video Lecture by Mr. Arif Irfanullah Part 1. • [Videoonline]Availableat:<http://www.youtube.com/watch?v=AkivwPaJSb0>[Accessed11April2014].Financial Management: Lecture 6, Chapter 7: Part 1 - Interest Rates and Bond Valuation. • [Videoonline]Availableat:<http://www.youtube.com/watch?v=HE7ZqYSNVsU>[Accessed11April2014].

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Recommended ReadingFabozzi, F. J., 2009. • Institutional Investment Management: Equity and Bond Portfolio Strategies and Applications. John Wiley & Sons.Epstein, L., 2009. • The Complete Idiot’s Guide to Value Investing. Penguin.Richelson, H. and Richelson, S., 2011. • Bonds: The Unbeaten Path to Secure Investment Growth. John Wiley & Sons.


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Self AssessmentThevalueofabondisthe________valueoftheexpectedcashflowsonthebond,discountedataninterest1. rate that is appropriate to the riskiness of that bond.

pasta. presentb. futurec. lostd.

Whatisdeterminedbyboththegenerallevelofinterestrates,whichappliestoallbondsandfinancialinvestments,2. andthedefaultpremiumspecifictotheentityissuingthebond?

Thecashflowchargedonabonda. The premium charged on a bondb. The interest rate charged on a bondc. The price charged on a bondd.

The value of a _________ bond is determined by the level of and changes in interest rates.3. lowa. highb. presentc. straightd.

Match the following4. 1.Expectedinflation A. It is an identity that cannot be proved or disproved.

2. The Fisher equation B. This theory is not an alternative to the expectations theory.

3. The maturity premium C. It is clearly the dominant variable determining interest rates.

4. The liquidity preferenceD. It refers to the difference in interest rates between a short term (or

instantaneous) default-free bond and a longer-maturity default-free bond.

1-C, 2-A, 3-D, 4-Ba. 1-D, 2-B, 3-A, 4-Cb. 1-B, 2-D, 3-C, 4-Ac. 1-A, 2-C, 3-B, 4-Dd.

How many features set bonds apart from equity investments?5. Threea. Twob. Fivec. Fourd.

Which of the following statement is true?6. Bonds never have special features embedded in them that have to be factored into the value.a. Bonds seldom have special features embedded in them that have to be factored into the value.b. Bonds rarely have special features embedded in them that have to be factored into the value.c. Bonds often have special features embedded in them that have to be factored into the value.d.

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Which of the following present value of bond is true?7.

PV of Bond = a.

PV of Bond = b.

PV of Bond = c.

PV of Bond = d.

Which of the following will always be less than the maturity for a coupon bond and equal to the maturity for a 8. zero-coupon bond, with no special features?

The duration of a bonda. The interest rateb. The maturity of the bondc. The coupon rate of the bondd.

Which of the following statement is false?9. Expectationsaboutfutureinflationareakeydeterminantoflongertermrates.a. Thepriceofbonds,likeanyothersecurity,isdeterminedbyfutureinflation.b. Treasury, corporate bonds or state/local bonds can default on interest or principal paymentsc. Firms generally add conversions options to bonds to lower the interest rate paid on the bonds.d.

Which of the following bond is a bond that can be converted into a pre-determined number of shares, at the 10. option of the bondholder?

A expected bonda. A traditional bondb. A callable bondc. A convertible bondd.


52

Chapter IV

Risk and Return

Aim


introduce risk and return•

explain return•

explicate variance and covariance•

Objectives


explain the sample variance•

elucidate the population return and variance •

explicate portfolio variance•

Learning outcome


identify two assets•

understand the concept of return•

definediversification•

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4.1 IntroductionWhen investment analysis is considered, the basic observation is that the market rewards those prepared to bear risk. An investor purchasing an asset faces two potential sources of risk. The future price at which the asset can be sold may be unknown, as may the payments received from ownership of the asset. For a stock, both of these features are immediately apparent. The trading price of stocks changes almost continually on the exchanges. The payment from stocks comes in the form of a dividend. Although companies attempt to maintain some degree of constancy in dividends, they are only a discretionary payment rather than a commitment and their levels are subject to change.

These arguments may not seem to apply to bonds whose maturity value and payments seem certain. However, bondpricesdofluctuateso,althoughthematurityvalueisknown,thevalueatanytimebeforematurityisnot.Furthermore,thematurityvalueisgiveninnominaltermswhereastherealvalueisuncertainasinflationmustbetaken into account. The same argument also applies to the real value of the coupon payments. Finally, there is the risk of default or early redemption. Only the shortest term bonds issued by major governments can ever be regarded as having approximately certain payoffs.

In order to guide investment choice, an investor must be able to quantify both the reward for holding an asset and the risk inherent in that reward. They must also be aware of how the rewards and risks of individual assets interact when the assets are combined into a portfolio. This chapter shows how this is done.

4.2 ReturnThemeasureofrewardthatisusedininvestmentanalysisiscalledthereturn.Althoughwefocusonfinancialassets,thereturncanbecalculatedforanyinvestmentprovidedweknowitsinitialvalueanditsfinalvalue.

Thereturnisdefinedastheincreaseinvalueoveragiventimeperiodasaproportionoftheinitialvalue.Thetimeover which the return is computed is often called the holding period. Returns can be written in the raw form just definedor,equallywell,convertedtopercentages.Allthatmattersinthechoicebetweenthetwoisthatconsistencyisused throughout a set of calculations. If you start using percentages, they must be used everywhere. The calculations here will typically give both.

The formula for calculating the return can now be introduced. Letting be the initial value of the investment and thefinalvalueattheendoftheholdingperiod,thereturn,r,isdefinedby:

r = (4.1)

Toexpressthereturnasapercentagetheformulaismodifiedto:

r = × 100 (4.2)

4.2.1 Stock ReturnsThe process for the calculation of a return can also be applied to stocks. When doing this it is necessary to take care withthepaymentofdividends,sincethesemustbeincludedaspartofthereturn.Wefirstshowhowtocalculatethe return for a stock that does not pay a dividend and then extend the calculation to include dividends.

Consider a stock that pays no dividends for the holding period over which the return is to be calculated. Assume that this period is one year. In the formula for the return, we take the initial value, V0, to be the purchase price of thestockandthefinalvalue,V1, to be its trading price one year later. If the initial price of the stock is p (0) and the finalpricep(1)thenthereturnonthestockis:

r = (4.3)

The method for calculating the return can now be extended to include the payment of dividends. To understand the calculation it needs to be recalled that the return is capturing the rate of increase of an investor’s wealth. As


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dividend payments are an addition to wealth, they need to be included in the calculation of the return. In fact, the total increase in wealth from holding the stock is the sum of its price increase plus the dividend received. So, in the formulaforthereturn,thedividendisaddedtothefinalstockprice.Letddenotethedividendpaidbyastockoverthe holding period, this gives the formula for the return as follows:

r = (4.4)

Stocks in the US pay dividends four time per year and stock in the UK pay dividends twice per year. What there are multiple dividend payments during the holding period the value of d is the sum of these dividend payments.

4.2.2 Portfolio ReturnItwasnotedintheintroductionthatthedefinitionofareturncouldbeappliedtoanyformofinvestment.Sofarithas only been applied to individual assets. We now show how the method of calculation can be applied to a portfolio of assets. The purchase of a portfolio is an example of an investment and consequently a return can be calculated.

Thecalculationofthereturnonaportfoliocanbeaccomplishedintwoways.Firstly,theinitialandfinalvaluesoftheportfoliocanbedetermined,dividendsaddedtothefinalvalue,andthereturncomputed.Alternatively,theprices and payments of the individual assets, and the holding of those assets, can be used directly.

Focusingfirstonthetotalvalueoftheportfolio,iftheinitialvalueisV0,thefinalvalueV1, and dividends received are d, then the return is given by:

r = (4.5)

The return on a portfolio can also be calculated by using the prices of the assets in the portfolio and the quantity of each asset that is held. Assume that an investor has constructed a portfolio composed of N different assets. The quantity held of asset i is .Iftheinitialpriceofassetiispi(0)andthefinalprice (1), then the initial value of the portfolio is:

V0 = (4.6)

andthefinalvalue:V1 = (4.7)

If there are no dividends, then these can be used to calculate the return as:

r = (4.8)

The calculation of the return can also be extended to incorporate short selling of stock. Remember that short-selling refers to the act of selling an asset you do not own by borrowing the asset from another investor. In the notation used here, short-selling means you are indebted to the investor from whom the stock has been borrowed so that you effectively hold a negative quantity of the stock. For example, if you have gone short 200 shares of Ford stock, then the holding for Ford is given by 200. The return on a short sale can only be positive if the price of Ford stock falls. In addition, during the period of the short sale the short-seller is responsible for paying the dividend on the stock that they have borrowed. The dividends therefore count against the return since they are a payment made.

4.2.3 Portfolio ProportionsThecalculationsofportfolioreturnsofarhaveusedthequantityheldofeachassettodeterminetheinitialandfinalportfolio values. What proves more convenient in later calculations is to use the proportion of the portfolio invested in each asset rather than the total holding. The two give the same answer but using proportions helps emphasise that the returns (and the risks discussed later) depend on the mix of assets held, not on the size of the total portfolio.

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Thefirststepistodeterminetheproportionoftheportfolioineachasset.Ifthevalueoftheinvestmentinassetiatthe start of the holding period is thentheproportioninvestedinassetiisdefinedby:

(4.9)

where istheinitialvalueoftheportfolio.Bydefinition,theseproportionsmustsumto1.ForaportfoliowithNassets this can be seen from writing:

(4.10)

Furthermore, if an asset i is short-sold then its proportion is negative, so <0.Thisagainreflectsthefactthatshort-selling is treated as a negative shareholding. Once the proportions have been calculated it is possible to evaluate the return on the portfolio. Using the proportions, the return is the weighted average of the returns on the individual assets.

4.2.4 Mean ReturnOver time the return on a stock or a portfolio may vary. The prices of the individual stocks will rise and fall and thiswillcausethevalueoftheportfoliotofluctuate.Oncethereturnhasbeenobservedforanumberofperiods,it becomes possible to determine the average, or mean, return. For the moment, the mean return is taken just as an average of past returns. It will be discussed later how it can be interpreted as a predictor of what may be expected in the future.

Ifareturn,onanassetorportfolio,isobservedinperiods1,2,3,...,T,themeanreturnisdefinedas:

(4.11)

where is the return in period t.

4.3 Variance and CovarianceTheessentialfeatureofinvestingisthatthereturnsonthevastmajorityoffinancialassetsarenotguaranteed.Theprice of stocks can fall just as easily as they can rise, so a positive return in one holding period may become a negative in the next. For example, an investment in the shares of Yahoo! Inc. would have earned a return of 137% between October 2002 and September 2003. Three years later the return from October 2005 through to September 2006 was−31%.Thefollowingyearthestockhadareturnof2%.Changesofthismagnitudeinthereturnsindifferentholding periods are not outstanding.

It has already been stressed that the return on an asset or a portfolio and investor has to be equally concerned with the risk. What risk means in this context is the variability of the return across different holding periods. Two portfolios may have an identical mean return but can have very different amounts of risk. There are few (if any) investors who would knowingly choose to hold the riskier of the two portfolios.

A measure of risk must capture the variability. The standard measure of risk used in investment analysis is the variance of return (or, equivalently, its square root which is called the standard deviation). An asset with a return that never changes has no risk. For this asset, the variance of return is 0. Any asset with a return that does vary will have a variance of return that is positive. The more risk is the return on an asset the larger is the variance of return.

When constructing a portfolio it is not just the risk on individual assets that matters but also the way in which this risk combines across assets to identify the portfolio variance. Two assets may be individually risky, but if these risks cancel when the assets are combined then a portfolio composed of the two assets may have very little risk. The risks on the two assets will cancel if a higher than average return on one of the assets always accompanies a lower than average return on the other. The measure of the way returns are related across assets is called the covariance of return. The covariance will be seen to be central to understanding portfolio construction.


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Theportfoliovarianceandcovariancearenowdevelopedbyfirstintroducingthevarianceofreturnasameasureof the risk and then developing the concept of covariance between assets.

4.3.1 Sample VarianceThe data in Table 4.1 details the annual return on General Motors stock traded in New York over a 10 year period. Fig. 4.1 provides a plot of this data. The variability of the return, from a maximum of 36% to a minimum of - 41%, can be seen clearly.. The issue is how to provide a quantitative measure of this variability.

Year 93-94 94-95 95-96 96-97 97-98

Return % 36.0 -9.2 17.6 7.2 34.1

Year 98-99 99-00 00-01 01-02 02-03

Return % -1.2 25.3 -16.6 12.7 -40.9

Table 4.1 Return on general motors stock 1993-2003

The sample variance is a single number that summarises the extent of the variation in return.

40

30

20

10

0

-10

-20

-30

-40

-50

93-94

95-96

94-95

96-97

97-98

98-99

99-00

00-01

01-02

02-03

Fig. 4.1 Graph of return(Source: http://people.exeter.ac.uk/gdmyles/Teaching/AFT/finb1.pdf)

The process is to take the mean return as a measure of the “normal” outcome. The difference between the mean and each observed return is then computed - this is termed as the deviation from the mean. Some of these deviations from the mean are positive (in periods when the observed return is above the mean) and few are negative (when the observed return is below the mean). The deviations from the mean are then squared and these squares are summed. The average is then obtained by dividing by the number of observations.

WithTobservations,thesamplevariancejustdescribedisdefinedbytheformula:

(4.12)

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The sample standard deviation is the square root of the sample variance, so:

(4.13)

It should be noted that the sample variance and the sample standard deviation are always non-negative, so ≥0and ≥0.Onlyifeveryobservationofthereturnisidenticalisthesamplevariancezero.

There is one additional statistical complication with the calculation of the variance. We can view the sample variance as being an estimate of the population variance of the return (meaning the true underlying value). The formula given in (4.12) for the sample variance produces an estimate of the population variance which is too low for small samples, that is when we have a small number of observations. (Although, it does converge to the true value for large samples.) Becauseofthis,wesaythatitisabiasedestimator.Thereisanalternativedefinitionofthepopulationvariancewhichisunbiased.Thisisnowdescribed.Theunbiasedestimatorofthepopulationvarianceisdefinedby:

(4.14)

with the unbiased estimator of the population standard deviation being:

(4.15)

Comparing the two formulas (4.12) and (4.14) it is observed that the distinction between the two is simply whether theaveragevalueisfoundbydividingbyTorT−1.

Either of these formulae is perfectly acceptable for a calculation of the sample variance. All that matters is that the same formula is used consistently. However, from this point onwards we will use division by T. It should be observed that as the number of observations increases, so T becomes large, the difference between dividing by T andbyT−1becomeseverlessimportant.ForverylargevaluesofTthetwoformulasprovideapproximatelythesame answer.

4.3.2 Sample CovarianceEvery sports fan knows that a team can be much more (or less) than the sum of its parts. It is not just the ability of the individual players that matters but how they combine. The same is true for assets when they are combined into portfolios.

For the assets in a portfolio it is not just the variability of the return on each asset that matters but also the way returns vary across assets. A set of assets that are individually high performers need not combine well in a portfolio. Just like a sports team the performance of a portfolio is subtly related to the interaction of the component assets.

To see this point very clearly, consider the example in Table 4.2. The table shows the returns on two stocks for the holding periods 2006 and 2007. Over the two years of data the mean return on each stock is 6 and the sample variances of the returns are . Both stocks have a positive sample variance so are individually risky investments.

Stock Returns in 2006 Returns in 2007A 10 2B 2 10

Table 4.2 Stock, returns in 2006 and returns in 2007

The outcome with respect to risk changes considerably when these stocks are combined into a portfolio. Consider a portfolio that has proportion of stock A and of stock B. With these proportions the return on the portfolioin 2006 was:


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(4.16)

and in 2007 the return was:

(4.17)

This gives the sample mean return on the portfolio as:

(4.18)

This value is the same as for the individual stocks. The key point is the sample variance of the portfolio. Calculation of the sample variance gives:

(4.19)

so the portfolio has no risk. Assets that are individually risky can be combined into a portfolio in such a way that their variability cancels and the portfolio, has a constant return.

As we move between years an increase in return on one of the assets is met with an equal reduction in the return on the other. These changes exactly cancel when the assets are placed into a portfolio. It is not just the variability of asset returns that matters but how the returns on the assets move relative to each other. The general property of portfolio construction is to obtain a reduction in risk by careful combination of assets.

In the same way that the variance is used to measure the variability of return of an asset or portfolio, we can also provide a measure of the extent to which the returns on different assets move relative to each other. To do this we needtodefinethecovariancebetweenthereturnsontwoassets,whichisthecommonly-usedmeasureofwhetherthe returns move together or in opposite directions.

The covariance takes the deviations from the mean return for the two assets at time t, multiplies these together, sums over time and then averages. Hence, when both assets have returns above the mean, or both below the mean, a positive amount is contributed to the sum. Conversely, when one is below the mean and the other above, a negative amount is contributed to the sum. It is therefore possible for the covariance to be negative, zero or positive. A negative value implies the returns on the two assets tend to move in opposite directions (when one goes up, the other goes down) and a positive value that they tend to move in the same direction. A value of zero shows that, on average, there is no pattern of coordination in their returns.

To provide the formula for the covariance, let the return on asset A at time t be and the mean return on asset A be . Similarly, the return on asset B at time t and the mean return are and . The covariance of the return between these assets, denoted AB, is:

(4.20)

Bydefinition,foranyassetiitfollowsfromcomparisonofformula(4.12)forthevarianceand(4.20)forthecovariancethat , so the covariance of the return between an asset and itself is its variance. Also, in the formula for the covariance it does not matter in which order we take asset A and asset B. This implies that the covariance of A with B is the same as the covariance of B with A or .

4.4 Population Return and VarianceThe concept of sample mean return that we have developed so far looks back over historical data to form an average of observed returns. The same is true of the formulation of the sample variance and sample covariance. The sample values are helpful to some degree to summarise the past behaviour of returns but what is really needed for investment analysis are predictions about what may happen in the future. An investor needs this information to guide their current investment decisions. We now discuss the extent to which the sample returns and sample variances calculated on historical data can become predictions of future outcomes.

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A conceptual framework for analysing future returns can be constructed as follows: take an asset and determine the possible levels of return it may achieve, and the probability with which each level of return may occur. For instance, after studying its current business model we may feel that over the next year IBM stock can achieve a return of 2% with probability , of 4% with probability , and 6% with probability . The possible payoffs, and the associated probabilities, capture both the essence of randomness in the return and the best view we can form on what might happen. It will be shown in this section, how forming predictions in this way can be used to construct measures of risk and return.

Beforeproceedingtodothis,itisworthreflectingonthelinkbetweenthisapproachandthecalculationsofsamplemeansandsamplevariancesusinghistoricaldata.Atfirstsight,itwouldseemthatthetwoaredistinctlydifferentprocesses. However, there is a clear link between the two. This link follows from adopting the perspective that the pastdatareflecttheoutcomesofearlierrandomevents.Theobserveddatathenconstituterandomdrawsfromtheset of possible outcomes, with the rate of occurrence governed by a probability distribution.

Adopting the usual approach of statistical analysis, the historical data on observed returns are a sample from which we can obtain estimates of the true values. The mean return we have calculated from the sample of observed returns is a best estimate of the mean for the entire population of possible returns. The mean return for the population is often called the expected return. The name of “mean” is correctly used for the value calculated from the outcome of observation, while the name of “expected” is reserved for the statistical expectation. However, since the mean return is the best estimate of the expected return, the terms are commonly used interchangeably.

The same comments also apply to the sample variance and the sample covariance developed previously. They, too, are sample estimates of the population variance and covariance. This was the point behind the discussion of the population variance being a measure of the true variance. The issue of unbiasedness arose as a desirable property of the sample variance as an estimator of the population variance.

4.4.1 ExpectationsThefirststepindevelopingthisnewperspectiveistoconsidertheformationofexpectations.Althoughnotessentialfor using the formulae developed below, it is important for understanding their conceptual basis. Consider rolling a dice and observing the number that comes up. This is a simple random experiment that can yield any integer between 1 and 6 with probability . The entire set of possible outcomes and their associated probabilities is then:

(4.21)

The expected value from this experiment can be thought of as the mean of the outcome observed if the experiment was repeated very many times. Let x denote the number obtained by observing a roll of the dice. This is one observation of the random variable X. The expected value of the random variable is denoted E (X) and is given by the sum of possible outcomes, x, weighted by their probabilities. For the dice experiment the expected value is:

E[X]= (4.22)

Notice the interesting feature that the expected value of 3.5 is not an outcome which will ever be observed - only the integers 1 to 6 ever appear. But this does not prevent 3.5 being the expected value. Expressed in formal terms, assume we have a random event in which there are M possible outcomes. If outcome j is a value xj , and occurs with probability j, then the expected value of the random variable X is:

(4.23)

The idea of taking an expectation is not restricted to just the observed values of the random experiment. Return to the dice rolling example. For this experiment we may also be interested in the expected value of X2. This can be computed as:


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E[ ]= (4.24)

This expression is just the value of each possible outcome squared, multiplied by the probability and summed.

Observingthisuseoftheexpectation,wecanrecallthatthevarianceisdefinedastheaveragevalueofthesquareofthe deviation from the mean. This, too, is easily expressed as an expectation. For the dice experiment the expected value was 3.5 (which we can use as the value of the mean), so the expected value of the square of the deviation from the mean is:

E[ ]= (4.25)

This is the population variance of the observed value of the dice rolling experiment.

4.4.2 Expected ReturnThe expectation can now be employed to evaluate the expected return on an asset and a portfolio. This is achieved by introducing the idea of states of the world. A state of the world summarises all the information that is relevant forthefuturereturnofanasset,sothesetofstatesdescribesallthepossibledifferentfuturefinancialenvironmentsthat may arise. Of course, only one of these states will actually be realised but when looking forward we do not know which one. These states of the world are the analyst’s way of thinking about, and modeling, what generates the randomness in asset returns.

Let there be M states of the world. If the return on an asset in state j is rj , and the probability of state j occurring is, then the expected return on asset:

(4.26)

or, using the same notation as for the mean,

(4.27)

4.4.3 Population VarianceThe population variance mirrors the interpretation of the sample variance as being the average of the square of the deviation from the mean. Where the sample variance found the average by dividing by the number of observations (or one less than the number of observations), the population variance averages by weighting each squared deviation from the mean by the probability of its occurrence. In making this calculation, we follow the procedure introduced for the population mean of:

Identifyingthedifferentstatesoftheworld;•Determiningthereturnineachstate;•Setting the probability of each state being realised.•

Webeginwiththedefinitionof thepopulationvarianceofreturnforasingleasset.Thepopulationvarianceisexpressed in terms of expectations by:

(4.28)

InthisformulaE[r]isthepopulationmeanreturn.Thisisthemostgeneralexpressionforthevariancewhichwerefineintoaformforcalculationbymakingexplicithowtheexpectationiscalculated.

To permit calculation using this formula the number of states of the world, their returns and the probability distribution ofstates,mustbespecified.LettherebeMstates,anddenotethereturnontheassetinstatejbyrj.Iftheprobabilityof state j occurring is j , the population variance of the return on the asset can be written as:

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(4.29)

As it is a positively weighted sum of squares the population variance is always non-negative. It can be zero, but only if the return on the asset is the same in every state.The population standard deviation is given by the square root of the variance, so:

(4.30)

4.4.4 Population CovarianceThe sample covariance was introduced as a measure of the relative movement of the returns on two assets. It was positive if the returns on the assets tended to move in the same direction, and negative if they had a tendency to move in opposite directions. The population covariance extends this concept to the underlying model of randomness in asset returns.

For two assets A and B, the population covariance, ,isdefinedby:

(4.31)

Theexpressionofthecovarianceusingtheexpectationprovidesthemostgeneraldefinition.Thisformisusefulfortheoretical derivations but needs to be given a more concrete form for calculations.

Assume there are M possible states of the world with state j having probability j . Denote the return to asset A in state j by rAj and the return to asset B in state j by rBj. The population covariance between the returns on two assets A and B can be written as:

(4.32)

where and are the expected returns on the two assets.

The population covariance may be positive or negative. A negative covariance arises when the returns on the two assets tend to move in opposite directions, so that if asset A has a return above its mean ( > 0) then asset B has a return below its mean ( <0)andviceversa.Apositivecovariancearisesifthereturnsontheassetstend to move in the same direction, so both are either above the mean or both are below the mean.

4.5 Portfolio VarianceThe calculations of the variance of the return on an asset and of the covariance of returns between two assets are essential ingredients to the determination of the variance of a portfolio. It has already been shown how a portfolio may have a very different variance from that of the assets from which it is composed. Why this occurs is one of thecentrallessonsofinvestmentanalysis.Thefactthatitdoeshasverysignificantimplicationsforinvestmentanalysis.

The variance of the return on a portfolio can be expressed in the same way as the variance on an individual asset. If the return on the portfolio is denoted by rPandthemeanreturnbyṝp, the portfolio variance, , is:

(4.33)

The aim now is to present a version of this formula from which the variance can be calculated. Achieving this aim should also lead to an understanding of how the variance of the return on the portfolio is related to the variances of the returns on the individual assets and the covariances between the returns on the assets.

The analysis begins by studying the variance of a portfolio with just two assets. The result obtained is then extended to portfolios with any number of assets.


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4.5.1 Two AssetsConsider a portfolio composed of two assets, A and B, in proportions XA and XB.Usingthedefinitionofthepopulationvariance, the variance of the return on the portfolio is given by the expected value of the deviation of the return from the mean return squared.

The analysis of portfolio return has shown that and.Theseexpressionscanbesubstitutedintothedefinitionofthevarianceofthereturnonthe

portfolio to write: (4.34)

Collecting together the terms relating to asset A and the terms relating to asset B gives:

Squaring the term inside the expectation:

(4.35)

The expectation of a sum of terms is equal to the sum of the expectations of the individual terms. This allows that variance to be broken down into separate expectations:

(4.36)

The portfolio proportions can then be extracted from the expectations because they are constants. This gives:

(4.37)

ThefirstexpectationinthisexpressionisthevarianceofreturnonassetA,thesecondexpectationisthevarianceofreturn on asset B, and the third expectation is the covariance of the returns of A and B. Employing these observation allowsthevarianceofthereturnonaportfoliooftwoassets,AandB,tobewrittenbrieflyas:

(4.38)

The expression in (4.38) can be used to calculate the variance of the return on the portfolio given the shares of the two assets in the portfolio, the variance of returns of the two assets, and the covariance. The result has been derived for the population variance (so, the values entering would be population values) but can be used equally well to calculate the sample variance of the return on the portfolio using sample variances and sample covariance.

4.5.2 Correlation CoefficientThe variance of the return on a portfolio can be expressed in an alternative way. The covariance has already been described as an indicator of the tendency of the returns on two assets to move in the same direction (either up or down) or in opposite directions. Although the sign of the covariance (whether it is positive or negative) indicates this tendency, the value of the covariance does not in itself reveal how strong the relationship is. For instance, a given value of covariance could be generated by two assets that each experience large deviations from the mean, but only have a weak relationship between their movements or by two assets whose returns are very closely related, but individually do not vary much from their means.

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In order to determine the strength of the relationship, it is necessary to measure the covariance relative to the deviationfromthemeanexperiencedbytheindividualassets.Thisisachievedbyusingthecorrelationcoefficientwhichrelatesthestandarddeviationsandcovariance.ThecorrelationcoefficientbetweenthereturnonassetAandthereturnonassetBisdefinedby:

(4.39)

Thevalueofthecorrelationcoefficientsatisfies−1≤ ≤1.A value of indicates perfect positive correlation: the returns on the two assets always move in unison. Interpreted in terms of returns in different states of the world, perfect positive correlation says that if the return on one asset is higher in state j than it is in state k, then so is the return on the other asset. Conversely, indicates perfect negative correlation: the returns on the two assets always move in opposing directions, so if the return on one asset is higher in state j than it is in state k, then the return on the other asset is lower in state j than in state k.

Usingthecorrelationcoefficient,thevarianceofthereturnofaportfoliocanbewrittenas:

(4.40)

It can be seen from this formula that a negative correlation coefficient reduces the overall variance of theportfolio.

4.5.3 General FormulaThe formula to calculate the variance of the return on a portfolio can now be extended to accommodate any number of assets. This extension is accomplished by noting that the formula for the variance of the return on a portfolio involves the variance of each asset plus its covariance with every other asset. For N assets in proportions Xi, i = 1, ...,N, the variance is thus given by:

(4.41)

ItshouldbeconfirmedthatwhenN=2thisreducesto(4.38).Thepresentationoftheformulacanbesimplifiedbyusing the fact that ii is identical to 2i to write

(4.42)

Thisformulacanalsobeexpressedintermsofthecorrelationcoefficients.

Thesignificanceofthisformulais thatitprovidesameasureoftheriskofanyportfolio,nomatterhowmanyassets are included. Conceptually, it can be applied even to very large (meaning thousands of assets) portfolios. All the information that is necessary to do this is the proportionate holdings of the assets and the variance-covariance matrix.

4.5.4 Effect of DiversificationAs an application of the formula for the variance of the return of a portfolio this section considers the effect of diversification.Diversificationmeanspurchasingalargernumberofdifferentassets.Itisnaturaltoviewdiversificationasameansofreducingriskbecauseinalargeportfoliotherandomfluctuationsofindividualassetswillhaveatendencytocancelout.Toformalisetheeffectofdiversification,considerholdingNassetsinequalproportions.This implies that the portfolio proportions satisfy Xi = for all assets i = 1, ...,N. From (4.41), the variance of this portfolio is:


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(4.43)

ObservethatthereareNtermsinthefirstsummationandN[N−1]inthesecond.Thissuggestsextractingatermfrom each summation to write the variance as 2P =

(4.44)

NowdefinethemeanofthevariancesoftheNassetsintheportfolioby:

(4.45)

and the mean covariance between all pairs of assets in the portfolio by:

(4.46)

Usingthesedefinitions,thevarianceofthereturnontheportfoliobecomes:

(4.47)

This formula applies whatever the number of assets (but the mean variance and mean covariance change in value as Nchanges).DiversificationmeanspurchasingabroaderrangeofassetswhichinthepresentcontextisreflectedinanincreaseinN.Theextremeofdiversificationoccursasthenumberofassetsintheportfolioisincreasedwithoutlimit.Formally,thiscanbemodelledbylettingN→∞anddeterminingtheeffectonthevarianceofthereturnonthe portfolio.

Itcanbeseenfrom(4.47)thatasN→∞thefirsttermwillconvergetozero(wearedividingthemeanvaluebyanever increasing value of N) and the second term will converge to (because as N increases tends to 1).Therefore,atthelimitofdiversification:

(4.48)

Thisresultshowsthatinawell-diversifiedportfolioonlythecovariancebetweenassetscountsforportfoliovariance.Inotherwords,thevarianceoftheindividualassetscanbeeliminatedbydiversification-whichconfirmstheinitialperspectiveontheconsequenceofdiversification.

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SummaryWhen investment analysis is considered the basic observation is that the market rewards those prepared to bear •risk.The future price at which the asset can be sold may be unknown, as may the payments received from ownership •of the asset.The measure of reward that is used in investment analysis is called the return.•Thereturnisdefinedastheincreaseinvalueoveragiventimeperiodasaproportionoftheinitialvalue.•The process for the calculation of a return can also be applied to stocks.•The calculations of portfolio return so far have used the quantity held of each asset to determine the initial and •finalportfoliovalues.Over time the return on a stock or a portfolio may vary.•A measure of risk must capture the variability.•An asset with a return that never changes has no risk.•A set of assets that are individually high performers need not combine well in a portfolio.•The concept of sample mean return that we have developed so far looks back over historical data to form an •average of observed returns.Thefirststepindevelopingthisnewperspectiveistoconsidertheformationofexpectations.•The expectation can now be employed to evaluate the expected return on an asset and a portfolio.•The population variance mirrors the interpretation of the sample variance as being the average of the square of •the deviation from the mean.As an application of the formula for the variance of the return of a portfolio this section considers the effect of •diversification.Diversificationmeanspurchasing a broader rangeof assetswhich in thepresent context is reflected in an•increase in N.

ReferencesRisk and Return. • [Pdf]Availableat:<http://www2.gsu.edu/~fnccwh/pdf/f03.pdf>[Accessed11April2014].Risk and Return. • [Pdf]Available at: <http://highered.mcgraw-hill.com/sites/dl/free/0070997594/918724/Peirson11e_Ch07.pdf>[Accessed11April2014].Tuller, L. W., 1994. • High-Risk, High-Return Investing. John Wiley & Sons.Hampton, J. J., 2011. • The AMA Handbook of Financial Risk Management. AMACOM Div American Mgmt Assn.Risk and Return Part 1.mp4. • [Videoonline]Availableat:<http://www.youtube.com/watch?v=lZceJi9XTnQ>[Accessed11April2014].Finance Lecture - Risk, Return and CAPM. • [Video online]Available at: <http://www.youtube.com/watch?v=3BIIiUyr3-w>[Accessed11April2014].

Recommended ReadingDamodaran, A., 2008. • Strategic Risk Taking: A Framework for Risk Management. Pearson Prentice Hall.Connor, G., Goldberg, L. R. and Korajczyk, R. A. 2010. • Portfolio Risk Analysis. P r i n c e t o n U n i v e r s i t y P r e s s .Denne, M. and Cleland-Huang, J. 2004. • Software by Numbers: Low-Risk, High-Return Development. Prentice Hall Professional.


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Self AssessmentAn investor purchasing an asset faces ________ potential sources of risk.1.

foura. fiveb. twoc. threed.

The payment from stocks comes in the form of a _________.2. riska. stockb. dividendc. returnd.

What is the measure of reward that is used in investment analysis called?3. Riska. Stockb. Dividendc. Returnd.


1. The return A. The measure of the way returns are related across assets.

2. The covariance of return B. It means purchasing a larger number of different assets.

3. The expected return C.Itisdefinedastheincreaseinvalueoveragiventimeperiod as a proportion of the initial value.

4.Diversification D. The mean return for the population.

1-C, 2-A, 3-D, 4-Ba. 1-B, 2-D, 3-A, 4-Cb. 1-A, 2-B, 3-C, 4-Dc. 1-D, 2-C, 3-B, 4-Ad.

Which of the following statement is true?5. The process for the calculation of a return can also be applied to risk.a. The process for the calculation of a return can also be applied to stocks.b. The process for the calculation of a return can also be applied to dividend.c. The process for the calculation of a return can also be applied to interest.d.

Which of the following may have an identical mean return but can have very different amounts of risk?6. Two portfoliosa. Two dividendb. Stockc. Returnd.

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The _________ takes the deviations from the mean return for the two assets at time t, multiplies these together, 7. sums over time and then averages.

riska. stockb. portfoliosc. covarianced.

Whatmeanspurchasingabroaderrangeofassetswhichinthepresentcontextisreflectedinanincreasein8. N?

Portfolioa. Diversificationb. The sample covariancec. The population varianced.

The formula to calculate the variance of the return on a portfolio can now be extended to accommodate any 9. number of________.

returnsa. varianceb. stocksc. assetsd.

Which of the following statement is false?10. Over time the return on a stock or a portfolio may vary.a. A measure of risk must capture the variability.b. An asset with a return that always changes has no risk.c. The more risk is the return on an asset the larger is the variance of return.d.


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Chapter V

Cost of Capital

Aim


introduce the concept of cost of capital•

explain assumption of cost of capital•

explicateclassificationofcostofcapital•

Objectives


explain cost of equity•

elucidate importance of cost of capital•

explicate dividend price plus growth approach•

Learning outcome


identify cost of debt and debt issued at par•

understand cost of retained earnings•

definecostofcapital•

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5.1 IntroductionCost of capital is an essential part of investment decision, as it is used to measure the worth of investment proposal providedbythebusinessfirm.Itisusedasadiscountrateindeterminingthepresentvalueoffuturecashflowsassociated with capital projects. Cost of capital is also called as cut-off rate, target rate, hurdle rate and required rateofreturn.Whenthefirmsareusingdifferentsourcesoffinance,thefinancemanagermusttakecarefuldecisionwithregardtothecostofcapital;becauseitiscloselyassociatedwiththevalueofthefirmandtheearningcapacityofthefirm.

5.2 Meaning of Cost of CapitalCostofcapitalistherateofreturnthatafirmmustearnonitsprojectinvestmentstomaintainitsmarketvalueand attract funds. Cost of capital is the required rate of return on its investments which belongs to equity, debt and retainedearnings.Ifafirmfailstoearnreturnattheexpectedrate,themarketvalueoftheshareswillfallanditwill result in the reduction of overall wealth of the shareholders.

5.2.1 DefinitionsThe following importantdefinitionsarecommonlyused tounderstand themeaningandconceptof thecostofcapital.

AccordingtothedefinitionofJohnJ.Hampton“Costofcapitalistherateofreturnthefirmrequiredfrominvestmentinordertoincreasethevalueofthefirminthemarketplace.”

AccordingtothedefinitionofSolomonEzra,“Costofcapitalistheminimumrequiredrateofearningsorthecut-off rate of capital expenditure.”

AccordingtothedefinitionofJamesC.VanHorne,Costofcapitalis“Acut-offratefortheallocationofcapitalto investment of projects. It is the rate of return on a project that will leave unchanged the market price of the stock.”

AccordingtothedefinitionofWilliamandDonaldson,“Costofcapitalmaybedefinedastheratethatmustbeearned on the net proceeds to provide the cost elements of the burden at the time they are due.”

5.3 Assumption of Cost of CapitalCost of capital is based on certain assumptions which are closely associated while calculating and measuring the cost of capital. It is to be considered that there are three basic concepts:

It is not a cost as such. It is merely a hurdle rate.•It is the minimum rate of return.•Itconsistsofthreeimportantriskssuchaszerorisklevel,businessriskandfinancialrisk.•

Cost of capital can be measured with the help of the following equation.

Where, K = Cost of capital

=Risklesscostoftheparticulartypeoffinance b = Business risk premium f = Financial risk premium


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5.4 Classification of Cost of CapitalCostofcapitalmaybeclassifiedintothefollowingtypesonthebasisofnatureandusage:

Cost of Capital

Explicit and Implicit Cost

Average and Marginal Cost

Historical and Future Cost

Specificand Combined Cost

Fig. 5.1 Classification of cost of capital

5.4.1 Explicit and Implicit CostThe cost of capital may be explicit or implicit cost on the basis of the computation of cost of capital.

Explicitcostistheratethatthefirmpaystoprocurefinancing.Thismaybecalculatedwiththehelpofthefollowingequation:

Where,

=initialcashinflow C=outflowintheperiodconcerned N = duration for which the funds are provided T = tax rate

Implicitcostistherateofreturnassociatedwiththebestinvestmentopportunityforthefirmanditsshareholdersthatwillbeforgoneiftheprojectspresentlyunderconsiderationbythefirmwereaccepted.

5.4.2 Average and Marginal CostAverage cost of capital is the weighted average cost of each component of capital employed by the company. It considersweightedaveragecostofallkindsoffinancingsuchasequity,debt,retainedearnings,etc.

Marginalcostistheweightedaveragecostofnewfinanceraisedbythecompany.Itistheadditionalcostofcapitalwhenthecompanygoesforfurtherrisingoffinance.

5.4.3 Historical and Future CostHistoricalcostisthecostwhichhasalreadybeenincurredforfinancingaparticularproject.Itisbasedontheactualcost incurred in the previous project.

Futurecostistheexpectedcostoffinancingintheproposedproject.Expectedcostiscalculatedonthebasisofprevious experience.

5.4.4 Specific and Combine CostThecostofeachsourcesofcapitalsuchasequity,debt,retainedearningsandloansiscalledasspecificcostofcapital.Itisveryusefultodeterminetheeachandeveryspecificsourceofcapital.

The composite or combined cost of capital is the combination of all sources of capital. It is also called as overall costofcapital.Itisusedtounderstandthetotalcostassociatedwiththetotalfinanceofthefirm.

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5.5 Importance of Cost of CapitalComputationofcostofcapitalisaveryimportantpartofthefinancialmanagementtodecidethecapitalstructureof the business concern.

Importance to capital budgeting decisionCapital budget decision largely depends on the cost of capital of each source. According to net present value method, presentvalueofcashinflowmustbemorethanthepresentvalueofcashoutflow.Hence,costofcapitalisusedtocapital budgeting decision.

Importance to structure decisionCapitalstructureisthemixorproportionofthedifferentkindsoflongtermsecurities.Afirmusesparticulartypeof sources if the cost of capital is suitable. Hence, cost of capital helps to take decision regarding structure.

Importance to evolution of financial performanceCost of capital is one of the important factors which affects the capital budgeting, capital structure and value of the firm.Hence,ithelpstoevaluatethefinancialperformanceofthefirm.

Importance to other financial decisionsApart from the above points, cost of capital is also used in some other areas such as, market value of share, earning capacityofsecurities,etc.Hence,itplaysamajorpartinthefinancialmanagement.

5.6 Computation of Cost of CapitalComputation of cost of capital consists of two important parts:

Measurementofspecificcosts•Measurement of overall cost of capital•

Measurement of cost of capitalItreferstothecostofeachspecificsourcesoffinancelike:

Cost of equity•Cost of debt•Cost of preference share•Cost of retained earnings•

5.6.1 Cost of EquityCostofequitycapitalistherateatwhichinvestorsdiscounttheexpecteddividendsofthefirmtodetermineitsshare value.

Conceptually the cost of equity capital (Ke)definedasthe“Minimumrateofreturnthatafirmmustearnontheequityfinancedportionofaninvestmentprojectinordertoleaveunchangedthemarketpriceoftheshares.”

Cost of equity can be calculated from the following approach:Dividend price (D/P) approach•Dividend price plus growth (D/P + g) approach•Earning price (E/P) approach•Realised yield approach•


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5.6.2 Dividend Price ApproachThe cost of equity capital will be that rate of expected dividend which will maintain the present market price of equity shares.Dividend price approach can be measured with the help of the following formula:

Where,

= Cost of equity capital D = Dividend per equity share

= Net proceeds of an equity share

Example 1: A company issues 10,000 equity shares of Rs. 100 each at a premium of 10%. The company has been paying25%dividendtoequityshareholdersforthepastfiveyearsandexpectstomaintainthesameinthefuturealso.Compute the cost of equity capital. Will it make any difference if the market price of equity share is Rs. 175?

Solution

= 22.72%

If the market price of a equity share is Rs. 175.

= 14.28%

5.6.3 Dividend Price plus Growth ApproachThe cost of equity is calculated on the basis of the expected dividend rate per share plus growth in dividend. It can be measured with the help of the following formula:

Where,

= Cost of equity capital D = Dividend per equity share g = Growth in expected dividend


Example 2: Acompanyplanstoissue10000newsharesofRs.100eachatapar.Thefloatationcostsareexpectedtobe•4% of the share price. The company pays a dividend of Rs. 12 per share initially and growth in dividends is expected to be 5%. Compute the cost of new issue of equity shares.If the current market price of an equity share is Rs. 120. Calculate the cost of existing equity share capital•

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Solution

5.6.4 Earning Price ApproachCost of equity determines the market price of the shares. It is based on the future earning prospects of the equity. The formula for calculating the cost of equity according to this approach is as follows.

Where,

= Cost of equity capital E = Earnings per share


Example 3: AfirmisconsideringanexpenditureofRs.75lakhsforexpandingitsoperations.The relevant information is as follows:Number of existing equity shares =10 lakhsMarket value of existing share =Rs.100Net earnings =Rs.100 lakhs

Compute the cost of existing equity share capital and of new equity capital assuming that new shares will be issued at a price of Rs. 92 per share and the costs of new issue will be Rs. 2 per share.

SolutionCost of existing equity share capital:

Earnings Per Share (EPS) = = Rs. 10

= 10%Cost of Equity Capital

= 11.11%


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5.6.5 Realised Yield ApproachIt is the easy method for calculating cost of equity capital. Under this method, cost of equity is calculated on the basis of return actually realised by the investor in a company on their equity capital.

Where,

= Cost of equity capital. PVƒ = Present value of discount factor. D = Dividend per share.

5.6.6 Cost of DebtCost of debt is the after tax cost of long-term funds through borrowing. Debt may be issued at par, at premium or at discount and also it may be perpetual or redeemable.

5.6.7 Debt Issued at ParDebt issued at par means, debt is issued at the face value of the debt. It may be calculated with the help of the following formula.

Where,

= Cost of debt capital t = Tax rate R = Debenture interest rate

5.6.8 Debt Issued at Premium or DiscountIf the debt is issued at premium or discount, the cost of debt is calculated with the help of the following formula.

Where, = Cost of debt capital

I = Annual interest payable = Net proceeds of debenture

t = Tax rate

Example 4: A Ltd. issues Rs. 10, 00,000, 8% debentures at par. The tax rate applicable to the company is 50%. Compute the cost of debt capital.

Solution

= 4%

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5.6.9 Cost of Perpetual Debt and Redeemable DebtIt is the rate of return which the lenders expect. The debt carries a certain rate of interest.

Where, I = Annual interest payable P = Par value of debt

= Net proceeds of the debenture n = Number of years to maturity

= Cost of debt before tax

Cost of debt after tax can be calculated with the help of the following formula:

Where,

= Cost of debt after tax

= Cost of debt before tax t = Tax rate

Example 5: A company issues Rs. 20, 00,000, 10% redeemable debentures at a discount of 5%.ThecostsoffloatationamounttoRs.50,000.Thedebenturesareredeemableafter8years.Calculatebeforetaxandafter tax. Cost of debt assuring a tax rate of 55%.

Solution

Note = 20, 00,000 – 10, 00,000 – 50,000

= 11.36%.After Tax Cost of Debt

=11.36 (1–0.55) =5.11%.

5.6.10 Cost of Preference Share CapitalCost of preference share capital is the annual preference share dividend by the net proceeds from the sale of preference share.

There are two types of preference shares, irredeemable and redeemable. Cost of redeemable preference share capital is calculated with the help of the following formula:


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Where,

= Cost of preference share

= Fixed preference dividend


Cost of irredeemable preference share is calculated with the help of the following formula:

Where,


= Fixed preference share P = Par value of debt

= Net proceeds of the preference share n = Number of maturity period.

Example 6: ABC Ltd. issues 20,000, 8% preference shares of Rs. 100 each at a premium of 5% redeemable after 8 years at par. The cost of issue is Rs. 2 per share. Calculate the cost of preference share capital.

Solution

= 7.51%

Where

= 20,000×100×8%=1, 60,000 P = 20, 00,000 n = 8 years

= 20, 00,000 + 10, 00,000 – 40,000 =20, 60,000

5.6.11 Cost of Retained Earnings‘Retainedearnings’isoneofthesourcesoffinanceforinvestmentproposal;itisdifferentfromothersourceslikedebt, equity and preference shares. Cost of retained earnings is the same as the cost of an equivalent fully subscripted issue of additional shares, which is measured by the cost of equity capital. Cost of retained earnings can be calculated with the help of the following formula:

Where,

=Cost of retained earnings

=Cost of equity

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t=Tax rate b=Brokerage cost

Example 7: Afirm’sKe(returnavailabletoshareholders)is10%,theaveragetaxrateofshareholdersis30%and it is expected that 2% is brokerage cost that shareholders will have to pay while investing their dividends in alternative securities. What is the cost of retained earnings?

SolutionCost of Retained Earnings, Where,

= = rate of return available to shareholders t = tax rate b = brokerage cost So, = 10% (1–0.5) (1–0.02) = 10%×0.5×0.98 = 4.9%

5.6.12 Measurement of Overall Cost of CapitalIt is also called as weighted average cost of capital and composite cost of capital. Weighted average cost of capital istheexpectedaveragefuturecostoffundsoverthelongrunfoundbyweightingthecostofeachspecifictypeofcapitalbyitsproportioninthefirm’scapitalstructure.

The computation of the overall cost of capital (Ko) involves the following steps:Assigningweightstospecificcosts.•Multiplying the cost of each of the sources by the appropriate weights.•Dividing the total weighted cost by the total weights.•

The overall cost of capital can be calculated with the help of the following formula:

Where,

= Overall cost of capital

= Cost of debt


= Cost of equity = Cost of retained earnings

= Percentage of debt of total capital = Percentage of preference share to total capital = Percentage of equity to total capital = Percentage of retained earnings

Weighted average cost of capital is calculated in the following formula also:

Where,

= Weighted average cost of capital X=Costofspecificsourcesoffinance W=Weight,proportionofspecificsourcesoffinance


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Example 8: ABC Ltd. has the following capital structure. Rs.Equity (expected dividend 12%) 10, 00,00010% preference 5, 00,0008% loan 15, 00,000

You are required to calculate the weighted average cost of capital, assuming 50% as the rate of income-tax, before and after tax.

SolutionSolution showing weighted average cost of capital:

Particulars Rs. After Weights Cost

EquityPreference8% Loan

10,00,0005,00,00015,00,000

12%10%4%

33.33%16.6750.00

3.991.672.007.66%

Weight average cost of capital = 7.66%

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SummaryCost of capital is an integral part of investment decision, as it is used to measure the worth of investment proposal •provided by the business concern.Cost of capital is also called as cut-off rate, target rate, hurdle rate and required rate of return.•Costofcapitalistherateofreturnthatafirmmustearnonitsprojectinvestmentstomaintainitsmarketvalue•and attract funds.Cost of capital is based on certain assumptions which are closely associated while calculating and measuring •the cost of capital.Explicitcostistheratethatthefirmpaystoprocurefinancing.•Implicitcostistherateofreturnassociatedwiththebestinvestmentopportunityforthefirmanditsshareholders•thatwillbeforgoneiftheprojectspresentlyunderconsiderationbythefirmwereaccepted.Average cost of capital is the weighted average cost of each component of capital employed by the company.•The composite or combined cost of capital is the combination of all sources of capital.•Capital budget decision largely depends on the cost of capital of each source.•Costofequitycapitalistherateatwhichinvestorsdiscounttheexpecteddividendsofthefirmtodetermine•its share value.Debt may be issued at par, at premium or at discount and also it may be perpetual or redeemable.•Cost of preference share capital is the annual preference share dividend by the net proceeds from the sale of •preference share.‘Retainedearnings’isoneofthesourcesoffinanceforinvestmentproposal;itisdifferentfromothersources•like debt, equity and preference shares.

ReferencesThe Cost of Capital. • [Pdf]Availableat:<http://www.goldsmithibs.com/resources/free/Cost-of-Capital/notes/Summary%20-%20Cost%20of%20Capital.pdf>[Accessed11April2014].The Cost of Capital. • [Pdf]Availableat:<http://www.prenhall.com/divisions/bp/app/Berk/docs/Chapter12.pdf>[Accessed11April2014].Patterson, C. S., 1995. • The Cost of Capital: Theory and Estimation. Greenwood Publishing Group.Pratt, S. P. and Grabowski, R. J., 2014. • Cost of Capital: Applications and Examples. John Wiley & Sons.CFA Level I Cost of Capital Video Lecture by Mr. Arif Irfanullah part 1. • [Videoonline]Availableat:<https://www.youtube.com/watch?v=kwkYfo7p9XI>[Accessed11April2014].Cost of Capital - Lecture 1. • [Videoonline]Availableat:<https://www.youtube.com/watch?v=cAB90p5RrW4>[Accessed11April2014].

Recommended ReadingOgier, T., 2013. • The Real Cost of Capital ePub. Pearson, UK.Jorgenson, D. W. and Lau, L. J., 2000. • Econometrics. M I T P r e s s .Armitage, J., 2005. • The Cost of Capital: Intermediate Theory. Cambridge University Press.


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Self AssessmentCost of capital is an integral part of investment decision, as it is used to measure the worth of _________ proposal 1. provided by the business concern.

riska. investmentb. bondc. capitald.

What is also called as cut-off rate, target rate, hurdle rate and required rate of return?2. Investmenta. Risk premiumb. Cost of capitalc. Minimum required rated.

Costofcapitalisthe_________ofreturnthatafirmmustearnonitsprojectinvestmentstomaintainitsmarket3. value and attract funds.

ratea. investmentb. pricec. valued.


1. Explicit cost A.Itisthecostwhichhasalreadybeenincurredforfinancingaparticular project.

2. Average cost of capital B.Itistheratethatthefirmpaystoprocurefinancing.

3. Historical cost C. The cost of each sources of capital such as equity, debt, retained earnings and loans.

4.Specificcostofcapital D. It is the weighted average cost of each component of capital em-ployed by the company.

1- D, 2- B, 3- C, 4- Aa. 1- A, 2- C, 3- B, 4- Db. 1- C, 2- A, 3- D, 4- Bc. 1- B, 2- D, 3- A, 4- Cd.

Whichofthefollowingistherateofreturnassociatedwiththebestinvestmentopportunityforthefirmandits5. shareholdersthatwillbeforgoneiftheprojectspresentlyunderconsiderationbythefirmwereaccepted?

Explicit costa. Historical cost b. Implicit costc. Specificcostd.

Whichofthefollowingistheweightedaveragecostofnewfinanceraisedbythecompany?6. Marginal costa. Historical cost b. Implicit costc. Specificcostd.

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What is also called as overall cost of capital?7. Historical costa. The composite or combined costb. Average cost of capitalc. Explicit costd.

Which of the following statement is true?8. Capital budget decision does not depend on the cost of capital of no source.a. Cost cutting decision mostly depends on the cost of capital of each source.b. Capital budget decision does not depend on the cost of capital of each source.c. Capital budget decision largely depends on the cost of capital of each source.d.

Costof______capitalistherateatwhichinvestorsdiscounttheexpecteddividendsofthefirmtodetermine9. its share value.

equitya. debtb. preferencec. retainedd.

Which of the following statement is false?10. Cost of debt is the after tax cost of long-term funds through borrowing.a. Debt issued at par means, debt is issued at the face value of the debt.b. There are two types of preference shares variable and consistency.c. The overall cost of capital is also called as weighted average cost of capital and composite cost of capital.d.


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Chapter VI

Capital Budgeting

Aim


introduce capital budgeting•

explain the need and importance of capital budgeting•

explicate capital budgeting process•

Objectives


enlist methods of capital budgeting of evaluation •

elucidate risk and uncertainty in capital budgeting•

explain kinds of capital budgeting decisions•

Learning outcome


identify the methods of evaluations•

understandunevencashinflows•

definecapitalbudgeting•

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6.1 IntroductionThewordcapitalreferstobethetotalinvestmentofacompanyoffirminmoney,tangibleandintangibleassets.Whereasbudgetingdefinedbythe“RowlandandWilliam”itmaybesaidtobetheartofbuildingbudgets.Budgetsare a blue print of a plan and action expressed in quantities and manners.

The examples of capital expenditure:Purchaseoffixedassetssuchaslandandbuilding,plantandmachinery,goodwill,etc.•Theexpenditurerelatingtoaddition,expansion,improvementandalterationtothefixedassets.•Thereplacementoffixedassets.•Research and development project.•

6.2 DefinitionsAccordingtothedefinitionofCharlesT.Hrongreen,“capitalbudgetingisalong-termplanningformakingandfinancingproposedcapitaloutlays."

AccordingtothedefinitionbyG.C.Philippatos,“capitalbudgetingisconcernedwiththeallocationofthefirmssourcefinancialresourcesamongtheavailableopportunities.Theconsiderationofinvestmentopportunitiesinvolvesthe comparison of the expected future streams of earnings from a project with the immediate and subsequent streams of earning from a project, with the immediate and subsequent streams of expenditure.”

According to the definition byRichard andGreen law, “capital budgeting is acquiring inputswith long-termreturn.”

AccordingtothedefinitionofLyrich,“capitalbudgetingconsistsinplanningdevelopmentofavailablecapitalforthepurposeofmaximisingthelong-termprofitabilityoftheconcern.”

It isclearlyexplainedintheabovedefinitionsthatafirm’sscarcefinancialresourcesareutilisingtheavailableopportunities.Theoverallobjectiveofanycompanyistomaximisetheprofitsandminimisetheexpenditureofcost.

6.3 Need and Importance of Capital BudgetingNeed and importance of capital budgeting is as follows:

Huge investmentsCapitalbudgetingrequireshugeinvestmentsoffunds,buttheavailablefundsarelimited,thereforethefirmbeforeinvesting projects, plan are control its capital expenditure.

Long-termCapitalexpenditureislong-terminnatureorpermanentinnature.Therefore,financialrisksinvolvedintheinvestmentdecision are more. If higher risks are involved, it needs careful planning of capital budgeting.

IrreversibleThe capital investment decisions are irreversible, are not changed back. Once the decision is taken for purchasing apermanentasset,itisverydifficulttodisposeofthoseassetswithoutinvolvinghugelosses.

Long-term effectCapitalbudgetingnotonlyreducesthecostbutalsoincreasestherevenueinlong-termandwillbringsignificantchangesintheprofitofthecompanybyavoidingoverormoreinvestmentorunderinvestment.Overinvestmentsleadstobeunabletoutiliseassetsoroverutilisationoffixedassets.Therefore,beforemakingtheinvestment,itisrequired carefully planning and analysis of the project thoroughly.


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6.4 Capital Budgeting ProcessCapitalbudgetingisadifficultprocesstotheinvestmentofavailablefunds.Thebenefitwillattainonlyinthenearfuture but, the future is uncertain. However, the following steps followed for capital budgeting, then the process may be easier are:

Identification of Various Investments

Evaluation of Proposals

Fixing Property

Final Approval

Implementation

Identification of VariousInvestment Proposals

Feedback

Step

s

Screening or Matching the Available Resources

Fig. 6.1 Capital budgeting process(Source: http://vcmdrp.tums.ac.ir/files/financial/istgahe_mali/moton_english/financial_management_[www.

accfile.com].pdf)

Identificationofvariousinvestmentsproposals:Thecapitalbudgetingmayhavevariousinvestmentproposals.•Theproposalfortheinvestmentopportunitiesmaybedefinedfromthetopmanagementormaybeevenfromthe lower rank. The heads of various departments analyse the various investment decisions, and will select proposals submitted to the planning committee of competent authority.Screening or matching the proposals: The planning committee will analyse various proposals and screenings. •The selected proposals are considered with the available resources of the concern. Here resources are referred asthefinancialpartoftheproposal.Thisreducesthegapbetweentheresourcesandtheinvestmentcost.Evaluation: After screening, the proposals are evaluated with the help of various methods, such as payback •period proposal, net discovered present value method, accounting rate of return and risk analysis. The proposals are evaluated by:

Independent proposals �Contingent of dependent proposals �Partially exclusive proposals. �

Independent proposals are not compared with another proposals and the same may be accepted or rejected. Whereas, higher proposals acceptance depends upon the other one or more proposals. For example, the expansion of plant machinery leads to constructing of new building, additional manpower, etc. Mutually exclusive projects are those which competed with other proposals and to implement the proposals after considering the risk and return, market demand, etc.

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Fixingproperty:Aftertheevolution,theplanningcommitteewillpredictwhichproposalswillgivemoreprofit•oreconomicconsideration.Iftheprojectsorproposalsarenotsuitablefortheconcern’sfinancialcondition,the projects are rejected without considering other nature of the proposals.Finalapproval:Theplanningcommitteeapprovesthefinalproposals,withthehelpofthefollowing:•

Profitability �Economic constituents �Financial violability �Market conditions. �

The planning committee prepares the cost estimation and submits to the management.Implementing: The competent authority spends the money and implements the proposals. While implementing •the proposals, assign responsibilities to the proposals, assign responsibilities for completing it, within the time allotted and reduce the cost for this purpose. The network techniques used such as PERT and CPM. It helps the management for monitoring and containing the implementation of the proposals.Performancereviewoffeedback:Thefinalstageofcapitalbudgetingisactualresultscomparedwiththestandard•results.Theadverseorunfavourableresultsidentifiedandremovingthevariousdifficultiesoftheproject.Thisis helpful for the future of the proposals.

6.5 Kinds of Capital Budgeting DecisionsTheoverallobjectiveofcapitalbudgetingistomaximisetheprofitability.Ifafirmconcentratesreturnoninvestment,this objective can be achieved either by increasing the revenues or reducing the costs. The increasing revenues can be achieved by expansion or the size of operations by adding a new product line. Reducing costs mean representing obsolete return on assets.

6.6 Methods of Capital Budgeting of EvaluationBy matching the available resources and projects it can be invested. The funds available are always living funds. There are many considerations taken for investment decision process such as environment and economic conditions.

Themethodsofevaluationsareclassifiedasfollows:Traditional methods (or Non-discount methods)•

Pay-back Period Methods �Post Pay-back Methods �Accounts Rate of Return �

Modern methods (or Discount methods)•Net Present Value Method �Internal Rate of Return Method �ProfitabilityIndexMethod �


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Methods of Capital Budgeting

Traditional Method

Post pay-backMethod

Accounting Rate of Return

Net presentValue

Method

Internal Rateof ReturnMethod

ProfitabilityIndex

Method

Modern Methods

Pay-back Method

Fig. 6.2 Capital Budgeting Methods(Source: http://vcmdrp.tums.ac.ir/files/financial/istgahe_mali/moton_english/financial_management_[www.

accfile.com].pdf)

6.6.1 Pay-back PeriodPay-back period is the time required to recover the initial investment in a project. (It is one of the non-discounted cashflowmethodsofcapitalbudgeting):

Merits of pay-back methodThe following are the important merits of the pay-back method:

It is easy to calculate and simple to understand.•Pay-back method provides further improvement over the accounting rate return.•Pay-back method reduces the possibility of loss on account of obsolescence.•

DemeritsThe following are the important demerits of the pay-back method:

It ignores the time value of money.•Itignoresallcashinflowsafterthepay-backperiod.•It is one of the misleading evaluations of capital budgeting.•

Accept /Reject criteriaIf the actual pay-back period is less than the predetermined pay-back period, the project would be accepted. If not, it would be rejected.

ExampleProjectcostisRs.30,000andthecashinflowsareRs.10,000,thelifeoftheprojectis5 years. Calculate the pay-back period.

Solution

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Theannualcashinflowiscalculatedbyconsideringtheamountofnetincomeontheamountofdepreciationproject(Asset) before taxation but after taxation. The income precision earned is expressed as a percentage of initial investment, is called unadjusted rate of return. The above problem will be calculated as below:

= 33.33%

Uneven cash inflowsNormallytheprojectsarenothavinguniformcashinflows.Inthosecasesthepay-backperiodiscalculated,cumulativecashinflowswillbecalculatedandtheninterpreted.

Example 1: CertainprojectsrequireaninitialcashoutflowofRs.25,000.Thecashinflowsfor6yearsareRs.5,000,Rs. 8,000, Rs. 10,000, Rs. 12,000, Rs. 7,000 and Rs. 3,000.

Solution

Year Cash Inflows (Rs.) Cumulative Cash Inflows (Rs.)

1 5,000 5,0002 8,000 13,0003 10,000 23,0004 12,000 35,0005 7,000 42,0006 3,000 45,000

Theabovecalculationshowsthatin3yearsRs.23,000hasbeenrecoveredRs.2,000,isbalanceoutofcashoutflow.Inthe4thyear,thecashinflowisRs.12,000.Itmeansthepay-backperiodisthreetofouryears,calculatedasfollows

Pay-back period = 3 years+2000/12000×12 months= 3 years 2 months.

6.6.2 Post Pay-back Profitability MethodOneofthemajorlimitationsofpay-backperiodmethodisthatitdoesnotconsiderthecashinflowsearnedafterpay-backperiodandiftherealprofitabilityoftheprojectcannotbeassessed.Toimproveoverthismethod,itcanbemadebyconsideringthereceivableafterthepay-backperiod.Thesereturnsarecalledpostpay-backprofits.

6.6.3 Accounting Rate of Return or Average Rate of ReturnAveragerateofreturnmeanstheaveragerateofreturnorprofittakenforconsideringtheprojectevaluation.Thismethod is one of the traditional methods for evaluating the project proposals.

MeritsThe following are the important merits:

It is easy to calculate and simple to understand.•Itisbasedontheaccountinginformationratherthancashinflow.•It is not based on the time value of money.•Itconsidersthetotalbenefitsassociatedwiththeproject.•


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DemeritsThe following are the important demerits:

It ignores the time value of money.•It ignores the reinvestment potential of a project.•Differentmethods areused for accountingprofit.So, it leads to somedifficulties in the calculationof the•project.

Accept/Reject criteriaIf the actual accounting rate of return is more than the predetermined required rate of return, the project would be accepted. If not it would be rejected.

6.6.4 Net Present ValueNet present value method is one of the modern methods for evaluating the project proposals. In this method cash inflowsareconsideredwiththetimevalueofthemoney.Netpresentvaluedescribesasthesummationofthepresentvalueofcashinflowandpresentvalueofcashoutflow.Netpresentvalueisthedifferencebetweenthetotalpresentvalueoffuturecashinflowsandthetotalpresentvalueoffuturecashoutflows.


It recognises the time value of money.•Itconsidersthetotalbenefitsarisingoutoftheproposal.•It is the best method for the selection of mutually exclusive projects.•It helps to achieve the maximisation of shareholders’ wealth.•


Itisdifficulttounderstandandcalculate.•It needs the discount factors for calculation of present values.•It is not suitable for the projects having different effective lives.•

Accept/Reject criteriaIfthepresentvalueofcashinflowsismorethanthepresentvalueofcashoutflows,itwouldbeaccepted.Ifnot,itwould be rejected.

6.6.5 Internal Rate of ReturnInternal rate of return is time adjusted technique and covers the disadvantages of the traditional techniques. In other wordsitisarateatwhichdiscountcashflowstozero.Itisexpectedbythefollowingratio:

Steps to be followed:Step1.findoutfactorFactor is calculated as follows:

Step 2. Find out positive net present valueStep 3. Find out negative net present value

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Step 4. Find out formula net present valueFormula:

Base factor = Positive discount rateDP = Difference in percentage


It considers the time value of money.•Ittakesintoaccountthetotalcashinflowandoutflow.•It does not use the concept of the required rate of return.•It gives the approximate/nearest rate of return.•


It involves complicated computational method.•It produces multiple rates which may be confusing for taking decisions.•Itisassumethatallintermediatecashflowsarereinvestedattheinternalrateofreturn.•

Accept/Reject criteriaIfthepresentvalueofthesumtotalofthecompoundedreinvestedcashflowsisgreaterthanthepresentvalueoftheoutflows,theproposedprojectisaccepted.Ifnotitwouldberejected.

Excess present value indexExcess present value is calculated on basis of net present value. It gives the results in percentage.

Example 2: TheinitialofequipmentisRs.10,000.Cashinflowfor5yearsisestimatedtobeRs.3,500peryear.The management is desired minimum rate of excess present value index.

SolutionPresent value of Rs. 1 received annually for 5 years can be had from the annuity table.

Present value of 3,500 received annually for 5 years.

= 117, 32%

6.6.6 Capital RationingIntherationing,thecompanyhasonlylimitedinvestmenttheprojectsareselectedaccordingtotheprofitability.The project has selected the combination of proposal that will yield the greatest portability.


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Example 3: LetusassumethatafirmhasonlyRs.20lakhstoinvestandfundscannotbeprovided.Thevariousproposalsalongwiththecostandprofitabilityindexareasfollows:

Proposal Pool of the project Profitability Index1 6,00,000 1.462 2,00,000 .0983 10,00,000 2.314 4,00,000 1.325 3,00,000 1.25

Solution:Inthisexample,allproposalsexpectnumber2giveprofitabilityexceedingoneandareprofitableinvestments.Thetotaloutlayrequiredtobeinvestedinallother(profitable)projectisRs.25,00,000(1+2+3+4+5)buttotalfundsavailablewiththefirmareRs.20lakhsandhencethefirmhastodocapitalcombinationofprojectwithinatotalwhichhasthelowestprofitabilityindexalongwiththeprofitableproposalscannotbetaken.

6.7 Risk and Uncertainly in Capital BudgetingCapitalbudgetingrequirestheprojectionofcashinflowandoutflowofthefuture.Thefutureinalwaysuncertain,estimate of demand, production, selling price, cost, etc., cannot be exact.

For example: The product at any time may become obsolete therefore, the future in unexpected. The following methods for considering the accounting of risk in capital budgeting. Various evaluation methods are used for risk and uncertainty in capital budgeting are as follows:

Risk-adjusted cut off rate (or method of varying discount rate)•Certainly equivalent method•Sensitivity technique•Probability technique•Standard deviation method•Co-efficientofvariationmethod•Decision tree analysis•

Risk-adjusted cut-off rate (or method of varying)This is one of the simplest methods while calculating the risk in capital budgeting increase cut of rate or discount factor by certain percentage an account of risk.

Certainly equivalent methodItisalsoanothersimplestmethodforcalculatingriskincapitalbudgetingintoreducedexpectedcashinflowsbycertainamounts.Itcanbeemployedbymultiplyingtheexpectedcashinflowsbycertainlyequivalentco-efficientinordertheuncertaincashinflowtocertaincashinflows.

Sensitivity techniqueWhencashinflowsaresensitiveunderdifferentcircumstancesmorethanoneforecastofthefuturecashinflowsmaybemade.Theseinflowsmayberegardedon‘Optimistic’,‘mostlikely’and‘pessimistic’.Furthercashinflowsmaybediscountedtofindoutthenetpresentvaluesunderthesethreedifferentsituations.Ifthenetpresentvaluesunderthe three situations differ widely it implies, that there is a great risk in the project and the investor’s is decision to accept or reject a project will depend upon his risk bearing activities.

Probability techniqueProbability technique refers to the each event of future happenings are assigned with relative frequency probability. Probabilitymeansthelikelihoodoffutureevent.Thecashinflowsofthefutureyearsfurtherdiscountedwiththeprobability. The higher present value may be accepted.

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Standard deviation methodTwoprojectshavethesamecashoutflowandtheirnetvaluesarealsothesame,standarddurationsoftheexpectedcashinflowsofthetwoprojectsmaybecalculatedtomeasurethecomparativeandriskoftheprojects.Theprojecthaving a higher standard deviation in said to be more risky as compared to the other.

Co-efficient of variation methodCo-efficientofvariationisarelativemeasureofdispersion.Ittheprojectshavethesamecostbutdifferentnetpresentvalues,relativesmeasure,i.e.,Co-efficientofvariationshouldberiskinduced.Itcanbecalculatedas:

Decision tree analysisIn the modern business world, putting the investments are become more complex and taking decisions in the risky situations. So, the decision tree analysis helpful for taking risky and complex decisions, because it considers all the possible events and each possible events are assigned with the probability.

6.7.1 Construction of Decision TreeConstruction of decision tree is as follows:

Definedtheproblem•Evaluate the different alternatives•Indicating the decision points•Assign the probabilities of the monetary values•Analysis the alternatives.•

Accept/Reject criteriaIf the net present values are in positive the project may be accepted otherwise it is rejected.


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SummaryThewordcapital refers tobe the total investmentofacompanyoffirm inmoney, tangibleand intangible•assets.Budgets are a blue print of a plan and action expressed in quantities and manners.•AccordingtothedefinitionofRichardandGreenlaw,“capitalbudgetingisacquiringinputswithlong-term•return”.Capitalbudgetingrequireshugeinvestmentsoffunds,buttheavailablefundsarelimited,thereforethefirm•before investing projects, plan are control its capital expenditure.Capitalbudgetingnotonlyreducesthecostbutalsoincreasestherevenueinlong-termandwillbringsignificant•changesintheprofitofthecompanybyavoidingoverormoreinvestmentorunderinvestment.Capitalbudgetingisadifficultprocesstotheinvestmentofavailablefunds.•Aftertheevolution,theplanningcommitteewillpredictwhichproposalswillgivemoreprofitoreconomic•consideration.Theoverallobjectiveofcapitalbudgetingistomaximisetheprofitability.•Pay-back period is the time required to recover the initial investment in a project.•If the actual pay-back period is less than the predetermined pay-back period, the project would be accepted.•Averagerateofreturnmeanstheaveragerateofreturnorprofittakenforconsideringtheprojectevaluation.•Net present value method is one of the modern methods for evaluating the project proposals.•Internal rate of return is time adjusted technique and covers the disadvantages of the traditional techniques.•Capitalbudgetingrequirestheprojectionofcashinflowandoutflowofthefuture.•Probability technique refers to the each event of future happenings are assigned with relative frequency •probability.Co-efficientofvariationisarelativemeasureofdispersion.•

ReferencesIntroduction to Capital Budgeting. • [Pdf]Availableat:<http://finance.wharton.upenn.edu/~benninga/pfe_chap07.pdf>[Accessed11April2014].Capital Budgeting. • [Pdf]Available at:<http://dosen.narotama.ac.id/wp-content/uploads/2013/02/Chapter-29-Capital-Budgeting.pdf>[Accessed11April2014].Peterson, P. P., 2004. • Capital Budgeting: Theory and Practice. John Wiley & Sons.Shapiro, A. C., 2008. • Capital Budgeting and Investment Analysis. Pearson Education India.Capital Budgeting Lecture in 10 min., Capital Budgeting Techniques Decisions NPV Net Present Value. • [Videoonline]Availableat:<https://www.youtube.com/watch?v=QRh0tiG2lVk>[Accessed11April2014].Capital Budgeting Lecture. • [Videoonline]Availableat:<https://www.youtube.com/watch?v=TrKVj_wLgUc>[Accessed11April2014].

Recommended ReadingBierman, H. & Smidt, S., 2007. • The Capital Budgeting Decision: Economic Analysis of Investment Projects. Routledge.Dayananda, D., 2002. • Capital Budgeting: Financial Appraisal of Investment Projects. C a m b r i d g e U n i v e r s i t y P r e s s .Baker, H. K., 2011. • Capital Budgeting Valuation: Financial Analysis for Today’s Investment Projects. John Wiley & Sons.

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Self AssessmentTheword__________referstobethetotalinvestmentofacompanyoffirminmoney,tangibleandintangible1. assets.

budgeta. capitalb. expenditurec. financed.

Whichofthefollowingdefinedcapitalbudgetas,“capitalbudgetingisalong-termplanningformakingand2. financingproposedcapitaloutlays”?

Charles Ta. G.C. Philippatosb. Richard and Green lawc. Lyrichd.

Match the following 3.

1. Reducing costs A. It is the time required to recover the initial investment in a proj-ect.

2. Pay-back period B. The income precision earned is expressed as a percentage of ini-tial investment.

3.Theannualcashinflow C. It means representing obsolete return on assets.

4. Unadjusted rate of returnD. It is calculated by considering the amount of net income on the amount of depreciation project (Asset) before taxation but after taxa-tion.

1- D, 2-B, 3-C, 4-Aa. 1- A, 2-C, 3-B, 4-Db. 1- C, 2-A, 3-D, 4-Bc. 1- B, 2-D, 3-A, 4-Cd.

The capital budgeting may have _______ investment proposals.4. noa. fourb. variousc. twod.

Which of the following statement is true?5. Capital expenditure is long-term in nature or permanent in nature.a. Capital expenditure is short-term in nature or permanent in nature.b. Capital expenditure is long-term in nature or temporary in nature.c. Capital expenditure is short-term in nature or temporary in nature.d.

_________ method is one of the traditional methods for evaluating the project proposals.6. Pay-back methoda. Post pay-back methodb. Average rate of returnc. Internal Rate of Return Methodd.


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Which of the following methods reduces the possibility of loss on account of obsolescence?7. Pay-back methoda. Post pay-back methodb. Average rate of returnc. Internal Rate of Return Methodd.

_________ present value is calculated on basis of net present value.8. Neta. Interestb. Internalc. Excessd.

Which of the following statement is false?9. The capital investment decisions are irreversible, are not changed back.a. Capital budgeting is an easy process to the investment of available funds.b. Theoverallobjectiveofcapitalbudgetingistomaximisetheprofitability.c. Pay-back method provides further improvement over the accounting rate return.d.

What means the likelihood of future event?10. Probabilitya. Optimisticb. Pessimisticc. Riskd.

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Chapter VII

Capitalisation and Capital Structure

Aim


introduce capitalisation•

explain meaning of capital•

explicate types of capitalisation•

Objectives


explain capital structure•

elucidatefinancialstructure•

explicate optimum capital structure•

Learning outcome


identify factors determining capital structure•

understand capital structure theories•

definecapital•


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7.1 IntroductionFinancialplanninganddecisionplayamajorroleinthefieldoffinancialmanagementwhichconsistsofthemajorareaoffinancialmanagementsuchas,capitalisation,financialstructure,capitalstructure,leverageandfinancialforecasting.

Financial planning includes the following important parts:Estimating the amount of capital to be raised.•Determining the form and proportionate amount of securities.•Formulatingpoliciestomanagethefinancialplan.•

7.2 Meaning of CapitalThe term capital refers to the total investment of the company in terms of money, and assets. It is also called as total wealthofthecompany.Whenthecompanyisgoingtoinvestlargeamountoffinanceintothebusiness,itiscalledas capital. Capital is the initial and integral part of new and existing business concern.

Thecapitalrequirementsofthebusinessconcernmaybeclassifiedintotwocategories:Fixed capital•Working capital.•

7.2.1 Fixed CapitalFixed capital is the capital, which is needed for meeting the permanent or long-term purpose of the business concern. Fixed capital is required mainly for the purpose of meeting capital expenditure of the business concern and it is usedoveralongperiod.Itistheamountinvestedinvariousfixedorpermanentassets,whicharenecessaryforabusiness concern.

Definition of fixed capitalAccordingtothedefinitionofHoagland,“Fixedcapitaliscomparativelyeasilydefinedtoincludeland,building,machinery and other assets having a relatively permanent existence”.

Character of fixed capitalFixed capital has the following features:

Fixedcapitalisusedtoacquirethefixedassetsofthebusinessconcern.•Fixed capital meets the capital expenditure of the business concern.•Fixed capital normally consists of long period.•Fixed capital expenditure is of nonrecurring nature.•Fixedcapitalcanberaisedonlywiththehelpoflong-termsourcesoffinance.•

7.2.2 Working CapitalWorking capital is the capital which is needed to meet the day-to-day transaction of the business concern. It may cross working capital and net working capital. Normally working capital consists of various compositions of current assets such as inventories, bills, receivable, debtors, cash, and bank balance and prepaid expenses.

AccordingtothedefinitionofBonneville,“anyacquisitionoffundswhichincreasesthecurrentassetsincreasestheWorking Capital also for they are one and the same”.

Working capital is needed to meet the following purposes:Purchase of raw material•Payment of wages to workers•Payment of day-to-day expenses•Maintenance expenditure, etc.•

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Working Capital

latipaC dexiFlatipaC

Position of Capital

Fig. 7.1 Position of capital(Source:http://vcmdrp.tums.ac.ir/files/financial/istgahe_mali/moton_english/financial_management_[www.

accfile.com].pdf)

7.3 CapitalisationCapitalisationisoneofthemostimportantpartsoffinancialdecision,whichisrelatedtothetotalamountofcapitalemployed in the business concern.

Understandingtheconceptofcapitalisationleadstosolvemanyproblemsinthefieldoffinancialmanagement,because, there is confusion among the capital, capitalisation and capital structure.

Meaning of capitalisationCapitalisation refers to theprocessofdetermining thequantumof funds that afirmneeds to run its business.Capitalisation is only the par value of share capital and debenture and it does not include reserve and surplus.

Definition of capitalisationCapitalisationcanbedefinedbythevariousfinancialmanagementexperts.Someofthedefinitionsarementionedbelow:

According to Guthman and Dougall, “capitalisation is the sum of the par value of stocks and bonds outstanding”.“Capitalisation is the balance sheet value of stocks and bonds outstands.” — Bonneville and Dewey

According to Arhur. S. Dewing, “capitalisation is the sum total of the par value of all shares.”

7.4 Types of CapitalisationCapitalisationmaybeclassifiedintothefollowingthreeimportanttypes,basedonitsnature:

Over capitalisation•Under capitalisation•Water capitalisation•

7.4.1 Over CapitalisationOver capitalisation refers to the company which possesses an excess of capital in relation to its activity level and requirements. In simple means, over capitalisation is more capital than actually required and the funds are not properly used.

According to Bonneville, Dewey and Kelly, over capitalisation means, “when a business is unable to earn fair rate on its outstanding securities.”


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Example 1:A company is earning a sum of Rs. 50,000 and the rate of return expected is 10%. This company will be said to be properly capitalised. Suppose the capital investment of the company is Rs. 60,000, it will be over capitalisation to the extent of Rs. 1,00,000. The new rate of earning would be:

When the company has over capitalisation, the rate of earnings will be reduced from10% to 8.33%.

Causes of over capitalisationOver capitalisation arises due to the following important causes:

Over issue of capital by the company.•Borrowing large amount of capital at a higher rate of interest.•Providinginadequatedepreciationtothefixedassets.•Excessive payment for acquisition of goodwill.•High rate of taxation.•Under estimation of capitalisation rate.•

Effects of over capitalisationOver capitalisation leads to the following important effects:

Reduces the rate of earning capacity of the shares.•Difficultiesinobtainingnecessarycapitaltothebusinessconcern.•It leads to fall in the market price of the shares.•It creates problems on re-organisation.•It leads under or misutilisation of available resources.•

Remedies for over capitalisationOver capitalisation can be reduced with the help of effective management and systematic design of the capital structure. The following are the major steps to reduce over capitalisation:

Efficientmanagementcanreduceovercapitalisation.•Redemption of preference share capital which consists of high rate of dividend.•Reorganisation of equity share capital.•Reduction of debt capital.•

7.4.2 Under CapitalisationUnder capitalisation is the opposite concept of over capitalisation and it will occur when the company’s actual capitalisation is lower than the capitalisation as warranted by its earning capacity. Under capitalisation is not the so called inadequate capital.

UndercapitalisationcanbedefinedbyGerstenberg,“acorporationmaybeundercapitalisedwhentherateofprofitis exceptionally high in the same industry.”

Hoaglanddefinedundercapitalisationas“anexcessoftrueassetsvalueovertheaggregateofstocksandbondsoutstanding.”

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Causes of under capitalisationUnder capitalisation arises due to the following important causes:

Under estimation of capital requirements.•Under estimation of initial and future earnings.•Maintaininghighstandardsofefficiency.•Conservative dividend policy.•Desire of control and trading on equity.•

Effects of under capitalisationUnder Capitalisation leads to the following effects on the company and its shareholders:

It leads to manipulate the market value of shares.•It increases the marketability of the shares.•It may lead to more government control and higher taxation.•Consumers feel that they are exploited by the company.•It leads to high competition.•

Remedies of under capitalisationUnder Capitalisation may be corrected by taking the following remedial measures:

Under capitalisation can be compensated with the help of fresh issue of shares.•Increasing the par value of share may help to reduce under capitalisation.•Under capitalisation may be corrected by the issue of bonus shares to the existing shareholders.•Reducing the dividend per share by way of splitting up of shares.•

7.4.3 Watered CapitalisationIf the stock or capital of the company is not mentioned by assets of equivalent value, it is called as watered stock. In simple words, watered capital means that the realisable value of assets of the company is less than its book value.

AccordingtoHoagland’sdefinition,“Astockissaidtobewateredwhenitstruevalueislessthanitsbookvalue.”

Causes of watered capitalGenerally watered capital arises at the time of incorporation of a company but it also arises during the life time of the business. The following are the main causes of watered capital:

Acquiring the assets of the company at high price.•Adopting ineffective depreciation policy.•Worthless intangible assets are purchased at higher price.•

7.5 Capital StructureCapital is the major part of all kinds of business activities, which are decided by the size, and nature of the business concern. Capital may be raised with the help of various sources. If the company maintains proper and adequate level ofcapital,itwillearnhighprofitandtheycanprovidemoredividendstoitsshareholders.

7.5.1 Meaning of Capital StructureCapital structure refers to the kinds of securities and the proportionate amounts that make up capitalisation. It is the mix of different sources of long-term sources such as equity shares, preference shares, debentures, long-term loans and retained earnings.


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Thetermcapitalstructurereferstotherelationshipbetweenthevariouslong-termsourcefinancingsuchasequitycapital, preference share capital and debt capital. Deciding the suitable capital structure is the important decision ofthefinancialmanagementbecauseitiscloselyrelatedtothevalueofthefirm.Capitalstructureisthepermanentfinancingofthecompanyrepresentedprimarilybylong-termdebtandequity.

7.5.2 Definition of Capital StructureThefollowingdefinitionsclearlyinitiatethemeaningandobjectiveofthecapitalstructures.

AccordingtothedefinitionofGerestenbeg,“CapitalStructureofacompanyreferstothecompositionormakeupof its capitalisation and it includes all long-term capital resources.”

AccordingtothedefinitionofJamesC.VanHorne,“Themixofafirm’spermanentlong-termfinancingrepresentedby debt, preferred stock, and common stock equity.”

AccordingtothedefinitionofPresanaChandra,“Thecompositionofafirm’sfinancingconsistsofequity,preference,and debt.”

AccordingtothedefinitionofR.H.Wessel,“Thelongtermsourcesoffundemployedinabusinessenterprise.”

7.6 Financial StructureThetermfinancialstructureisdifferentfromthecapitalstructure.Financialstructureshowsthepatterntotalfinancing.Itmeasurestheextenttowhichtotalfundsareavailabletofinancethetotalassetsofthebusiness.

or

Thefollowingpointsindicatethedifferencebetweenthefinancialstructureandcapitalstructure.

Financial Structures Capital Structures

It includes both long-term and short-term sources of funds It includes only the long-term sources of funds.

It means the entire liabilities side of the balance sheet.

It means only the long-term liabilities of the company.

Financial structures consist of all sources of capital.

It consists of equity, preference and retained earning capital.

It will not be more important while determining thevalueofthefirm.

It is one of the major determinations of the value ofthefirm.

Table 7.1 Difference between the financial structure and capital structure

7.7 Optimum Capital StructureOptimum capital structure is the capital structure at which the weighted average cost of capital is minimum and therebythevalueofthefirmismaximum.Optimumcapitalstructuremaybedefinedasthecapitalstructureorcombinationofdebtandequitythatleadstothemaximumvalueofthefirm.

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7.7.1 Objectives of Capital StructureDecision of capital structure aims at the following two important objectives:

Maximisethevalueofthefirm.•Minimise the overall cost of capital.•

7.7.2 Forms of Capital StructureCapitalstructurepatternvariesfromcompanytocompanyandtheavailabilityoffinance.Normally the following forms of capital structure are popular in practice.

Equity shares only.•Equity and preference shares only.•Equity and Debentures only.•Equity shares, preference shares and debentures.•

7.8 Factors Determining Capital StructureThefollowingfactorsareconsideredwhiledecidingthecapitalstructureofthefirm:LeverageItisthebasicandimportantfactor,whichaffectsthecapitalstructure.Itusesthefixedcostfinancing,suchasdebt,equity and preference share capital. It is closely related to the overall cost of capital.

Cost of capitalCostofcapitalconstitutesthemajorpartfordecidingthecapitalstructureofafirm.Normallylong-termfinancesuchasequityanddebtconsistoffixedcostwhilemobilisation.Whenthecostofcapitalincreases,valueofthefirmwillalsodecrease.Hence,thefirmmusttakecarefulstepstoreducethecostofcapital.

Natureofthebusiness:Useoffixedinterest/dividendbearingfinancedependsuponthenatureofthebusiness.•If the business consists of long period of operation, it will apply for equity than debt, and it will reduce the cost of capital.Sizeofthecompany:Italsoaffectsthecapitalstructureofafirm.Ifthefirmbelongstolarge-scale,itcanmanage•thefinancialrequirementswiththehelpofinternalsources.However,itissmallsize,theywillgoforexternalfinance.Itconsistsofhighcostofcapital.Legal requirements: Legal requirements are also one of the considerations while dividing the capital structure •ofafirm.Forexample,bankingcompaniesarerestrictedtoraisefundsfromsomesources.Requirement of investors: In order to collect funds from different type of investors, it will be appropriate for •the companies to issue different sources of securities.

Government policyPromotercontributionisfixedbythecompanyAct.Itrestrictstomobiliselarge,long-termfundsfromexternalsources. Hence, the company must consider government policy regarding the capital structure.

7.9 Capital Structure TheoriesCapitalstructureisthemajorpartofthefirm’sfinancialdecisionwhichaffectsthevalueofthefirmanditleadsto change EBIT and market value of the shares. There is a relationship among the capital structure, cost of capital andvalueofthefirm.Theaimofeffectivecapitalstructureistomaximisethevalueofthefirmandtoreducethecost of capital.

There are two major theories explaining the relationship between capital structure, cost of capital and value of the firm.


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Capital Structure Theories

Modern Approach

Net Income Approach

Modigliani-Miller Approach

Traditional Approach

Net Operating Income

Fig. 7.2 Capital structure theories

7.9.1 Traditional ApproachIt is the mix of Net Income approach and Net Operating Income approach. Hence, it is also called as intermediate approach.Accordingtothetraditionalapproach,mixofdebtandequitycapitalcanincreasethevalueofthefirmby reducing overall cost of capital up to certain level of debt. Traditional approach states that the Ko decreases only withintheresponsiblelimitoffinancialleverageandwhenreachingtheminimumlevel,itstartsincreasingwithfinancialleverage.

AssumptionsCapital structure theories are based on certain assumption to analysis in a single and convenient manner:

Thereareonlytwosourcesoffundsusedbyafirm;debtandshares.•Thefirmpays100%ofitsearningasdividend.•The total assets are given and do not change.•Thetotalfinanceremainsconstant.•Theoperatingprofits(EBIT)arenotexpectedtogrow.•The business risk remains constant.•Thefirmhasaperpetuallife.•The investors behave rationally.•

7.9.2 Net Income (NI) ApproachNet income approach suggested by the Durand. According to this approach, the capital structure decision is relevant tothevaluationofthefirm.Inotherwords,achangeinthecapitalstructureleadstoacorrespondingchangeintheoverallcostofcapitalaswellasthetotalvalueofthefirm.

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Accordingtothisapproach,usemoredebtfinancetoreducetheoverallcostofcapitalandincreasethevalueoffirm.

Net income approach is based on the following three important assumptions:There are no corporate taxes.•The cost debt is less than the cost of equity.•The use of debt does not change the risk perception of the investor.•

where, V = S+B V=Valueoffirm S = Market value of equity B = Market value of debt

Market value of the equity can be ascertained by the following formula:

where, NI = Earnings available to equity shareholder

= Cost of equity/equity capitalisation rate

FormatforcalculatingvalueofthefirmonthebasisofNIapproach.

Particulars Amount

Net operating income (EBIT)Less: interest on debenture (i)Earnings available to equity holder (NI)

Equity capitalisation rate ( )Market value of equity (S)Market value of debt (B)Totalvalueofthefirm(S+B)

Overall cost of capital = = EBIT/V (%)

XXXXXX

XXX

XXXXXXXXXXXXXXX%

Table 7.2 Format for calculating value of the firm on the basis of NI approach

7.9.3 Net Operating Income (NOI) ApproachAnother modern theory of capital structure, suggested by Durand. This is just the opposite to the Net Income approach. Accordingtothisapproach,CapitalStructuredecisionisirrelevanttothevaluationofthefirm.Themarketvalueofthefirmisnotatallaffectedbythecapitalstructurechanges.

Accordingtothisapproach,thechangeincapitalstructurewillnotleadtoanychangeinthetotalvalueofthefirmand market price of shares as well as the overall cost of capital.

NI approach is based on the following important assumptions:The overall cost of capital remains constant.•There are no corporate taxes.•Themarketcapitalisesthevalueofthefirmasawhole.•


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Valueofthefirm(V)canbecalculatedwiththehelpofthefollowingformula:

Where, V=Valueofthefirm EBIT = Earnings before interest and tax

= Overall cost of capital

7.9.4 Modigliani and Miller ApproachModiglianiandMillerapproachstatesthatthefinancingdecisionofafirmdoesnotaffectthemarketvalueofafirminaperfectcapitalmarket.Inotherwords,MMapproachmaintainsthattheaveragecostofcapitaldoesnotchangewithchangeinthedebtweightedequitymixorcapitalstructuresofthefirm.

Modigliani and Miller approach is based on the following important assumptions:There is a perfect capital market.•There are no retained earnings.•There are no corporate taxes.•The investors act rationally.•The dividend payout ratio is 100%.•The business consists of the same level of business risk.•

Valueofthefirmcanbecalculatedwiththehelpofthefollowingformula:

Where, EBIT = Earnings before interest and tax

= Overall cost of capital t = Tax rate

Ke

Ko

k

D/ERisk Bearing Debt

Risk Due Debt

Rat

e of

Ret

urn

Fig. 7.3 Modigliani and miller approach(Source: http://vcmdrp.tums.ac.ir/files/financial/istgahe_mali/moton_english/financial_management_[www.

accfile.com].pdf)

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SummaryFinancialplanninganddecisionplayamajorroleinthefieldoffinancialmanagementwhichconsistsofthe•majorareaoffinancialmanagementsuchas,capitalisation,financialstructure,capitalstructure,leverageandfinancialforecasting.The term capital refers to the total investment of the company in terms of money and assets.•Fixed capital is the capital, which is needed for meeting the permanent or long-term purpose of the business •concern.Working capital is the capital which is needed to meet the day-to-day transaction of the business concern.•Capitalisationisoneofthemostimportantpartsoffinancialdecision,whichisrelatedtothetotalamountof•capital employed in the business concern.Capitalisationreferstotheprocessofdeterminingthequantumoffundsthatafirmneedstorunitsbusiness.•Over capitalisation refers to the company which possesses an excess of capital in relation to its activity level •and requirements.Under capitalisation is the opposite concept of over capitalisation and it will occur when the company’s actual •capitalisation is lower than the capitalisation as warranted by its earning capacity.Capital structure refers to the kinds of securities and the proportionate amounts that make up capitalisation.•Capital structure is the permanentfinancingof the company represented primarily by long-termdebt and•equity.Thetermfinancialstructureisdifferentfromthecapitalstructure.•Optimum capital structure is the capital structure at which the weighted average cost of capital is minimum and •therebythevalueofthefirmismaximum.Costofcapitalconstitutesthemajorpartfordecidingthecapitalstructureofafirm.•Capitalstructureisthemajorpartofthefirm’sfinancialdecisionwhichaffectsthevalueofthefirmanditleads•to change EBIT and market value of the shares.There are two major theories explaining the relationship between capital structure, cost of capital and value of •thefirm.ModiglianiandMillerapproachstatesthatthefinancingdecisionofafirmdoesnotaffectthemarketvalueof•afirminaperfectcapitalmarket.

ReferencesCapital Structure. • [Pdf]Available at: <http://www.unext.in/assets/Pu18CF3017/SLM-V/UNIT%207%20CAPITAL%20STRUCTURE.pdf>[Accessed11April2014].Cost of Capital. • [Pdf]Available at: <http://www2.sunysuffolk.edu/rosesr/ACC212/Lessons/CapitalBudget/CostCapital.pdf>[Accessed11April2014].Singla, R. K., 1996. • Corporate Capital Structure: Planning and Determinants: Theory and Practice. Deep and Deep Publications.Bierman, H., 2003. • The Capital Structure Decision. Springer.Capital Structure Part 1.mp4. • [Videoonline]Availableat:<https://www.youtube.com/watch?v=RoRmKV5UOl0>[Accessed11April2014].“Net Income Theory of capital Structure” lecture by Ms.Shaziya Naz, Biyani group of colleges. • [Videoonline]Availableat:<https://www.youtube.com/watch?v=y0j5upJys3s>[Accessed11April2014].

Recommended ReadingGhosh, A., 2012. • Capital Structure and Firm Performance. Transaction Publishers.Periasamy, P., 2009. • Financial Management. 2nd ed., Tata McGraw-Hill Education.Singla, R. K., • Business Studies. FK Publications.


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Self Assessment________anddecisionplayamajorroleinthefieldoffinancialmanagementwhichconsistsofthemajorarea1. offinancialmanagement.

Financial planninga. Capitalisationb. Financial structurec. Leveraged.

Which of the following term refers to the total investment of the company in terms of money and assets?2. Financea. Capitalb. Leveragec. Requirementd.


1. Fixed capital A. It is the capital which is needed to meet the day-to-day transaction of the business concern.

2. Working capital B. It is the capital, which is needed for meeting the permanent or long-term purpose of the business concern.

3. Over capitalisation C. This will occur when the company’s actual capitalisation is lower than the capitalisation as warranted by its earning capacity.

4. Under capitalisation D. It refers to the company which possesses an excess of capital in relation to its activity level and requirements.

1- C, 2- D, 3- A, 4-Ba. 1- D, 2- C, 3- B, 4-Ab. 1- A, 2- B, 3- C, 4-Dc. 1- B, 2- A, 3- D, 4-Cd.

Which of the following statement is true?4. Leverage is also called as total wealth of the company.a. Finance is also called as total wealth of the company.b. Capital is also called as total wealth of the company.c. Investment is also called as total wealth of the company.d.

_________capitalcanberaisedonlywiththehelpoflong-termsourcesoffinance.5. Workinga. Fixedb. Noc. Averaged.

Whichofthefollowingreferstotheprocessofdeterminingthequantumoffundsthatafirmneedstorunits6. business?

Capitalisationa. Financial structureb. Leveragec. Financial planningd.

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Which of the following statement is false?7. Fixedcapitalisusedtoacquirethefixedassetsofthebusinessconcern.a. Fixed capital normally consists of short period.b. Fixed capital expenditure is of nonrecurring nature.c. Fixed capital meets the capital expenditure of the business concern.d.

Capital ________ refers to the kinds of securities and the proportionate amounts that make up capitalisation.8. planninga. structureb. costc. approachd.

Whichofthefollowingshowsthepatterntotalfinancing?9. Capital structurea. Capitalisationb. Financial planningc. Financial structured.

Whichofthefollowingapproachstatesthatthefinancingdecisionofafirmdoesnotaffectthemarketvalueof10. afirminaperfectcapitalmarket?

Modigliani and Miller approacha. Net Operating Income (NOI) approachb. Net Income (NI) approachc. Income approachd.


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Chapter VIII

Leverage and Dividend Decisions

Aim


introduce leverage and dividend decisions•

explain the meaning of leverage•

explicate the types of leverages•

Objectives


enlist the factors determining dividend policy•

elucidate dividend decisions•

explain types of dividends•

Learning outcome


identify types of dividend policy•

understand relevance of dividend•

defineleverageanddividend•

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8.1 IntroductionFinancialdecisionisoneoftheessentialandimportantpartsoffinancialmanagementinanykindofbusinessfirm.Asoundfinancialdecisionmustconsidertheboardcoverageofthefinancialmix(CapitalStructure),totalamountofcapital (capitalisation) and cost of capital ( ).Capitalstructureisoneofthesignificantthingsforthemanagement,sinceitinfluencesthedebtequitymixofthebusinessconcern,whichaffectstheshareholder’sreturnandrisk.

Hence, deciding the debt-equity mix plays a major role in the part of the value of the company and market value of the shares. The debt equity mix of the company can be examined with the help of leverage. The concept of leverage is discussed in this part. Types and effects of leverage are discussed in the part of EBIT and EPS.

8.2 Meaning of LeverageThe term leverage refers to an increased means of accomplishing some purpose. Leverage is used to lifting heavy objects,whichmaynotbeotherwisepossible.Inthefinancialpointofview,leveragereferstofurnishtheabilitytousefixedcostassetsorfundstoincreasethereturntoitsshareholders.

8.2.1 Definition of LeverageJamesHornehasdefinedleverageas,“theemploymentofanassetorfundforwhichthefirmpaysafixedcostorfixedreturn."

8.2.2 Types of LeveragesLeveragecanbeclassifiedintothreemajorheadingsaccordingtothenatureofthefinancemixofthecompany.

Leverage

Finacial Leverage

Operating Leverage

CompositeLeverage

Fig. 8.1 Types of leverages

Thecompanymayusefinanceorleverageoroperatingleverage,toincreasetheEBITandEPS.

8.3 Operating LeverageTheleverageassociatedwithinvestmentactivitiesiscalledasoperatingleverage.Itiscausedduetofixedoperatingexpensesinthecompany.Operatingleveragemaybedefinedasthecompany’sabilitytousefixedoperatingcoststo magnify the effects of changes in sales on its earnings before interest and taxes. Operating leverage consists of twoimportantcosts,viz.,fixedcostandvariablecost.Whenthecompanyissaidtohaveahighdegreeofoperatingleverage,itemploysagreatamountoffixedcostandsmalleramountofvariablecost.Thus,thedegreeofoperatingleverage depends upon the amount of various cost structure. Operating leverage can be determined with the help of a break even analysis.


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Operating leverage can be calculated with the help of the following formula:

Where, OL = Operating Leverage C = Contribution OP=OperatingProfits

8.3.1 Degree of Operating LeverageThedegreeofoperatingleveragemaybedefinedaspercentagechangeintheprofitsresultingfromapercentagechange in the sales. It can be calculated with the help of the following formula:

8.3.2 Uses of Operating LeverageOperating leverage is one of the techniques to measure the impact of changes in sales which lead for change in the profitsofthecompany.

Ifanychangeinthesales,itwillleadtocorrespondingchangesinprofit.Operatingleveragehelpstoidentifythepositionoffixedcostandvariablecost.

Operating leverage measures the relationship between the sales and revenue of the company during a particular period.Operatingleveragehelpstounderstandtheleveloffixedcostwhichisinvestedintheoperatingexpensesofbusinessactivities.Operatingleveragedescribestheoverallpositionofthefixedoperatingcost.

8.4 Financial LeverageLeverageactivitieswithfinancingactivitiesarecalledfinancialleverage.Financialleveragerepresentstherelationshipbetweenthecompany’searningsbeforeinterestandtaxes(EBIT)oroperatingprofitandtheearningavailabletoequity shareholders.

Financialleverageisdefinedas“theabilityofafirmtousefixedfinancialchargestomagnifytheeffectsofchangesinEBITontheearningspershare.”Itinvolvestheuseoffundsobtainedatafixedcostinthehopeofincreasingthereturntotheshareholders.“Theuseoflong-termfixedinterestbearingdebtandpreferencesharecapitalalongwithsharecapitaliscalledfinancialleverageortradingonequity.”

Financialleveragemaybefavourableorunfavourabledependsupontheuseoffixedcostfunds.Favourablefinancialleverageoccurswhenthecompanyearnsmoreontheassetspurchasedwiththefunds,thenthefixedcostoftheiruse.Hence,itisalsocalledaspositivefinancialleverage.Unfavourablefinancialleverageoccurswhenthecompanydoesnotearnasmuchasthefundscost.Hence,itisalsocalledasnegativefinancialleverage.

Financial leverage can be calculated with the help of the following formula:

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Where, FL = Financial leverage OP=Operatingprofit(EBIT) PBT=Profitbeforetax.

8.4.1 Degree of Financial LeverageDegreeoffinancialleveragemaybedefinedasthepercentagechangeintaxableprofitasaresultofpercentagechange in earning before interest and tax (EBIT). This can be calculated by the following formula:

8.4.2 Alternative Definition of Financial LeverageAccordingtoGitmar,“financialleverageistheabilityofafirmtousefixedfinancialchangestomagnifytheeffectsof change in EBIT and EPS.”

Where, FL = Financial Leverage EBIT = Earning Before Interest and Tax EPS = Earning Per share.

8.4.3 Uses of Financial LeverageUsesoffinancialleverageareasfollows:

Financial leverage helps to examine the relationship between EBIT and EPS.•Profit•Financial leverage measures the percentage of change in taxable income to the percentage change in EBIT.•Financialleveragelocatesthecorrectprofitablefinancialdecisionregardingcapitalstructureofthecompany.•Financialleverageisoneoftheimportantdeviceswhichisusedtomeasurethefixedcostproportionwiththe•total capital of the company.Ifthefirmacquiresfixedcostfundsatahighercost,thentheearningsfromthoseassets,theearningpershare•and return on equity capital will decrease.

Operating Leverage Financial Leverage

Operating leverage is associated with investment activities of the company.

Financialleverageisassociatedwithfinancingactivities of the company.

Operatingleverageconsistsoffixedoperatingexpenses of the company.

Financialleverageconsistsofoperatingprofitofthecompany.

Itrepresentstheabilitytousefixedoperatingcost. It represents the relationship between EBIT and EPS.

Operating leverage can be calculated by Financial leverage can be calculated by

Apercentagechangeintheprofitsresultingfromapercentage change in the sales is called as degree of operating leverage.

Apercentagechangeintaxableprofitistheresultofpercentage change in EBIT.

Trading on equity is not possible while the company is operating leverage.

Trading on equity is possible only when the company usesfinancialleverage.


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Operatingleveragedependsuponfixedcostandvariable cost.

Financial leverage depends upon the operating profits.

Tax rate and interest rate will not affect the operating leverage.

Financial leverage will change due to tax rate and interest rate.

Table 8.1 Difference between operating leverage and financial leverage

EPSDR = 70%

X1 X2

X3

EBITC1 C2 C3

DR = 0%

DR = 30%

Where, DR= Debt Ratio C1, C2, C3 = Indifference Point X1, X2, X3 = Financial BEP

8.4.4 Financial BEPItisthelevelofEBITwhichcoversallfixedfinancingcostsofthecompany.ItisthelevelofEBITatwhichEPSis zero.

8.4.5 Indifference PointIt is the point at which different sets of debt ratios (percentage of debt to total capital employed in the company) gives the same EPS.

8.5 Combined LeverageWhenthecompanyusesbothfinancialandoperatingleveragetomagnificationofanychangeinsalesintoalargerrelative changes in earning per share. Combined leverage is also called as composite leverage or total leverage.

Combined leverage express the relationship between the revenue in the account of sales and the taxable income.

Combined leverage can be calculated with the help of the following formulae:

Where, CL = Combined Leverage OL = Operating Leverage FL = Financial Leverage

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C = Contribution OP=OperatingProfit(EBIT) PBT=ProfitBeforeTax

8.5.1 Degree of Combined LeverageThepercentagechangeinafirm’searningpershare(EPS)resultsfromonepercentchangeinsales.Thisisalsoequaltothefirm’sdegreeofoperatingleverage(DOL)timesitsdegreeoffinancialleverage(DFL)ataparticularlevel of sales.

Calculation of financial leverage

Calculation of financial leverageEarning before Interest and Tax (EBIT) 5, 00,000Less: Interest on Debenture ( 8% of 12,50,000) 1,00,000Earnings before Tax 4,00,000

8.6 Working Capital LeverageOne of the new models of leverage is working capital leverage which is used to locate the investment in working capital or current assets in the company.

Working capital leverage measures the sensitivity of return in investment of charges in the level of current assets.

If the earnings are not affected by the changes in current assets, the working capital leverage can be calculated with the help of the following formula:

Where, CA = Current Assets TA = Total Assets DCA = Changes in the level of Current Assets


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8.7 Dividend DecisionsThefinancialmanagermusttakecarefuldecisionsonhowtheprofitshouldbedistributedamongshareholders.It is very important and crucial part of the business concern, because these decisions are directly related with the valueofthebusinessconcernandshareholder’swealth.Likefinancingdecisionandinvestmentdecision,dividenddecisionisalsoamajorpartofthefinancialmanager.Whenthebusinessconcernsdecidedividendpolicy,theyhaveto consider certain factors such as retained earnings and the nature of shareholder of the business concern.

8.7.1 Meaning of DividendDividendreferstothebusinessconcernsnetprofitsdistributedamongtheshareholders.Itmayalsobetermedasthepartoftheprofitofabusinessconcern,whichisdistributedamongitsshareholders.

AccordingtotheInstituteofCharteredAccountantofIndia,dividendisdefinedas“adistributiontoshareholdersoutofprofitsorreservesavailableforthispurpose.”

8.8 Types of DividendDividendmaybedistributedamongtheshareholdersintheformofcashorstock.Hence,dividendsareclassifiedinto:

Cash dividend•Stock dividend•Bond dividend•Property dividend•

Dividend

Cash Dividend Bond Dividend Stock Dividend Property Dividend

Fig. 8.2 Types of dividends

8.8.1 Cash DividendIf the dividend is paid in the form of cash to the shareholders, it is called cash dividend. It is paid periodically out the business concerns EAIT (Earnings after interest and tax). Cash dividends are common and popular types followed by majority of the business concerns.

8.8.2 Stock DividendStockdividendispaidintheformofthecompanystockduetorisingofmorefinance.Underthistype,cashisretainedby the business concern. Stock dividend may be bonus issue. This issue is given only to the existing shareholders of the business concern.

8.8.3 Bond DividendBonddividendisalsoknownasscriptdividend.Ifthecompanydoesnothavesufficientfundstopaycashdividend,thecompanypromisestopaytheshareholderatafuturespecificdatewiththehelpofissueofbondornotes.

8.8.4 Property DividendProperty dividends are paid in the form of some assets other than cash. It will distribute under the exceptional circumstance. This type of dividend is not published in India.

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8.9 Dividend DecisionDividenddecisionofthebusinessconcernisoneofthecrucialpartsofthefinancialmanager,becauseitdeterminestheamountofprofittobedistributedamongshareholdersandamountofprofittobetreatedasretainedearningsforfinancingitslong-termgrowth.Hence,dividenddecisionplaysveryimportantpartinthefinancialmanagement.

Dividend decision consists of two important concepts which are based on the relationship between dividend decision andvalueofthefirm.

DividendTheories

Irrelevance of Dividend

Relevance of Dividend

Solomon Approach MM Approach Walter's Model Godon's Model

Fig. 8.3 Dividend theories

8.9.1 Irrelevance of DividendAccording to professors Soloman, Modigliani and Miller, dividend policy has no effect on the share price of the company.Thereisnorelationbetweenthedividendrateandvalueofthefirm.Dividenddecisionisirrelevantofthevalueofthefirm.ModiglianiandMillercontributedamajorapproachtoprovetheirrelevancedividendconcept.

8.9.2 Modigliani and Miller’s ApproachAccording to MM, under a perfect market condition, the dividend policy of the company is irrelevant and it does notaffectthevalueofthefirm.

“Under conditions of perfect market, rational investors, absence of tax discrimination between dividend income and capitalappreciation,giventhefirm’sinvestmentpolicy,itsdividendpolicymayhavenoinfluenceonthemarketprice of shares.”

AssumptionsMM approach is based on the following important assumptions:

Perfect capital market.•Investors are rational.•There are no tax.•Thefirmhasfixedinvestmentpolicy.•No risk or uncertainty.•

Proof for MM approachMM approach can be proved with the help of the following formula:


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Where, = Prevailing market price of a share.= Cost of equity capital. = Dividend to be received at the end of period one.= Market price of the share at the end of period one.

can be calculated with the help of the following formula.

= (1+ ) –

The number of new shares to be issued can be determined by the following formula:

Where, M = Number of new share to be issued.

= Price at which new issue is to be made. I = Amount of investment required. X=Totalnetprofitofthefirmduringtheperiod. n = Total dividend paid during the period.

Criticism of MM approachMM approach consists of certain criticisms also. The following are the major criticisms of MM approach:

MMapproachassumesthattaxdoesnotexist.Itisnotapplicableinthepracticallifeofthefirm.•MM approach assumes that, there is no risk and uncertain of the investment. It is also not applicable in present •day business life.MMapproachdoesnotconsiderfloatationcostandtransactioncost.Itleadstoaffectthevalueofthefirm.•MM approach considers only single decrement rate, it does not exist in real practice.•MM approach assumes that, investor behaves rationally. But we cannot give assurance that all the investors •will behave rationally.

8.10 Relevance of DividendAccordingtothisconcept,dividendpolicyisconsideredtoaffectthevalueofthefirm.Dividendrelevanceimpliesthat shareholders prefer current dividend and there is no direct relationship between dividend policy and value of thefirm.RelevanceofdividendconceptissupportedbytwoeminentpersonslikeWalterandGordon.

8.10.1 Walter’s ModelProf.JamesE.Walterarguesthatthedividendpolicyalmostalwaysaffectsthevalueofthefirm.

Walter model is based in the relationship between the following important factors:Rate of return I•Cost of capital (k)•

AccordingtotheWalter’smodel,ifr>k,thefirmisabletoearnmorethanwhattheshareholderscouldbyreinvesting,if the earnings are paid to them. The implication of r > k is that the shareholders can earn a higher return by investing elsewhere.

Ifthefirmhasr=k,itisamatterofindifferentwhetherearningsareretainedordistributed.

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AssumptionsWalters model is based on the following important assumptions:

Thefirmusesonlyinternalfinance.•Thefirmdoesnotusedebtorequityfinance.•Thefirmhasconstantreturnandcostofcapital.•Thefirmhas100recentpayout.•ThefirmhasconstantEPSanddividend.•Thefirmhasaverylonglife.•

Walter has evolved a mathematical formula for determining the value of market share.

Where, P = Market price of an equity share D = Dividend per share r = Internal rate of return E = Earning per share

= Cost of equity capital

Criticism of Walter’s modelThe following are some of the important criticisms against Walter model:

Waltermodelassumesthatthereisnoextractedfinanceusedbythefirm.Itisnotpracticallyapplicable.•There is no possibility of constant return. Return may increase or decrease, depending upon the business situation. •Hence, it is applicable.According to Walter model, it is based on constant cost of capital. But it is not applicable in the real life of the •business.

8.10.2 Gordon’s ModelMyronGordensuggestsoneofthepopularmodelwhichassumesthatdividendpolicyofafirmaffectsitsvalue,and it is based on the following important assumptions:

Thefirmisanallequityfirm.•Thefirmhasnoexternalfinance.•Cost of capital and return are constant.•Thefirmhasperpetuallife.•There are no taxes.•Constant relation ratio (g=br).•Cost of capital is greater than growth rate (K• e>br).

Gordon’s model can be proved with the help of the following formula:

Where, P = Price of a share E = Earnings per share 1 – b = D/p ratio (i.e., percentage of earnings distributed as dividends)

= Capitalisation rate br=Growthrate=rateofreturnoninvestmentofanallequityfirm.


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Criticism of Gordon’s modelGordon’s model consists of the following important criticisms:

Gordonmodelassumesthatthereisnodebtandequityfinanceusedbythefirm.Itisnotapplicabletopresent•day business.

• and r cannot be constant in the real practice.AccordingtoGordon’smodel,therearenotaxpaidbythefirm.Itisnotpracticallyapplicable.•

8.11 Factors Determining Dividend PolicyFactors determining dividend policy are as follows:

Profitablepositionofthefirm:• Dividenddecisiondependsontheprofitablepositionofthebusinessconcern.Whenthefirmearnsmoreprofit,theycandistributemoredividendstotheshareholders.Uncertainty of future income: Future income is a very important factor, which affects the dividend policy. When •theshareholderneedsregularincome,thefirmshouldmaintainregulardividendpolicy.Legal constrains: The Companies Act 1956 has put several restrictions regarding payments and declaration of •dividends. Similarly, Income Tax Act, 1961 also lays down certain restrictions on payment of dividends.Liquidityposition:Liquiditypositionofthefirmsleadstoeasypaymentsofdividend.Ifthefirmshavehigh•liquidity,thefirmscanprovidecashdividendotherwise,theyhavetopaystockdividend.Sourcesoffinance:Ifthefirmhasfinancesources,itwillbeeasytomobiliselargefinance.Thefirmshallnot•go for retained earnings.Growth rate of the firm: High growth rate implies that the firm can distribute more dividend to its •shareholders.Taxpolicy:Taxpolicyofthegovernmentalsoaffectsthedividendpolicyofthefirm.Whenthegovernment•gives tax incentives, the company pays more dividend.Capital market conditions: Due to the capital market conditions, dividend policy may be affected. If the capital •market is prefect, it leads to improve the higher dividend.

8.12 Types of Dividend PolicyDividendpolicydependsuponthenatureofthefirm,typeofshareholderandprofitableposition.Onthebasisofthedividenddeclarationbythefirm,thedividendpolicymaybeclassifiedunderthefollowingtypes:

Regular dividend policy•Stable dividend policy•Irregular dividend policy•No dividend policy•

Regular dividend policyDividend payable at the usual rate is called as regular dividend policy. This type of policy is suitable to the small investors, retired persons and others.

Stable dividend policyStable dividend policy means payment of certain minimum amount of dividend regularly.This dividend policy consists of the following three important forms:

Constant dividend per share•Constant payout ratio•Stable rupee dividend plus extra dividend.•

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Irregular dividend policyWhen the companies are facing constraints of earnings and unsuccessful business operation, they may follow irregulardividendpolicy.Itisoneofthetemporaryarrangementstomeetthefinancialproblems.Thesetypesarehavingadequateprofit.Forothersnodividendisdistributed.

No dividend policySometimes the company may follow no dividend policy because of its unfavourable working capital position of the amount required for future growth of the concerns.


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SummaryFinancialdecisionisoneoftheintegralandimportantpartsoffinancialmanagementinanykindofbusiness•concern.Asoundfinancialdecisionmustconsider theboardcoverageof thefinancialmix (CapitalStructure), total•amount of capital (capitalisation) and cost of capital ( ).The term leverage refers to an increased means of accomplishing some purpose.•JamesHornehasdefinedleverageas,“theemploymentofanassetorfundforwhichthefirmpaysafixedcost•orfixedreturn."The leverage associated with investment activities is called as operating leverage.•Leverageactivitieswithfinancingactivitiesarecalledfinancialleverage.•Financialleveragemaybefavourableorunfavourabledependsupontheuseoffixedcostfunds.•One of the new models of leverage is working capital leverage which is used to locate the investment in working •capital or current assets in the company.The financial manager must take careful decisions on how the profit should be distributed among •shareholders.Dividendreferstothebusinessconcernsnetprofitsdistributedamongtheshareholders.•Dividend may be distributed among the shareholders in the form of cash or stock.•Accordingtothisconcept,dividendpolicyisconsideredtoaffectthevalueofthefirm.•Dividendpolicydependsuponthenatureofthefirm,typeofshareholderandprofitableposition.•Dividend payable at the usual rate is called as regular dividend policy.•Stable dividend policy means payment of certain minimum amount of dividend regularly.•

ReferencesDividend Policy. • [Pdf]Available at: <http://pages.stern.nyu.edu/~adamodar/pdfiles/acf2E/Chap10.pdf >[Accessed11April2014].Leverage. • [Pdf]Availableat:<http://ocw.mit.edu/courses/urban-studies-and-planning/11-431j-real-estate-finance-and-investment-fall-2006/lecture-notes/lec7.pdf>[Accessed11April2014].Baker, H. K., 2009. • Dividends and Dividend Policy. John Wiley & Sons.Paramasivan, C., 2009. • Financial Management. New Age International.Dividend Policy. CMA CS CA Video Lectures for CA CS Video Classes for CA FINAL and CS Professional. •[Videoonline]Availableat:<https://www.youtube.com/watch?v=XOvCtP3cdSI>[Accessed11April2014].Financial Management: Lecture 13, Chapter 17 - Dividends and Payout Policy. • [Videoonline]Availableat:<https://www.youtube.com/watch?v=P7DXvGZwKog>[Accessed11April2014].

Recommended ReadingShah, M., 2009. • Capital Management Accounting. Ane Books Pvt Ltd.Sarkar, S., 2011. • International Journal of Finance and Policy Analysis: Volume 3. U n i v e r s a l -P u b l i s h e r s .Chandra, P., 2005. • Fundamentals of Financial Management. Tata McGraw-Hill Education.

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Self Assessment__________decisionisoneoftheintegralandimportantpartsoffinancialmanagementinanykindofbusiness1. concern.

Dividenda. Financialb. Leveragec. Capitald.

The term _______ refers to an increased means of accomplishing some purpose.2. capitala. dividendb. leveragec. financed.

Match the following 3.

1. Operating leverage A. It is also called as composite leverage or total leverage.

2. Financial leverage B. It measures the sensitivity of return in investment of charges in the level of current assets.

3. Combined leverage C. The leverage associated with investment activities.

4. Working capital leverage D. It represents the relationship between the company’s earnings before interest and taxes (EBIT)

1- B, 2- A, 3- D, 4- Ca. 1- D, 2- C, 3- B, 4- Ab. 1- A, 2- B, 3- C, 4- Dc. 1- C, 2- D, 3- A, 4- Bd.

Whatreferstothebusinessconcernsnetprofitsdistributedamongtheshareholders?4. Leveragea. Dividendb. Financec. Bondd.

Which of the following dividend is paid in the form of cash to the shareholders?5. Cash dividenda. Stock dividendb. Bond dividendc. Property dividendd.

Which of the following is also known as script dividend?6. Cash dividenda. Stock dividendb. Bond dividendc. Property dividendd.


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__________decisiondependsontheprofitablepositionofthebusinessconcern.7. Leveragea. Dividendb. Financec. Bondd.

Which of the following statement is true?8. Thereisaffirmativerelationbetweenthedividendrateandvalueofthefirm.a. Thereispositiverelationbetweenthedividendrateandvalueofthefirm.b. Thereisnorelationbetweenthedividendrateandvalueofthefirm.c. Thereisarelationbetweenthedividendrateandvalueofthefirm.d.

_______policyofthegovernmentalsoaffectsthedividendpolicyofthefirm.9. Bonda. Leverageb. Cashc. Taxd.

Which of the following statement is false?10. MM approach assumes that tax does exist.a. MM approach assumes that, there is no risk and uncertain of the investment.b. MMapproachdoesnotconsiderfloatationcostandtransactioncost.c. MM approach considers only single decrement rate, it does not exist in real practice.d.

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Case Study I

Financial Report Analysis

Three Executives of a well-known multi-national company decided to form a new company, named New Star CompanyLimitedin1974.Thesethreeexecutiveswerebecomingclosetotheirretirementage.Pifco-ZenChenCompany Limited, the company that they worked for had been in business for the last 80 years. It was their previous employer’s policy to retire the executives with a “golden hand-shake” worth approximately US$120,000 each. The threeexecutivesoccupiedthefollowingpositionwithPifco-ZenChenCompanyLimited,

FinanceManager–Mr.ZuChang,•Sales & Marketing Manager, Mr. Lim Lam, and •Risk Management Manager, Mr. Shu Ching.•

IntheirpreviouspositionwithPifco-ZenChenCompanyLimited,theywereregardedasthemostrespectedexecutivesbecausethecompanymadesignificantprogressintermsoforganicgrowthanddiversification.TheChairmanoftheBoardofDirectors,Dr.WingWanusedtocallthem“thethreewisemen”.Pifco-ZenChenCompanyLimitedmainbusiness activities were the manufacturing of “twisties” and acted as wholesale distributor of a special drink called “Wysalt”. The drink is full of calcium and protein and it is very popular in the South East Asia. Each year’s Annual GeneralMeetingofPifco-ZenChenCompanyLimited’sgrossincomeandnetprofitbeforetaxationincreasedby10%, while its main competitor’s performance was declining at an alarming rate.

ChairmanWanalwayswantedtofindoutwhatisthemainreasondrivingitscompany’soperationalsuccess.Inanutshell,ChairmanWanalwaysbelievedthatthefinancialresultwas“toogoodtobetrue”becausewheneverhehas a chance to play golf with one of the Chairman of his competitor company, he was told that life as the head of a corporate is becoming unbearable due to competition and increased in the cost of living. Still, Mr. Wan kept quiet while congratulating his three wise men for a fantastic job each year. Even the external Auditors could not believe thesignificantprogress,whichthecompanyusedto,whenthethreewisemenwereworkingforPifco-ZenChenCompany Limited.

The auditors knowing too well the performance of the company before the departure of Mr. Chang, Mr. Lam, and Mr. Ching cautioned the Chairman that it would be a great loss for the company to loose three key executives in onego.Inviewofthecontinuedpressureandperplexitiesofthesituation,oneafternoon,ChairmanofPifco-ZenChen Company Limited, Dr. Wan called a special Board of Directors meeting to address his concern regarding the retirement of Mr. Chang, Mr. Lam, and Mr. Ching. One of the vocal directors who did not get along very well with these three managers, said “it does not matter if all of the three men were to leave the company today because they are not indispensable people”. He went on to argue further that “we can replace them easily because there are other professionals looking for work”.

Accordingtotheemploymentcontractofthethreewisemen,theywerepaidabasicsalaryplustheyalsobenefitedwitha2%commissiononthenetprofitofthecompanyeachyearaftertheaccountshavebeenfinalisedbytheexternal auditors. The Internal Auditor, Miss Wen always queried this employment terms that it favours mostly these three managers at the detriment of the other hard-working employees. One day in a management meeting, Miss Wen expressed her frustration of the favourable treatment of the three managers because she felt that they are working verycloseandperhaps,manipulatingthefiguressothattheycanbenefitaheftyremunerationeveryyear.ChairmanWan felt every uneasy during this meeting and closed the meeting earlier than expected. After the meeting, Miss Wen wrote a memo to the Chairman of the Board of Directors to complain that the external auditors come on the premises ofthecompanyforaveryshorttimetoperformtheaudit.TheydonotcarryoutanefficientauditandthePifco-ZenChen Company Limited runs the risk of facing a corporate collapse, when those three managers had left.


124

IntheabridgedversionofthefinancialstatementofPifco-ZenChenCompanyLimited,thefollowingitemappearsattheendofthefinancialyear1975. US$ (miilion)Net Fixed Assets 45Investment in Subsidiaries 30

Current Assets US$ (miilion)Stocks 125Debtors 90 Prepaid Expenses 40 Bank Deposits (7 Day Call Account) 60 Cash at Banks 30 Petty Cash 1 346

Less: Current Liabilities Creditors 45 Accrued Expenses 30 Short-Term Debt 55 Overdraft Balance 75 205 Net Current Assets/(Liabilities) 141 Total Net Assets 216 Financed by: Long-term Debts 80 Capital 90 AccumulatedProfituntil1975 46 136 216

InthefinancialstatementthereisanamountofUS$25millionworthofover-valuedstocks,whichhasbeeninthe accounts for the last 5 years. No provision has been made in the Debtors Account for non-performing account worth US$9 million. Current operating expenditure to the value of US$ 7 million has been accounted as “prepaid expenditure”. The bank reconciliation has not been done properly for the last 3 years, and the external auditors haveacceptedtheFinanceManager’sfigureofUS$30million.Itappearsthatthereare10chequesvaluedtoUS$3million has been deposited in the accounts, and have been returned by the banks because the customers did not havefunds.Therehasneednoadjustmentmadesubsequentlytocorrectthebalancesatbanks.Theexactfigurefor the Short-Term Debts should be US$ 65 million and not US$ 55 million as disclosed. There is a mistake in the disclosureofOverdraftFacility;thefigureshouldappearasUS$85millionandnotUS$75million.Inaddition,theSales&MarketingManagerhasenteredintoafinancialcontractforoneoftherawmaterialsupplierstosupplyequipmenttothevalueofUS$15milliontoincreaseproductionoftwistiesandthiscontractdoesnotreflectinthestatement of accounts.

Theexternalauditorstatedthatsincethereisonlyacommercialcontractandtheofficialinvoicehasnotbeenreceivedby the company, then there is no point to account for this transaction. A review of the quarterly report issued by the RiskManagerdoesnotindicateanyabnormalityinthefinancialstatementfromariskmanagementperspective.Instead, the Risk Manager would normally end his report with the words “I foresee that the company is operating in a very sound and successful manner. The Board of Directors should be proud of such achievement”. The Sales & Marketing Manager would give the indication that the company is progressing very well and eventually, it should be able to launch a “bid” to takeover one of its competitive rivals. The Finance Manager would normally end his

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reports with such phrases such as” good performance”, “we are on the right track” “the Board of Directors should feelproudofthecompany’sfinancialperformance”.

(Source: Case Study – Financial Report Analysis. [Online]Availableat:<http://predoc.org/docs/index-102996.html>[Accessed14April2014]).

QuestionsIsthecompanyontherighttrackafteryouhavereadthefinancialstatement?1. AnswerNo,whenallthefinancialadjustmentshavebeenmadetocorrectthestateofaffairs,thecompanyendsupinaverypoorfinancialstanding.

Thecompany’saccumulatedprofitofUS$46millionhasbeenturnedintoaNetLossofUS$18million.Itmeans that the total manipulation of the transactions amount to US$ 64 million.

Haveyouidentifiedanyproblemwiththiscompany?2. AnswerThe major problem of this company’s management is that the Chairman had relied too much on the professional judgement and honesty of the three managers.

Thecompanyriskslosingmoremoneyandperhapsofatake-overbid,whenthenewsfiltersinthemarket.

The New Star Company Limited also runs the risk of its own demise that customers would not trust the three owners,whentheywillgettoknowthefinancialmanipulationofPifco-ZenChenCompanyLtd.

Whoisresponsibleforthesadstateofaffairs,whichthecompanyfindsitself?3. AnswerNormally, when such a development takes place, the entire responsibility should be attributable to the Chairman as the Head of the Company and all the other directors.

It is the Board of Directors responsibility to ensure that the company, which they are managing from a strategic level, must perform in the best interest of all the stakeholders(e.g., shareholders,. employees, customers, suppliers, Government, media, Taxation, Competitor, Bankers, Financial Analysts, Community, etc.).


126

Case Study II

Quilici Family Case Study: Time Value of Money

GregandDebraQuiliciownafourbedroomhomeinanaffluentneighbourhoodjustnorthofSanFrancisco,California.Greg is a partner in the family-owned commercial painting business. Debra now stays home with their child, Brady, whoisagefive.Untilrecently,theQuilicishavefeltverycomfortablewiththeirfinancialposition.

AftervisitingLawrenceKrause,afamilyfinancialplanner,thecouplebecameconcernedthattheywerespendingtoo much and not putting enough funds aside for both their child’s future education needs and their own retirement. Greg earns $85 000 per year, but with the rising costs of education, their past contribution efforts have left them shortoftheirfinancialgoals.

To estimate the amount of money the Quilicis need to begin putting away for future security some general information wasobtainedby theirfinancialplanner.Thecouple felt that theamountofmoney theycurrentlycontribute totheirKoeghplanwouldbesufficient for their retirementneeds.What theyhadnotaccounted forwasBrady’seducation.

Greg is an alumnus of Stanford University, a private school with an extremely high tuition fee of approximately $20 000 per year. Debra graduated from the University of North Carolina at Chapel Hill. The tuition expense there is only $2 500 per year. When Brady turns 18, the couple wishes to send him to either of these exceptional universities. They have a slight preference for the much more local Stanford University. The problem, however, is that with the rate at which tuition is increasing the Quilicis are not sure they can raise enough money.

Toassistinthecalculations,assumethetuitionatbothuniversitieswillincreaseatanannualrateoffivepercent.Living expenses are currently estimated at $6 000 per year at both schools. This expense is expected to grow at only three per cent per year. Further assume the Quilicis can deposit their money into a growth oriented mutual fund at Neuberger & Berman Management, Inc., which has historically earned a 12 per cent return per annum (one per cent per month).

The couple wishes to have a pre-determined monthly amount automatically drafted from their checking account. When Brady starts college they will slowly liquidate the account by making an annual payment to Brady to cover tuition and living expenses at the beginning of each year for the four years he will be in college.

(Source: Quilici Family Case Study: Time value of money. [Online]Availableat:<http://wps.pearsoned.com.au/au_be_gitman_prinmgrlfin_4/25/6455/1652657.cw/-/1652701/index.html>[Accessedon14April2014])

QuestionsWhat is the problem faced by Quilici family?1. What is the solution for this problem?2. How much will the tuition and living expenses be per year when Brady is ready to attend?3.

127

Case Study III

Basic concepts: The time value of money

After graduating from Ohio State University with a degree in Finance, Kate Myers took a position as a stock broker with Merrill Lynch in Cleveland. Although she had several college loans to make payments on, her goal was to set aside funds for the next eight years in order to make a down payment on a house. After considering the various suburbs of Cleveland, Kate chose Lakewood as her desired future residency. Based on median house price data, she learned that a three-bedroom, two-bath house currently costs $98 000. To avoid paying Private Mortgage Insurance (PMI), Kate wanted to make a down payment of 20 per cent.

Because it will be eight years before Kate buys a house, the $98 000 price will surely not be the same in the future. To estimate the rate at which the median house price will increase, she considered the historical price appreciation in Lakewood.Inthepast,homesappreciatedbynearlyfourpercentperannum.Katewassatisfiedwiththisestimation.Merrill Lynch provides several opportunities for Kate to invest the funds that will be devoted to the purchase of her future home. She feels that a balanced account containing stocks, bonds, and government securities would realistically achieve an annual rate of return of eight per cent.

(Source: Quilici Family Case Study: Time value of money. [Online]Availableat:<http://wps.pearsoned.com.au/au_be_gitman_prinmgrlfin_4/25/6455/1652657.cw/-/1652701/index.html>[Accessedon14April2014])

QuestionsWhat is the issue here?1. Taking into consideration the fact that the $98 000 home price will grow at four per cent per year, what will 2. be the future median home selling price in Lakewood in eight years? What amount will Kate Myers have to accumulate as a down payment if she does decide to buy a house in Lakewood?If Kate decides to make end-of-the-year deposits into the Merrill Lynch account, how much would these deposits 3. be?


128

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Hampton, J. J., 2011. • The AMA Handbook of Financial Risk Management. AMACOM Div American Mgmt Assn.Introduction to Bond Valuation. • [Pdf]Available at:<http://www.arts.uwaterloo.ca/~kvetzal/AFM271/bond.pdf>[Accessed11April2014].Introduction to Capital Budgeting. • [Pdf]Availableat:<http://finance.wharton.upenn.edu/~benninga/pfe_chap07.pdf>[Accessed11April2014].Introduction to Financial Statement Analysis. • [Pdf]Availableat:<http://www.swlearning.com/ibc/albrecht9e/pdf/Albrecht9e_c05_202-253_low.pdf>[Accessed11April2014].Introduction to Financial Statements. • [Video online]Available at: <http://www.youtube.com/watch?v=sAMSQ02X0-o>[Accessed11April2014].Johnson, R. S., 2010. • Bond Evaluation, Selection, and Management. John Wiley & Sons.Leverage. • [Pdf]Availableat:<http://ocw.mit.edu/courses/urban-studies-and-planning/11-431j-real-estate-finance-and-investment-fall-2006/lecture-notes/lec7.pdf>[Accessed11April2014].Lieuallen, G. G., 2009. • Basic Federal Income Tax, Aspen Publishers Online.Paramasivan, C., 2009. • Financial Management. New Age International.Patterson, C. S., 1995. • The Cost of Capital: Theory and Estimation. Greenwood Publishing Group.Peterson, P. P., 2004. • Capital Budgeting: Theory and Practice. John Wiley & Sons.Pratt, S. P. & Grabowski, R. J., 2014. • Cost of Capital: Applications and Examples. John Wiley & Sons.Risk and Return Part 1.mp4. • [Videoonline]Availableat:<http://www.youtube.com/watch?v=lZceJi9XTnQ>[Accessed11April2014].Risk and Return. • [Pdf]Availableat:<http://www2.gsu.edu/~fnccwh/pdf/f03.pdf>[Accessed11April2014].Risk and Return. • [Pdf]Available at:<http://highered.mcgraw-hill.com/sites/dl/free/0070997594/918724/Peirson11e_Ch07.pdf>[Accessed11April2014].Robinson, T. R., Henry, E., Pirie, W. L., & Broihanhn, M. A., 2012. • International Financial Statement Analysis, 3rd ed., John Wiley & Sons, UK.Shapiro, A. C., 2008. • Capital Budgeting and Investment Analysis. Pearson Education India.Singla, R. K., 1996. • Corporate Capital Structure: Planning and Determinants: Theory and Practice. Deep and Deep Publications.The Cost of Capital. • [Pdf]Availableat:<http://www.goldsmithibs.com/resources/free/Cost-of-Capital/notes/Summary%20-%20Cost%20of%20Capital.pdf>[Accessed11April2014].The Cost of Capital. • [Pdf]Availableat:<http://www.prenhall.com/divisions/bp/app/Berk/docs/Chapter12.pdf>[Accessed11April2014].The Time Value of Money. • [Pdf]Availableat:<http://homepages.rpi.edu/~tealj2/arch4.pdf>[Accessed11April2014].Time Value of Money (concept explained). • [Video online]Available at: <http://www.youtube.com/watch?v=gkoEAPAW7eg>[Accessed11April2014].Time Value of Money Overview. • [Videoonline]Availableat:<http://www.youtube.com/watch?v=rZXuh3ECzlc>[Accessed11April2014].Tuller, L. W., 1994. • High-Risk, High-Return Investing. John Wiley & Sons.

Recommended ReadingArmitage, J., 2005. • The Cost of Capital: Intermediate Theory. Cambridge University Press.Baker, H. K., 2011. • Capital Budgeting Valuation: Financial Analysis for Today’s Investment Projects. John Wiley & Sons.Bierman, H., & Smidt, S., 2007. • The Capital Budgeting Decision: Economic Analysis of Investment Projects. Routledge.


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Chandra, P., 2005. • Fundamentals of Financial Management. Tata McGraw-Hill Education.Connor, G., Goldberg, L. R. & Korajczyk, R. A. 2010. • Portfolio Risk Analysis. P r i n c e t o n U n i v e r s i t y P r e s s .Damodaran, A., 2008. • Strategic Risk Taking: A Framework for Risk Management. Pearson Prentice Hall.Dayananda, D., 2002. • Capital Budgeting: Financial Appraisal of Investment Projects. C a m b r i d g e U n i v e r s i t y P r e s s .Denne, M. & Cleland-Huang, J. 2004. • Software by Numbers: Low-Risk, High-Return Development. Prentice Hall Professional.Doss, D. A., Sumrall III, W. H., Jones, D. W., 1999. • Strategic Finance for Criminal Justice Organizations. CRC Press.Epstein, L., 2009. • The Complete Idiot’s Guide to Value Investing. P e n g u i n .Fabozzi, F. J., 2009. • Institutional Investment Management: Equity and Bond Portfolio Strategies and Applications. John Wiley & Sons.Foster, G. , 1978. • Financial Statement Analysis, 2/e. Springer. Ghosh, A., 2012. • Capital Structure and Firm Performance. Transaction Publishers.Gibson, C., 2012. • Financial Reporting and Analysis. Cengage Learning.Jorgenson, D. W. & Lau, L. J., 2000. • Econometrics. M I T P r e s s .Keown, • Financial Management: Principles and Applications, 10/e. Pearson Education India.Ogier, T., 2013. • The Real Cost of Capital ePub. Pearson, UK.Periasamy, P., 2009. • Financial Management. 2 n d e d . , Ta t a M c G r a w - H i l l E d u c a t i o n .Peterson, P. P., & Fabozzi, F. J., 1999. • Analysis of Financial Statements. John Wiley & Sons.Richelson, H. & Richelson, S., 2011. • Bonds: The Unbeaten Path to Secure Investment Growth. John Wiley & Sons.Sarkar, S., 2011. • International Journal of Finance and Policy Analysis: Volume 3. U n i v e r s a l -P u b l i s h e r s .Shah, M., 2009. • Capital Management Accounting. Ane Books Pvt Ltd.Sheeba, K., • Financial Management. Pearson Education India. Singla, R. K., • Business Studies. FK Publications.

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Self Assessment Answers

Chapter Ic1. c2. d3. d4. d5. a6. b7. c8. a9. c10.

Chapter IIa1. d2. c3. d4. a5. d6. a7. b8. d9. c10.

Chapter IIIb1. c2. d3. a4. b5. d6. d7. a8. b9. d10.

Chapter IVc1. c2. d3. a4. b5. a6. d7. b8. d9. c10.


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Chapter Vb1. c2. a3. d4. c5. a6. b7. d8. a9. c10.

Chapter VIb1. a2. c3. c4. a5. c6. a7. d8. b9. a10.

Chapter VIIa1. b2. d3. c4. b5. a6. b7. b8. d9. a10.

Chapter VIIIb1. c2. d3. b4. a5. c6. b7. c8. d9. a10.

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