mastering financial mathematics in microsoft excel contents
DESCRIPTION
Mastering Financial Mathematics in Microsoft Excel ContentsTRANSCRIPT
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 117
MASTERINGFINANCIAL
MATHEMATICS
A practical guide forbusiness calculations
in Microsoftreg Excel
ALASTAIR L DAY
second edition
bull An invaluable explanation of basic calculations and
their underlying financial concepts
bull Includes a companion CD with practical examples
exercises and templates
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 217
Mastering Financial Mathematicsin Microsoftreg Excel
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 317
In an increasingly competitive world we believe itrsquos quality of
thinking that gives you the edge ndash an idea that opens new doors a technique that solves a problem or an insight that
simply makes sense of it all The more you know the smarterand faster you can go
Thatrsquos why we work with the best minds in business and financeto bring cutting-edge thinking and best learning practice to a
global market
Under a range of leading imprints including Financial Times
Prentice Hall we create world-class print publications andelectronic products bringing our readers knowledge skills and
understanding which can be applied whether studying or at work
To find out more about Pearson Education publications or tellus about the books yoursquod like to find you can visit us at
wwwpearsonedcouk
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 417
Mastering FinancialMathematics in
Microsoftreg Excel
A practical guide for business calculations
Second Edition
ALASTAIR L DAY
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 517
PEARSON EDUCATION LIMITED
Edinburgh GateHarlow CM20 2JETel +44 (0)1279 623623Fax +44 (0)1279 431059
Website wwwpearsonedcouk
First published in Great Britain in 2005Second edition 2010
copy Pearson Education Limited 2005 2010
The right of Alastair Day to be identified as author of this work has been assertedby him in accordance with the Copyright Designs and Patents Act 1988
ISBN 978-0-273-73033-0
British Library Cataloguing-in-Publication DataA catalogue record for this book is available from the British Library
Library of Congress Cataloging-in-Publication DataDay Alastair L Mastering financial mathematics in Microsoft Excel a practical guide forbusiness calculations Alastair Day -- 2nd ed p cm -- (Market editions) Includes index ISBN 978-0-273-73033-0 (pbk) 1 Business mathematics 2 Microsoft Excel (Computer file) I Title HF5691D39 2010
6500285554--dc22 2010005343
All rights reserved No part of this publication may be reproduced storedin a retrieval system or transmitted in any form or by any means electronicmechanical photocopying recording or otherwise without either the priorwritten permission of the publisher or a licence permitting restricted copyingin the United Kingdom issued by the Copyright Licensing Agency LtdSaffron House 6ndash10 Kirby Street London EC1N 8TS This book may not belent resold hired out or otherwise disposed of by way of trade in any form ofbinding or cover other than that in which it is published without the priorconsent of the Publishers
Microsoft product screen shots reprinted with permission from MicrosoftCorporation
10 9 8 7 6 5 4 3 2 114 13 12 11 10
Typeset in Garamond 115135pt by 30Printed and bound in Great Britain by Ashford Colour Press Ltd Gosport Hants
The Publisherrsquos policy is to use paper manufactured from sustainable forests
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 617
v
Contents
Acknowledgements x
About the author xi
Conventions xii
Overview xiii
Warranty and disclaimer xv
1 Introduction 1
Overview 3 Common Excel errors 4 Systematic design method 6 Auditing 10 Summary 12
2 Basic financial arithmetic 13
Simple interest 15 Compound interest 19 Nominal and effective rates 24 Continuous discounting 26 Conversions and comparisons 27 Exercise 28 Summary 28
3 Cash flows 29
Net present value 31 Internal rate of return 34 XNPV and XIRR 37 XNPV periodic example 38 Modified internal rate of return 39 Exercise 41 Summary 41
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 717
vi
4 Bonds calculations 43
Description 45 Cash flows 48 Zero coupons 50
Yield 51 Yield to call 51 Price and yield relationship 53 Yield curve pricing 53 Other yield measures 55 Yield measures 57 Exercise 59 Summary 59
5 Bonds risks61
Risks 63 Duration 66 Convexity 70 Comparison 75 Exercise 77 Summary 77
6 Floating rate securities 79
Floating rates 81 Characteristics of interest rate securities 82 Yield evaluation 84 Coupon stripping 89 Exercise 90 Summary 91
7 Amortization and depreciation 93
Amortization 95
Full amortization 97 Delayed payments 97 Sum of digits 100 Straight line and declining balance depreciation 101 UK declining balance method 103 Double declining balance depreciation 104 French depreciation 105 Exercise 107 Summary 108
Contents
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 817
vii
8 Swaps 109
Definitions 111 How swaps save money 114 Advantages of swaps 115
Terminating interest rate swaps 116 Implicit credit risk 117 Worked single currency swap 117 Valuation 119 Cross currency swap 120 Worked example 121 Swaptions 122 Exercise 124 Summary 124
9 Forward interest rates 125
Definitions 127 Example forward rates 127 Hedging principles 130 Forward rate agreement 131 Yield curves 134 Exercise 138 Summary 138
10 Futures 139
Futures market 141 Terminology 142 Benefits 143 Clearinghouse operation 144 Bond futures 145 Hedging mechanisms 145 Hedging example one 147
Hedging example two 149 Exercise 152 Summary 152
11 Foreign exchange 153
Risk 155 Spot rates 157 Longer dates 161 Equivalence 162
Comparisons and arbitrage 164 Exercise 165 Summary 165
Contents
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 917
12 Options 167
Description 169 Terminology 170 Underlying asset 172
Call options 172 Put options 176 Example 178 Covered call 180 Insurance using a stock and a long put 182 Pricing models 182 Black Scholes model 184 Call put parity 187 Greeks 188
Binomial models 191 Comparison to Black Scholes 194 Exercise 198 Summary 198
13 Real options 199
Real options 201 Black Scholes model 202 Binomial model 203
Exercise 205 Summary 205
14 Valuation 207
Valuation methods 209 Assets 210 Market methods 211 Multi-period dividend discount models 213 Free cash flow valuation 215
Adjusted present value 224 Economic profit 227 Exercise 229 Summary 230
15 Leasing 231
Economics of leasing 233 Interest rates 235 Classification 236
Amortization 241 Accounting 242 Settlements 243
viii
Contents
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1017
Lessor evaluation 246 Lessee evaluation 250 Exercise 252 Summary 253
16 Basic statistics 255
Methods 257 Descriptive statistics 257 Probability distributions 270 SamplingCentral Limit Theorem 277 Hypothesis testing 282 Correlation and regression 293 LINEST function 302
Exercise 304 Summary 304
Appendices 307
1 Exercise answers functions list software installation and licence 309
2 An introduction to Microsoftreg Office 2007 (Office 12) 345
Index 359
ix
Contents
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1117
Acknowledgements
I would like to thank Angela Matthew and Frances for their support
and assistance with the completion of this book In addition Christopher
Cudmore Martina OrsquoSullivan and Laura Blake of Pearson Education have
provided valuable support and backing for this project
x
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1217
xi
About the author
Alastair Day has worked in the finance industry for more than 25 yearsin treasury and marketing functions and was formerly a director of avendor leasing company specializing in the IT and technology indus-
tries After rapid growth the directors sold the enterprise to a publiccompany and he established Systematic Finance as a consultancy special-izing in
983119 financial modelling ndash review design build and audit
983119 training in financial modelling corporate finance leasing and credit
analysis on an in-house and public basis throughout Europe Middle East
Africa and America
983119 finance and operating lease structuring as a consultant and lessor
Alastair is author of three modelling books published by FT Prentice Hall Mastering Financial Modelling Mastering Risk Modelling and Mastering
Financial Mathematics in Excel apart from other books and publications on
financial analysis and leasing
Alastair has a degree in Economics and German from LondonUniversity and an MBA from the Open University Business School
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1317
xii
Conventions
983119 The main part of the text is set in AGaramond whereas entries are set in
Courier For example
Enter the Scenario Name as Base Case
983119 Items on the menu bars also shown in Courier For example
Select Tools Goal Seek
983119 The names of functions are in Courier capitals This is the payment
function which requires inputs for the interest rate number of periods
present value and future value
=PMT(INTNPERPVFVTYPE)
983119 Cell formulas are also shown in Courier For example
=IF($C$75=1IF($B25gtC$22$B25-C$22-C$23-
C$23)IF($B25ltC$22C$22-$B25-C$23-C$23))
983119 Equations are formed with the equation editor and shown in normal
notation For example net present value
(CashFlow) N
NPV = ndashndashndashndashndashndashndashndashndashndash (1 + r) N
983119 Genders The use of lsquohersquo or lsquohimrsquo refers to masculine or feminine and this
is used for simplicity to avoid repetition
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1417
xiii
Overview
WHO NEEDS THIS BOOK
More than 20 years ago I used a Hewlett Packard 38C to calculate interest
rates and analyse cash flows and then progressed to an HP 41C with a printer
magnetic strip reader and plug-in finance and mathematics packs This wasan early alphanumeric calculator which gave me the opportunity to program
lease versus purchase or lessor lease evaluation cash flows and structure more
complex lease structures This is before IBM launched the personal compu-
ter in the early 1980s Since that time I have progressed through calculators
such as the HP 12C HP 17BII HP 19B or TI BAII Plus which all provide
dedicated user screens and allow you to undertake financial mathematics
While calculators are much easier than tables or earlier methods they can
be difficult to use without errors When I run training courses on the basic
financial calculations the main drawback is only too obvious you cannot see
your inputs or check the interim calculations and therefore delegates always
want to see a map of the variables to understand the answer
While I have continued to use financial calculators which have now been
augmented with other programs on mobile phones using Windows Mobile
or a selection of applications on Apple iPhones and have in the past created
programs in Basic the most comprehensive medium for financial mathe-
matics has grown to be Microsoftreg Excel I first used Lotus in 1988 and
Excel 30 in 1990 and through various upgrades Excel grew into Microsoftreg
Office 2007 which remains little changed in the core financial functions
through to todayrsquos versions Given that almost everybody in finance has Excel on their desks and
increasingly on their laptops phones or pocket computers the objective
of this book is to explain the basic calculations for mathematical finance
backed up by simple templates for further use and development together
with examples and exercises If you work through each of the chapters in the
book and try the exercises you will improve your Excel skills and obtain a
better grasp of the underlying financial concepts
My other modelling books published by FT Prentice Hall Mastering
Financial Modelling and Mastering Risk Modelling provide complete modelsfor some of the topics in this book and combine finance with model design
using ideas of best practice coupled with methods of auditing and testing
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1517
xiv
This book adheres to systematic spreadsheet best practice and adopts the
same colour scheme method and layout
The key objectives for this book are to
983119 provide explanation of key financial formulas and subject areas
983119 show the use of the formulas using straightforward Excel templates
983119 introduce examples and exercises for extension work
983119 provide a library of basic templates for further development
This book aims to assist two key groups
983119 practitioners who want a manual of financial mathematics from which
they can gain immediate use and payback
983119 business students who need a textbook which is more geared to Excel
solutions than some college manualsThe areas of responsibility where the book should be of interest are
983119 CFOs and finance directors
983119 financial controllers
983119 financial analysts and executives
983119 accountants
983119 corporate finance specialists
983119
treasury managers 983119 risk managers
983119 academics business and MBA students
Therefore people interested in this book range from a company accountant
who wants a reference book to academics and business students who need a
financial mathematics manual in Excel The book has an international bias
and will provide examples which are relevant to the UK and overseas
HOW TO USE THIS BOOK
983119 Install the Excel application templates using the simple SETUP com-
mand The files will install automatically together with a program group
and icons There is a key to the file names on page 343
983119 Work through each of the chapters and the examples
983119 Use the manual spreadsheets and templates as a reference guide for fur-
ther work
983119 Practise develop and improve your efficiency and competence with Excel
Alastair L Day
Email adaysystemcouk or Internet wwwfinancial-modelscom
Overview
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1617
xv
Warranty and disclaimer
The financial models used in the book have not been formally audited and
no representation warranty or undertaking (express or implied) is made and
no responsibility is taken or accepted by Systematic Finance and its direc-
tors as to the adequacy accuracy completeness or reasonableness of the
financial models and the company excludes liability thereof
In particular no responsibility is taken or accepted by the company and
all liability is excluded by the company for the accuracy of the computations
comprised therein and the assumptions upon which such computations are
based In addition the reader receives and uses the financial models entirely
at his own risk and no responsibility is taken or accepted by the Company
and accordingly all liability is excluded by the company for any losses which
may result from the use of the financial models whether as a direct or indi-
rect consequence of a computer virus or otherwise
Microsoft Microsoft Excel Windows and Windows XP are either re-
gistered trademarks or trademarks of Microsoft Corporation in the United
States andor other countries Screen shots reprinted by permission from
Microsoft Corporation
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1717
1
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 217
Mastering Financial Mathematicsin Microsoftreg Excel
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 317
In an increasingly competitive world we believe itrsquos quality of
thinking that gives you the edge ndash an idea that opens new doors a technique that solves a problem or an insight that
simply makes sense of it all The more you know the smarterand faster you can go
Thatrsquos why we work with the best minds in business and financeto bring cutting-edge thinking and best learning practice to a
global market
Under a range of leading imprints including Financial Times
Prentice Hall we create world-class print publications andelectronic products bringing our readers knowledge skills and
understanding which can be applied whether studying or at work
To find out more about Pearson Education publications or tellus about the books yoursquod like to find you can visit us at
wwwpearsonedcouk
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 417
Mastering FinancialMathematics in
Microsoftreg Excel
A practical guide for business calculations
Second Edition
ALASTAIR L DAY
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 517
PEARSON EDUCATION LIMITED
Edinburgh GateHarlow CM20 2JETel +44 (0)1279 623623Fax +44 (0)1279 431059
Website wwwpearsonedcouk
First published in Great Britain in 2005Second edition 2010
copy Pearson Education Limited 2005 2010
The right of Alastair Day to be identified as author of this work has been assertedby him in accordance with the Copyright Designs and Patents Act 1988
ISBN 978-0-273-73033-0
British Library Cataloguing-in-Publication DataA catalogue record for this book is available from the British Library
Library of Congress Cataloging-in-Publication DataDay Alastair L Mastering financial mathematics in Microsoft Excel a practical guide forbusiness calculations Alastair Day -- 2nd ed p cm -- (Market editions) Includes index ISBN 978-0-273-73033-0 (pbk) 1 Business mathematics 2 Microsoft Excel (Computer file) I Title HF5691D39 2010
6500285554--dc22 2010005343
All rights reserved No part of this publication may be reproduced storedin a retrieval system or transmitted in any form or by any means electronicmechanical photocopying recording or otherwise without either the priorwritten permission of the publisher or a licence permitting restricted copyingin the United Kingdom issued by the Copyright Licensing Agency LtdSaffron House 6ndash10 Kirby Street London EC1N 8TS This book may not belent resold hired out or otherwise disposed of by way of trade in any form ofbinding or cover other than that in which it is published without the priorconsent of the Publishers
Microsoft product screen shots reprinted with permission from MicrosoftCorporation
10 9 8 7 6 5 4 3 2 114 13 12 11 10
Typeset in Garamond 115135pt by 30Printed and bound in Great Britain by Ashford Colour Press Ltd Gosport Hants
The Publisherrsquos policy is to use paper manufactured from sustainable forests
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 617
v
Contents
Acknowledgements x
About the author xi
Conventions xii
Overview xiii
Warranty and disclaimer xv
1 Introduction 1
Overview 3 Common Excel errors 4 Systematic design method 6 Auditing 10 Summary 12
2 Basic financial arithmetic 13
Simple interest 15 Compound interest 19 Nominal and effective rates 24 Continuous discounting 26 Conversions and comparisons 27 Exercise 28 Summary 28
3 Cash flows 29
Net present value 31 Internal rate of return 34 XNPV and XIRR 37 XNPV periodic example 38 Modified internal rate of return 39 Exercise 41 Summary 41
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 717
vi
4 Bonds calculations 43
Description 45 Cash flows 48 Zero coupons 50
Yield 51 Yield to call 51 Price and yield relationship 53 Yield curve pricing 53 Other yield measures 55 Yield measures 57 Exercise 59 Summary 59
5 Bonds risks61
Risks 63 Duration 66 Convexity 70 Comparison 75 Exercise 77 Summary 77
6 Floating rate securities 79
Floating rates 81 Characteristics of interest rate securities 82 Yield evaluation 84 Coupon stripping 89 Exercise 90 Summary 91
7 Amortization and depreciation 93
Amortization 95
Full amortization 97 Delayed payments 97 Sum of digits 100 Straight line and declining balance depreciation 101 UK declining balance method 103 Double declining balance depreciation 104 French depreciation 105 Exercise 107 Summary 108
Contents
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 817
vii
8 Swaps 109
Definitions 111 How swaps save money 114 Advantages of swaps 115
Terminating interest rate swaps 116 Implicit credit risk 117 Worked single currency swap 117 Valuation 119 Cross currency swap 120 Worked example 121 Swaptions 122 Exercise 124 Summary 124
9 Forward interest rates 125
Definitions 127 Example forward rates 127 Hedging principles 130 Forward rate agreement 131 Yield curves 134 Exercise 138 Summary 138
10 Futures 139
Futures market 141 Terminology 142 Benefits 143 Clearinghouse operation 144 Bond futures 145 Hedging mechanisms 145 Hedging example one 147
Hedging example two 149 Exercise 152 Summary 152
11 Foreign exchange 153
Risk 155 Spot rates 157 Longer dates 161 Equivalence 162
Comparisons and arbitrage 164 Exercise 165 Summary 165
Contents
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 917
12 Options 167
Description 169 Terminology 170 Underlying asset 172
Call options 172 Put options 176 Example 178 Covered call 180 Insurance using a stock and a long put 182 Pricing models 182 Black Scholes model 184 Call put parity 187 Greeks 188
Binomial models 191 Comparison to Black Scholes 194 Exercise 198 Summary 198
13 Real options 199
Real options 201 Black Scholes model 202 Binomial model 203
Exercise 205 Summary 205
14 Valuation 207
Valuation methods 209 Assets 210 Market methods 211 Multi-period dividend discount models 213 Free cash flow valuation 215
Adjusted present value 224 Economic profit 227 Exercise 229 Summary 230
15 Leasing 231
Economics of leasing 233 Interest rates 235 Classification 236
Amortization 241 Accounting 242 Settlements 243
viii
Contents
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1017
Lessor evaluation 246 Lessee evaluation 250 Exercise 252 Summary 253
16 Basic statistics 255
Methods 257 Descriptive statistics 257 Probability distributions 270 SamplingCentral Limit Theorem 277 Hypothesis testing 282 Correlation and regression 293 LINEST function 302
Exercise 304 Summary 304
Appendices 307
1 Exercise answers functions list software installation and licence 309
2 An introduction to Microsoftreg Office 2007 (Office 12) 345
Index 359
ix
Contents
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1117
Acknowledgements
I would like to thank Angela Matthew and Frances for their support
and assistance with the completion of this book In addition Christopher
Cudmore Martina OrsquoSullivan and Laura Blake of Pearson Education have
provided valuable support and backing for this project
x
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1217
xi
About the author
Alastair Day has worked in the finance industry for more than 25 yearsin treasury and marketing functions and was formerly a director of avendor leasing company specializing in the IT and technology indus-
tries After rapid growth the directors sold the enterprise to a publiccompany and he established Systematic Finance as a consultancy special-izing in
983119 financial modelling ndash review design build and audit
983119 training in financial modelling corporate finance leasing and credit
analysis on an in-house and public basis throughout Europe Middle East
Africa and America
983119 finance and operating lease structuring as a consultant and lessor
Alastair is author of three modelling books published by FT Prentice Hall Mastering Financial Modelling Mastering Risk Modelling and Mastering
Financial Mathematics in Excel apart from other books and publications on
financial analysis and leasing
Alastair has a degree in Economics and German from LondonUniversity and an MBA from the Open University Business School
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1317
xii
Conventions
983119 The main part of the text is set in AGaramond whereas entries are set in
Courier For example
Enter the Scenario Name as Base Case
983119 Items on the menu bars also shown in Courier For example
Select Tools Goal Seek
983119 The names of functions are in Courier capitals This is the payment
function which requires inputs for the interest rate number of periods
present value and future value
=PMT(INTNPERPVFVTYPE)
983119 Cell formulas are also shown in Courier For example
=IF($C$75=1IF($B25gtC$22$B25-C$22-C$23-
C$23)IF($B25ltC$22C$22-$B25-C$23-C$23))
983119 Equations are formed with the equation editor and shown in normal
notation For example net present value
(CashFlow) N
NPV = ndashndashndashndashndashndashndashndashndashndash (1 + r) N
983119 Genders The use of lsquohersquo or lsquohimrsquo refers to masculine or feminine and this
is used for simplicity to avoid repetition
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1417
xiii
Overview
WHO NEEDS THIS BOOK
More than 20 years ago I used a Hewlett Packard 38C to calculate interest
rates and analyse cash flows and then progressed to an HP 41C with a printer
magnetic strip reader and plug-in finance and mathematics packs This wasan early alphanumeric calculator which gave me the opportunity to program
lease versus purchase or lessor lease evaluation cash flows and structure more
complex lease structures This is before IBM launched the personal compu-
ter in the early 1980s Since that time I have progressed through calculators
such as the HP 12C HP 17BII HP 19B or TI BAII Plus which all provide
dedicated user screens and allow you to undertake financial mathematics
While calculators are much easier than tables or earlier methods they can
be difficult to use without errors When I run training courses on the basic
financial calculations the main drawback is only too obvious you cannot see
your inputs or check the interim calculations and therefore delegates always
want to see a map of the variables to understand the answer
While I have continued to use financial calculators which have now been
augmented with other programs on mobile phones using Windows Mobile
or a selection of applications on Apple iPhones and have in the past created
programs in Basic the most comprehensive medium for financial mathe-
matics has grown to be Microsoftreg Excel I first used Lotus in 1988 and
Excel 30 in 1990 and through various upgrades Excel grew into Microsoftreg
Office 2007 which remains little changed in the core financial functions
through to todayrsquos versions Given that almost everybody in finance has Excel on their desks and
increasingly on their laptops phones or pocket computers the objective
of this book is to explain the basic calculations for mathematical finance
backed up by simple templates for further use and development together
with examples and exercises If you work through each of the chapters in the
book and try the exercises you will improve your Excel skills and obtain a
better grasp of the underlying financial concepts
My other modelling books published by FT Prentice Hall Mastering
Financial Modelling and Mastering Risk Modelling provide complete modelsfor some of the topics in this book and combine finance with model design
using ideas of best practice coupled with methods of auditing and testing
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1517
xiv
This book adheres to systematic spreadsheet best practice and adopts the
same colour scheme method and layout
The key objectives for this book are to
983119 provide explanation of key financial formulas and subject areas
983119 show the use of the formulas using straightforward Excel templates
983119 introduce examples and exercises for extension work
983119 provide a library of basic templates for further development
This book aims to assist two key groups
983119 practitioners who want a manual of financial mathematics from which
they can gain immediate use and payback
983119 business students who need a textbook which is more geared to Excel
solutions than some college manualsThe areas of responsibility where the book should be of interest are
983119 CFOs and finance directors
983119 financial controllers
983119 financial analysts and executives
983119 accountants
983119 corporate finance specialists
983119
treasury managers 983119 risk managers
983119 academics business and MBA students
Therefore people interested in this book range from a company accountant
who wants a reference book to academics and business students who need a
financial mathematics manual in Excel The book has an international bias
and will provide examples which are relevant to the UK and overseas
HOW TO USE THIS BOOK
983119 Install the Excel application templates using the simple SETUP com-
mand The files will install automatically together with a program group
and icons There is a key to the file names on page 343
983119 Work through each of the chapters and the examples
983119 Use the manual spreadsheets and templates as a reference guide for fur-
ther work
983119 Practise develop and improve your efficiency and competence with Excel
Alastair L Day
Email adaysystemcouk or Internet wwwfinancial-modelscom
Overview
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1617
xv
Warranty and disclaimer
The financial models used in the book have not been formally audited and
no representation warranty or undertaking (express or implied) is made and
no responsibility is taken or accepted by Systematic Finance and its direc-
tors as to the adequacy accuracy completeness or reasonableness of the
financial models and the company excludes liability thereof
In particular no responsibility is taken or accepted by the company and
all liability is excluded by the company for the accuracy of the computations
comprised therein and the assumptions upon which such computations are
based In addition the reader receives and uses the financial models entirely
at his own risk and no responsibility is taken or accepted by the Company
and accordingly all liability is excluded by the company for any losses which
may result from the use of the financial models whether as a direct or indi-
rect consequence of a computer virus or otherwise
Microsoft Microsoft Excel Windows and Windows XP are either re-
gistered trademarks or trademarks of Microsoft Corporation in the United
States andor other countries Screen shots reprinted by permission from
Microsoft Corporation
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1717
1
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 317
In an increasingly competitive world we believe itrsquos quality of
thinking that gives you the edge ndash an idea that opens new doors a technique that solves a problem or an insight that
simply makes sense of it all The more you know the smarterand faster you can go
Thatrsquos why we work with the best minds in business and financeto bring cutting-edge thinking and best learning practice to a
global market
Under a range of leading imprints including Financial Times
Prentice Hall we create world-class print publications andelectronic products bringing our readers knowledge skills and
understanding which can be applied whether studying or at work
To find out more about Pearson Education publications or tellus about the books yoursquod like to find you can visit us at
wwwpearsonedcouk
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 417
Mastering FinancialMathematics in
Microsoftreg Excel
A practical guide for business calculations
Second Edition
ALASTAIR L DAY
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 517
PEARSON EDUCATION LIMITED
Edinburgh GateHarlow CM20 2JETel +44 (0)1279 623623Fax +44 (0)1279 431059
Website wwwpearsonedcouk
First published in Great Britain in 2005Second edition 2010
copy Pearson Education Limited 2005 2010
The right of Alastair Day to be identified as author of this work has been assertedby him in accordance with the Copyright Designs and Patents Act 1988
ISBN 978-0-273-73033-0
British Library Cataloguing-in-Publication DataA catalogue record for this book is available from the British Library
Library of Congress Cataloging-in-Publication DataDay Alastair L Mastering financial mathematics in Microsoft Excel a practical guide forbusiness calculations Alastair Day -- 2nd ed p cm -- (Market editions) Includes index ISBN 978-0-273-73033-0 (pbk) 1 Business mathematics 2 Microsoft Excel (Computer file) I Title HF5691D39 2010
6500285554--dc22 2010005343
All rights reserved No part of this publication may be reproduced storedin a retrieval system or transmitted in any form or by any means electronicmechanical photocopying recording or otherwise without either the priorwritten permission of the publisher or a licence permitting restricted copyingin the United Kingdom issued by the Copyright Licensing Agency LtdSaffron House 6ndash10 Kirby Street London EC1N 8TS This book may not belent resold hired out or otherwise disposed of by way of trade in any form ofbinding or cover other than that in which it is published without the priorconsent of the Publishers
Microsoft product screen shots reprinted with permission from MicrosoftCorporation
10 9 8 7 6 5 4 3 2 114 13 12 11 10
Typeset in Garamond 115135pt by 30Printed and bound in Great Britain by Ashford Colour Press Ltd Gosport Hants
The Publisherrsquos policy is to use paper manufactured from sustainable forests
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 617
v
Contents
Acknowledgements x
About the author xi
Conventions xii
Overview xiii
Warranty and disclaimer xv
1 Introduction 1
Overview 3 Common Excel errors 4 Systematic design method 6 Auditing 10 Summary 12
2 Basic financial arithmetic 13
Simple interest 15 Compound interest 19 Nominal and effective rates 24 Continuous discounting 26 Conversions and comparisons 27 Exercise 28 Summary 28
3 Cash flows 29
Net present value 31 Internal rate of return 34 XNPV and XIRR 37 XNPV periodic example 38 Modified internal rate of return 39 Exercise 41 Summary 41
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 717
vi
4 Bonds calculations 43
Description 45 Cash flows 48 Zero coupons 50
Yield 51 Yield to call 51 Price and yield relationship 53 Yield curve pricing 53 Other yield measures 55 Yield measures 57 Exercise 59 Summary 59
5 Bonds risks61
Risks 63 Duration 66 Convexity 70 Comparison 75 Exercise 77 Summary 77
6 Floating rate securities 79
Floating rates 81 Characteristics of interest rate securities 82 Yield evaluation 84 Coupon stripping 89 Exercise 90 Summary 91
7 Amortization and depreciation 93
Amortization 95
Full amortization 97 Delayed payments 97 Sum of digits 100 Straight line and declining balance depreciation 101 UK declining balance method 103 Double declining balance depreciation 104 French depreciation 105 Exercise 107 Summary 108
Contents
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 817
vii
8 Swaps 109
Definitions 111 How swaps save money 114 Advantages of swaps 115
Terminating interest rate swaps 116 Implicit credit risk 117 Worked single currency swap 117 Valuation 119 Cross currency swap 120 Worked example 121 Swaptions 122 Exercise 124 Summary 124
9 Forward interest rates 125
Definitions 127 Example forward rates 127 Hedging principles 130 Forward rate agreement 131 Yield curves 134 Exercise 138 Summary 138
10 Futures 139
Futures market 141 Terminology 142 Benefits 143 Clearinghouse operation 144 Bond futures 145 Hedging mechanisms 145 Hedging example one 147
Hedging example two 149 Exercise 152 Summary 152
11 Foreign exchange 153
Risk 155 Spot rates 157 Longer dates 161 Equivalence 162
Comparisons and arbitrage 164 Exercise 165 Summary 165
Contents
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 917
12 Options 167
Description 169 Terminology 170 Underlying asset 172
Call options 172 Put options 176 Example 178 Covered call 180 Insurance using a stock and a long put 182 Pricing models 182 Black Scholes model 184 Call put parity 187 Greeks 188
Binomial models 191 Comparison to Black Scholes 194 Exercise 198 Summary 198
13 Real options 199
Real options 201 Black Scholes model 202 Binomial model 203
Exercise 205 Summary 205
14 Valuation 207
Valuation methods 209 Assets 210 Market methods 211 Multi-period dividend discount models 213 Free cash flow valuation 215
Adjusted present value 224 Economic profit 227 Exercise 229 Summary 230
15 Leasing 231
Economics of leasing 233 Interest rates 235 Classification 236
Amortization 241 Accounting 242 Settlements 243
viii
Contents
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1017
Lessor evaluation 246 Lessee evaluation 250 Exercise 252 Summary 253
16 Basic statistics 255
Methods 257 Descriptive statistics 257 Probability distributions 270 SamplingCentral Limit Theorem 277 Hypothesis testing 282 Correlation and regression 293 LINEST function 302
Exercise 304 Summary 304
Appendices 307
1 Exercise answers functions list software installation and licence 309
2 An introduction to Microsoftreg Office 2007 (Office 12) 345
Index 359
ix
Contents
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1117
Acknowledgements
I would like to thank Angela Matthew and Frances for their support
and assistance with the completion of this book In addition Christopher
Cudmore Martina OrsquoSullivan and Laura Blake of Pearson Education have
provided valuable support and backing for this project
x
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1217
xi
About the author
Alastair Day has worked in the finance industry for more than 25 yearsin treasury and marketing functions and was formerly a director of avendor leasing company specializing in the IT and technology indus-
tries After rapid growth the directors sold the enterprise to a publiccompany and he established Systematic Finance as a consultancy special-izing in
983119 financial modelling ndash review design build and audit
983119 training in financial modelling corporate finance leasing and credit
analysis on an in-house and public basis throughout Europe Middle East
Africa and America
983119 finance and operating lease structuring as a consultant and lessor
Alastair is author of three modelling books published by FT Prentice Hall Mastering Financial Modelling Mastering Risk Modelling and Mastering
Financial Mathematics in Excel apart from other books and publications on
financial analysis and leasing
Alastair has a degree in Economics and German from LondonUniversity and an MBA from the Open University Business School
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1317
xii
Conventions
983119 The main part of the text is set in AGaramond whereas entries are set in
Courier For example
Enter the Scenario Name as Base Case
983119 Items on the menu bars also shown in Courier For example
Select Tools Goal Seek
983119 The names of functions are in Courier capitals This is the payment
function which requires inputs for the interest rate number of periods
present value and future value
=PMT(INTNPERPVFVTYPE)
983119 Cell formulas are also shown in Courier For example
=IF($C$75=1IF($B25gtC$22$B25-C$22-C$23-
C$23)IF($B25ltC$22C$22-$B25-C$23-C$23))
983119 Equations are formed with the equation editor and shown in normal
notation For example net present value
(CashFlow) N
NPV = ndashndashndashndashndashndashndashndashndashndash (1 + r) N
983119 Genders The use of lsquohersquo or lsquohimrsquo refers to masculine or feminine and this
is used for simplicity to avoid repetition
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1417
xiii
Overview
WHO NEEDS THIS BOOK
More than 20 years ago I used a Hewlett Packard 38C to calculate interest
rates and analyse cash flows and then progressed to an HP 41C with a printer
magnetic strip reader and plug-in finance and mathematics packs This wasan early alphanumeric calculator which gave me the opportunity to program
lease versus purchase or lessor lease evaluation cash flows and structure more
complex lease structures This is before IBM launched the personal compu-
ter in the early 1980s Since that time I have progressed through calculators
such as the HP 12C HP 17BII HP 19B or TI BAII Plus which all provide
dedicated user screens and allow you to undertake financial mathematics
While calculators are much easier than tables or earlier methods they can
be difficult to use without errors When I run training courses on the basic
financial calculations the main drawback is only too obvious you cannot see
your inputs or check the interim calculations and therefore delegates always
want to see a map of the variables to understand the answer
While I have continued to use financial calculators which have now been
augmented with other programs on mobile phones using Windows Mobile
or a selection of applications on Apple iPhones and have in the past created
programs in Basic the most comprehensive medium for financial mathe-
matics has grown to be Microsoftreg Excel I first used Lotus in 1988 and
Excel 30 in 1990 and through various upgrades Excel grew into Microsoftreg
Office 2007 which remains little changed in the core financial functions
through to todayrsquos versions Given that almost everybody in finance has Excel on their desks and
increasingly on their laptops phones or pocket computers the objective
of this book is to explain the basic calculations for mathematical finance
backed up by simple templates for further use and development together
with examples and exercises If you work through each of the chapters in the
book and try the exercises you will improve your Excel skills and obtain a
better grasp of the underlying financial concepts
My other modelling books published by FT Prentice Hall Mastering
Financial Modelling and Mastering Risk Modelling provide complete modelsfor some of the topics in this book and combine finance with model design
using ideas of best practice coupled with methods of auditing and testing
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1517
xiv
This book adheres to systematic spreadsheet best practice and adopts the
same colour scheme method and layout
The key objectives for this book are to
983119 provide explanation of key financial formulas and subject areas
983119 show the use of the formulas using straightforward Excel templates
983119 introduce examples and exercises for extension work
983119 provide a library of basic templates for further development
This book aims to assist two key groups
983119 practitioners who want a manual of financial mathematics from which
they can gain immediate use and payback
983119 business students who need a textbook which is more geared to Excel
solutions than some college manualsThe areas of responsibility where the book should be of interest are
983119 CFOs and finance directors
983119 financial controllers
983119 financial analysts and executives
983119 accountants
983119 corporate finance specialists
983119
treasury managers 983119 risk managers
983119 academics business and MBA students
Therefore people interested in this book range from a company accountant
who wants a reference book to academics and business students who need a
financial mathematics manual in Excel The book has an international bias
and will provide examples which are relevant to the UK and overseas
HOW TO USE THIS BOOK
983119 Install the Excel application templates using the simple SETUP com-
mand The files will install automatically together with a program group
and icons There is a key to the file names on page 343
983119 Work through each of the chapters and the examples
983119 Use the manual spreadsheets and templates as a reference guide for fur-
ther work
983119 Practise develop and improve your efficiency and competence with Excel
Alastair L Day
Email adaysystemcouk or Internet wwwfinancial-modelscom
Overview
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1617
xv
Warranty and disclaimer
The financial models used in the book have not been formally audited and
no representation warranty or undertaking (express or implied) is made and
no responsibility is taken or accepted by Systematic Finance and its direc-
tors as to the adequacy accuracy completeness or reasonableness of the
financial models and the company excludes liability thereof
In particular no responsibility is taken or accepted by the company and
all liability is excluded by the company for the accuracy of the computations
comprised therein and the assumptions upon which such computations are
based In addition the reader receives and uses the financial models entirely
at his own risk and no responsibility is taken or accepted by the Company
and accordingly all liability is excluded by the company for any losses which
may result from the use of the financial models whether as a direct or indi-
rect consequence of a computer virus or otherwise
Microsoft Microsoft Excel Windows and Windows XP are either re-
gistered trademarks or trademarks of Microsoft Corporation in the United
States andor other countries Screen shots reprinted by permission from
Microsoft Corporation
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1717
1
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 417
Mastering FinancialMathematics in
Microsoftreg Excel
A practical guide for business calculations
Second Edition
ALASTAIR L DAY
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 517
PEARSON EDUCATION LIMITED
Edinburgh GateHarlow CM20 2JETel +44 (0)1279 623623Fax +44 (0)1279 431059
Website wwwpearsonedcouk
First published in Great Britain in 2005Second edition 2010
copy Pearson Education Limited 2005 2010
The right of Alastair Day to be identified as author of this work has been assertedby him in accordance with the Copyright Designs and Patents Act 1988
ISBN 978-0-273-73033-0
British Library Cataloguing-in-Publication DataA catalogue record for this book is available from the British Library
Library of Congress Cataloging-in-Publication DataDay Alastair L Mastering financial mathematics in Microsoft Excel a practical guide forbusiness calculations Alastair Day -- 2nd ed p cm -- (Market editions) Includes index ISBN 978-0-273-73033-0 (pbk) 1 Business mathematics 2 Microsoft Excel (Computer file) I Title HF5691D39 2010
6500285554--dc22 2010005343
All rights reserved No part of this publication may be reproduced storedin a retrieval system or transmitted in any form or by any means electronicmechanical photocopying recording or otherwise without either the priorwritten permission of the publisher or a licence permitting restricted copyingin the United Kingdom issued by the Copyright Licensing Agency LtdSaffron House 6ndash10 Kirby Street London EC1N 8TS This book may not belent resold hired out or otherwise disposed of by way of trade in any form ofbinding or cover other than that in which it is published without the priorconsent of the Publishers
Microsoft product screen shots reprinted with permission from MicrosoftCorporation
10 9 8 7 6 5 4 3 2 114 13 12 11 10
Typeset in Garamond 115135pt by 30Printed and bound in Great Britain by Ashford Colour Press Ltd Gosport Hants
The Publisherrsquos policy is to use paper manufactured from sustainable forests
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 617
v
Contents
Acknowledgements x
About the author xi
Conventions xii
Overview xiii
Warranty and disclaimer xv
1 Introduction 1
Overview 3 Common Excel errors 4 Systematic design method 6 Auditing 10 Summary 12
2 Basic financial arithmetic 13
Simple interest 15 Compound interest 19 Nominal and effective rates 24 Continuous discounting 26 Conversions and comparisons 27 Exercise 28 Summary 28
3 Cash flows 29
Net present value 31 Internal rate of return 34 XNPV and XIRR 37 XNPV periodic example 38 Modified internal rate of return 39 Exercise 41 Summary 41
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 717
vi
4 Bonds calculations 43
Description 45 Cash flows 48 Zero coupons 50
Yield 51 Yield to call 51 Price and yield relationship 53 Yield curve pricing 53 Other yield measures 55 Yield measures 57 Exercise 59 Summary 59
5 Bonds risks61
Risks 63 Duration 66 Convexity 70 Comparison 75 Exercise 77 Summary 77
6 Floating rate securities 79
Floating rates 81 Characteristics of interest rate securities 82 Yield evaluation 84 Coupon stripping 89 Exercise 90 Summary 91
7 Amortization and depreciation 93
Amortization 95
Full amortization 97 Delayed payments 97 Sum of digits 100 Straight line and declining balance depreciation 101 UK declining balance method 103 Double declining balance depreciation 104 French depreciation 105 Exercise 107 Summary 108
Contents
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 817
vii
8 Swaps 109
Definitions 111 How swaps save money 114 Advantages of swaps 115
Terminating interest rate swaps 116 Implicit credit risk 117 Worked single currency swap 117 Valuation 119 Cross currency swap 120 Worked example 121 Swaptions 122 Exercise 124 Summary 124
9 Forward interest rates 125
Definitions 127 Example forward rates 127 Hedging principles 130 Forward rate agreement 131 Yield curves 134 Exercise 138 Summary 138
10 Futures 139
Futures market 141 Terminology 142 Benefits 143 Clearinghouse operation 144 Bond futures 145 Hedging mechanisms 145 Hedging example one 147
Hedging example two 149 Exercise 152 Summary 152
11 Foreign exchange 153
Risk 155 Spot rates 157 Longer dates 161 Equivalence 162
Comparisons and arbitrage 164 Exercise 165 Summary 165
Contents
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 917
12 Options 167
Description 169 Terminology 170 Underlying asset 172
Call options 172 Put options 176 Example 178 Covered call 180 Insurance using a stock and a long put 182 Pricing models 182 Black Scholes model 184 Call put parity 187 Greeks 188
Binomial models 191 Comparison to Black Scholes 194 Exercise 198 Summary 198
13 Real options 199
Real options 201 Black Scholes model 202 Binomial model 203
Exercise 205 Summary 205
14 Valuation 207
Valuation methods 209 Assets 210 Market methods 211 Multi-period dividend discount models 213 Free cash flow valuation 215
Adjusted present value 224 Economic profit 227 Exercise 229 Summary 230
15 Leasing 231
Economics of leasing 233 Interest rates 235 Classification 236
Amortization 241 Accounting 242 Settlements 243
viii
Contents
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1017
Lessor evaluation 246 Lessee evaluation 250 Exercise 252 Summary 253
16 Basic statistics 255
Methods 257 Descriptive statistics 257 Probability distributions 270 SamplingCentral Limit Theorem 277 Hypothesis testing 282 Correlation and regression 293 LINEST function 302
Exercise 304 Summary 304
Appendices 307
1 Exercise answers functions list software installation and licence 309
2 An introduction to Microsoftreg Office 2007 (Office 12) 345
Index 359
ix
Contents
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1117
Acknowledgements
I would like to thank Angela Matthew and Frances for their support
and assistance with the completion of this book In addition Christopher
Cudmore Martina OrsquoSullivan and Laura Blake of Pearson Education have
provided valuable support and backing for this project
x
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1217
xi
About the author
Alastair Day has worked in the finance industry for more than 25 yearsin treasury and marketing functions and was formerly a director of avendor leasing company specializing in the IT and technology indus-
tries After rapid growth the directors sold the enterprise to a publiccompany and he established Systematic Finance as a consultancy special-izing in
983119 financial modelling ndash review design build and audit
983119 training in financial modelling corporate finance leasing and credit
analysis on an in-house and public basis throughout Europe Middle East
Africa and America
983119 finance and operating lease structuring as a consultant and lessor
Alastair is author of three modelling books published by FT Prentice Hall Mastering Financial Modelling Mastering Risk Modelling and Mastering
Financial Mathematics in Excel apart from other books and publications on
financial analysis and leasing
Alastair has a degree in Economics and German from LondonUniversity and an MBA from the Open University Business School
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1317
xii
Conventions
983119 The main part of the text is set in AGaramond whereas entries are set in
Courier For example
Enter the Scenario Name as Base Case
983119 Items on the menu bars also shown in Courier For example
Select Tools Goal Seek
983119 The names of functions are in Courier capitals This is the payment
function which requires inputs for the interest rate number of periods
present value and future value
=PMT(INTNPERPVFVTYPE)
983119 Cell formulas are also shown in Courier For example
=IF($C$75=1IF($B25gtC$22$B25-C$22-C$23-
C$23)IF($B25ltC$22C$22-$B25-C$23-C$23))
983119 Equations are formed with the equation editor and shown in normal
notation For example net present value
(CashFlow) N
NPV = ndashndashndashndashndashndashndashndashndashndash (1 + r) N
983119 Genders The use of lsquohersquo or lsquohimrsquo refers to masculine or feminine and this
is used for simplicity to avoid repetition
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1417
xiii
Overview
WHO NEEDS THIS BOOK
More than 20 years ago I used a Hewlett Packard 38C to calculate interest
rates and analyse cash flows and then progressed to an HP 41C with a printer
magnetic strip reader and plug-in finance and mathematics packs This wasan early alphanumeric calculator which gave me the opportunity to program
lease versus purchase or lessor lease evaluation cash flows and structure more
complex lease structures This is before IBM launched the personal compu-
ter in the early 1980s Since that time I have progressed through calculators
such as the HP 12C HP 17BII HP 19B or TI BAII Plus which all provide
dedicated user screens and allow you to undertake financial mathematics
While calculators are much easier than tables or earlier methods they can
be difficult to use without errors When I run training courses on the basic
financial calculations the main drawback is only too obvious you cannot see
your inputs or check the interim calculations and therefore delegates always
want to see a map of the variables to understand the answer
While I have continued to use financial calculators which have now been
augmented with other programs on mobile phones using Windows Mobile
or a selection of applications on Apple iPhones and have in the past created
programs in Basic the most comprehensive medium for financial mathe-
matics has grown to be Microsoftreg Excel I first used Lotus in 1988 and
Excel 30 in 1990 and through various upgrades Excel grew into Microsoftreg
Office 2007 which remains little changed in the core financial functions
through to todayrsquos versions Given that almost everybody in finance has Excel on their desks and
increasingly on their laptops phones or pocket computers the objective
of this book is to explain the basic calculations for mathematical finance
backed up by simple templates for further use and development together
with examples and exercises If you work through each of the chapters in the
book and try the exercises you will improve your Excel skills and obtain a
better grasp of the underlying financial concepts
My other modelling books published by FT Prentice Hall Mastering
Financial Modelling and Mastering Risk Modelling provide complete modelsfor some of the topics in this book and combine finance with model design
using ideas of best practice coupled with methods of auditing and testing
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1517
xiv
This book adheres to systematic spreadsheet best practice and adopts the
same colour scheme method and layout
The key objectives for this book are to
983119 provide explanation of key financial formulas and subject areas
983119 show the use of the formulas using straightforward Excel templates
983119 introduce examples and exercises for extension work
983119 provide a library of basic templates for further development
This book aims to assist two key groups
983119 practitioners who want a manual of financial mathematics from which
they can gain immediate use and payback
983119 business students who need a textbook which is more geared to Excel
solutions than some college manualsThe areas of responsibility where the book should be of interest are
983119 CFOs and finance directors
983119 financial controllers
983119 financial analysts and executives
983119 accountants
983119 corporate finance specialists
983119
treasury managers 983119 risk managers
983119 academics business and MBA students
Therefore people interested in this book range from a company accountant
who wants a reference book to academics and business students who need a
financial mathematics manual in Excel The book has an international bias
and will provide examples which are relevant to the UK and overseas
HOW TO USE THIS BOOK
983119 Install the Excel application templates using the simple SETUP com-
mand The files will install automatically together with a program group
and icons There is a key to the file names on page 343
983119 Work through each of the chapters and the examples
983119 Use the manual spreadsheets and templates as a reference guide for fur-
ther work
983119 Practise develop and improve your efficiency and competence with Excel
Alastair L Day
Email adaysystemcouk or Internet wwwfinancial-modelscom
Overview
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1617
xv
Warranty and disclaimer
The financial models used in the book have not been formally audited and
no representation warranty or undertaking (express or implied) is made and
no responsibility is taken or accepted by Systematic Finance and its direc-
tors as to the adequacy accuracy completeness or reasonableness of the
financial models and the company excludes liability thereof
In particular no responsibility is taken or accepted by the company and
all liability is excluded by the company for the accuracy of the computations
comprised therein and the assumptions upon which such computations are
based In addition the reader receives and uses the financial models entirely
at his own risk and no responsibility is taken or accepted by the Company
and accordingly all liability is excluded by the company for any losses which
may result from the use of the financial models whether as a direct or indi-
rect consequence of a computer virus or otherwise
Microsoft Microsoft Excel Windows and Windows XP are either re-
gistered trademarks or trademarks of Microsoft Corporation in the United
States andor other countries Screen shots reprinted by permission from
Microsoft Corporation
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1717
1
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 517
PEARSON EDUCATION LIMITED
Edinburgh GateHarlow CM20 2JETel +44 (0)1279 623623Fax +44 (0)1279 431059
Website wwwpearsonedcouk
First published in Great Britain in 2005Second edition 2010
copy Pearson Education Limited 2005 2010
The right of Alastair Day to be identified as author of this work has been assertedby him in accordance with the Copyright Designs and Patents Act 1988
ISBN 978-0-273-73033-0
British Library Cataloguing-in-Publication DataA catalogue record for this book is available from the British Library
Library of Congress Cataloging-in-Publication DataDay Alastair L Mastering financial mathematics in Microsoft Excel a practical guide forbusiness calculations Alastair Day -- 2nd ed p cm -- (Market editions) Includes index ISBN 978-0-273-73033-0 (pbk) 1 Business mathematics 2 Microsoft Excel (Computer file) I Title HF5691D39 2010
6500285554--dc22 2010005343
All rights reserved No part of this publication may be reproduced storedin a retrieval system or transmitted in any form or by any means electronicmechanical photocopying recording or otherwise without either the priorwritten permission of the publisher or a licence permitting restricted copyingin the United Kingdom issued by the Copyright Licensing Agency LtdSaffron House 6ndash10 Kirby Street London EC1N 8TS This book may not belent resold hired out or otherwise disposed of by way of trade in any form ofbinding or cover other than that in which it is published without the priorconsent of the Publishers
Microsoft product screen shots reprinted with permission from MicrosoftCorporation
10 9 8 7 6 5 4 3 2 114 13 12 11 10
Typeset in Garamond 115135pt by 30Printed and bound in Great Britain by Ashford Colour Press Ltd Gosport Hants
The Publisherrsquos policy is to use paper manufactured from sustainable forests
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 617
v
Contents
Acknowledgements x
About the author xi
Conventions xii
Overview xiii
Warranty and disclaimer xv
1 Introduction 1
Overview 3 Common Excel errors 4 Systematic design method 6 Auditing 10 Summary 12
2 Basic financial arithmetic 13
Simple interest 15 Compound interest 19 Nominal and effective rates 24 Continuous discounting 26 Conversions and comparisons 27 Exercise 28 Summary 28
3 Cash flows 29
Net present value 31 Internal rate of return 34 XNPV and XIRR 37 XNPV periodic example 38 Modified internal rate of return 39 Exercise 41 Summary 41
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 717
vi
4 Bonds calculations 43
Description 45 Cash flows 48 Zero coupons 50
Yield 51 Yield to call 51 Price and yield relationship 53 Yield curve pricing 53 Other yield measures 55 Yield measures 57 Exercise 59 Summary 59
5 Bonds risks61
Risks 63 Duration 66 Convexity 70 Comparison 75 Exercise 77 Summary 77
6 Floating rate securities 79
Floating rates 81 Characteristics of interest rate securities 82 Yield evaluation 84 Coupon stripping 89 Exercise 90 Summary 91
7 Amortization and depreciation 93
Amortization 95
Full amortization 97 Delayed payments 97 Sum of digits 100 Straight line and declining balance depreciation 101 UK declining balance method 103 Double declining balance depreciation 104 French depreciation 105 Exercise 107 Summary 108
Contents
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 817
vii
8 Swaps 109
Definitions 111 How swaps save money 114 Advantages of swaps 115
Terminating interest rate swaps 116 Implicit credit risk 117 Worked single currency swap 117 Valuation 119 Cross currency swap 120 Worked example 121 Swaptions 122 Exercise 124 Summary 124
9 Forward interest rates 125
Definitions 127 Example forward rates 127 Hedging principles 130 Forward rate agreement 131 Yield curves 134 Exercise 138 Summary 138
10 Futures 139
Futures market 141 Terminology 142 Benefits 143 Clearinghouse operation 144 Bond futures 145 Hedging mechanisms 145 Hedging example one 147
Hedging example two 149 Exercise 152 Summary 152
11 Foreign exchange 153
Risk 155 Spot rates 157 Longer dates 161 Equivalence 162
Comparisons and arbitrage 164 Exercise 165 Summary 165
Contents
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 917
12 Options 167
Description 169 Terminology 170 Underlying asset 172
Call options 172 Put options 176 Example 178 Covered call 180 Insurance using a stock and a long put 182 Pricing models 182 Black Scholes model 184 Call put parity 187 Greeks 188
Binomial models 191 Comparison to Black Scholes 194 Exercise 198 Summary 198
13 Real options 199
Real options 201 Black Scholes model 202 Binomial model 203
Exercise 205 Summary 205
14 Valuation 207
Valuation methods 209 Assets 210 Market methods 211 Multi-period dividend discount models 213 Free cash flow valuation 215
Adjusted present value 224 Economic profit 227 Exercise 229 Summary 230
15 Leasing 231
Economics of leasing 233 Interest rates 235 Classification 236
Amortization 241 Accounting 242 Settlements 243
viii
Contents
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1017
Lessor evaluation 246 Lessee evaluation 250 Exercise 252 Summary 253
16 Basic statistics 255
Methods 257 Descriptive statistics 257 Probability distributions 270 SamplingCentral Limit Theorem 277 Hypothesis testing 282 Correlation and regression 293 LINEST function 302
Exercise 304 Summary 304
Appendices 307
1 Exercise answers functions list software installation and licence 309
2 An introduction to Microsoftreg Office 2007 (Office 12) 345
Index 359
ix
Contents
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1117
Acknowledgements
I would like to thank Angela Matthew and Frances for their support
and assistance with the completion of this book In addition Christopher
Cudmore Martina OrsquoSullivan and Laura Blake of Pearson Education have
provided valuable support and backing for this project
x
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1217
xi
About the author
Alastair Day has worked in the finance industry for more than 25 yearsin treasury and marketing functions and was formerly a director of avendor leasing company specializing in the IT and technology indus-
tries After rapid growth the directors sold the enterprise to a publiccompany and he established Systematic Finance as a consultancy special-izing in
983119 financial modelling ndash review design build and audit
983119 training in financial modelling corporate finance leasing and credit
analysis on an in-house and public basis throughout Europe Middle East
Africa and America
983119 finance and operating lease structuring as a consultant and lessor
Alastair is author of three modelling books published by FT Prentice Hall Mastering Financial Modelling Mastering Risk Modelling and Mastering
Financial Mathematics in Excel apart from other books and publications on
financial analysis and leasing
Alastair has a degree in Economics and German from LondonUniversity and an MBA from the Open University Business School
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1317
xii
Conventions
983119 The main part of the text is set in AGaramond whereas entries are set in
Courier For example
Enter the Scenario Name as Base Case
983119 Items on the menu bars also shown in Courier For example
Select Tools Goal Seek
983119 The names of functions are in Courier capitals This is the payment
function which requires inputs for the interest rate number of periods
present value and future value
=PMT(INTNPERPVFVTYPE)
983119 Cell formulas are also shown in Courier For example
=IF($C$75=1IF($B25gtC$22$B25-C$22-C$23-
C$23)IF($B25ltC$22C$22-$B25-C$23-C$23))
983119 Equations are formed with the equation editor and shown in normal
notation For example net present value
(CashFlow) N
NPV = ndashndashndashndashndashndashndashndashndashndash (1 + r) N
983119 Genders The use of lsquohersquo or lsquohimrsquo refers to masculine or feminine and this
is used for simplicity to avoid repetition
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1417
xiii
Overview
WHO NEEDS THIS BOOK
More than 20 years ago I used a Hewlett Packard 38C to calculate interest
rates and analyse cash flows and then progressed to an HP 41C with a printer
magnetic strip reader and plug-in finance and mathematics packs This wasan early alphanumeric calculator which gave me the opportunity to program
lease versus purchase or lessor lease evaluation cash flows and structure more
complex lease structures This is before IBM launched the personal compu-
ter in the early 1980s Since that time I have progressed through calculators
such as the HP 12C HP 17BII HP 19B or TI BAII Plus which all provide
dedicated user screens and allow you to undertake financial mathematics
While calculators are much easier than tables or earlier methods they can
be difficult to use without errors When I run training courses on the basic
financial calculations the main drawback is only too obvious you cannot see
your inputs or check the interim calculations and therefore delegates always
want to see a map of the variables to understand the answer
While I have continued to use financial calculators which have now been
augmented with other programs on mobile phones using Windows Mobile
or a selection of applications on Apple iPhones and have in the past created
programs in Basic the most comprehensive medium for financial mathe-
matics has grown to be Microsoftreg Excel I first used Lotus in 1988 and
Excel 30 in 1990 and through various upgrades Excel grew into Microsoftreg
Office 2007 which remains little changed in the core financial functions
through to todayrsquos versions Given that almost everybody in finance has Excel on their desks and
increasingly on their laptops phones or pocket computers the objective
of this book is to explain the basic calculations for mathematical finance
backed up by simple templates for further use and development together
with examples and exercises If you work through each of the chapters in the
book and try the exercises you will improve your Excel skills and obtain a
better grasp of the underlying financial concepts
My other modelling books published by FT Prentice Hall Mastering
Financial Modelling and Mastering Risk Modelling provide complete modelsfor some of the topics in this book and combine finance with model design
using ideas of best practice coupled with methods of auditing and testing
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1517
xiv
This book adheres to systematic spreadsheet best practice and adopts the
same colour scheme method and layout
The key objectives for this book are to
983119 provide explanation of key financial formulas and subject areas
983119 show the use of the formulas using straightforward Excel templates
983119 introduce examples and exercises for extension work
983119 provide a library of basic templates for further development
This book aims to assist two key groups
983119 practitioners who want a manual of financial mathematics from which
they can gain immediate use and payback
983119 business students who need a textbook which is more geared to Excel
solutions than some college manualsThe areas of responsibility where the book should be of interest are
983119 CFOs and finance directors
983119 financial controllers
983119 financial analysts and executives
983119 accountants
983119 corporate finance specialists
983119
treasury managers 983119 risk managers
983119 academics business and MBA students
Therefore people interested in this book range from a company accountant
who wants a reference book to academics and business students who need a
financial mathematics manual in Excel The book has an international bias
and will provide examples which are relevant to the UK and overseas
HOW TO USE THIS BOOK
983119 Install the Excel application templates using the simple SETUP com-
mand The files will install automatically together with a program group
and icons There is a key to the file names on page 343
983119 Work through each of the chapters and the examples
983119 Use the manual spreadsheets and templates as a reference guide for fur-
ther work
983119 Practise develop and improve your efficiency and competence with Excel
Alastair L Day
Email adaysystemcouk or Internet wwwfinancial-modelscom
Overview
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1617
xv
Warranty and disclaimer
The financial models used in the book have not been formally audited and
no representation warranty or undertaking (express or implied) is made and
no responsibility is taken or accepted by Systematic Finance and its direc-
tors as to the adequacy accuracy completeness or reasonableness of the
financial models and the company excludes liability thereof
In particular no responsibility is taken or accepted by the company and
all liability is excluded by the company for the accuracy of the computations
comprised therein and the assumptions upon which such computations are
based In addition the reader receives and uses the financial models entirely
at his own risk and no responsibility is taken or accepted by the Company
and accordingly all liability is excluded by the company for any losses which
may result from the use of the financial models whether as a direct or indi-
rect consequence of a computer virus or otherwise
Microsoft Microsoft Excel Windows and Windows XP are either re-
gistered trademarks or trademarks of Microsoft Corporation in the United
States andor other countries Screen shots reprinted by permission from
Microsoft Corporation
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1717
1
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 617
v
Contents
Acknowledgements x
About the author xi
Conventions xii
Overview xiii
Warranty and disclaimer xv
1 Introduction 1
Overview 3 Common Excel errors 4 Systematic design method 6 Auditing 10 Summary 12
2 Basic financial arithmetic 13
Simple interest 15 Compound interest 19 Nominal and effective rates 24 Continuous discounting 26 Conversions and comparisons 27 Exercise 28 Summary 28
3 Cash flows 29
Net present value 31 Internal rate of return 34 XNPV and XIRR 37 XNPV periodic example 38 Modified internal rate of return 39 Exercise 41 Summary 41
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 717
vi
4 Bonds calculations 43
Description 45 Cash flows 48 Zero coupons 50
Yield 51 Yield to call 51 Price and yield relationship 53 Yield curve pricing 53 Other yield measures 55 Yield measures 57 Exercise 59 Summary 59
5 Bonds risks61
Risks 63 Duration 66 Convexity 70 Comparison 75 Exercise 77 Summary 77
6 Floating rate securities 79
Floating rates 81 Characteristics of interest rate securities 82 Yield evaluation 84 Coupon stripping 89 Exercise 90 Summary 91
7 Amortization and depreciation 93
Amortization 95
Full amortization 97 Delayed payments 97 Sum of digits 100 Straight line and declining balance depreciation 101 UK declining balance method 103 Double declining balance depreciation 104 French depreciation 105 Exercise 107 Summary 108
Contents
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 817
vii
8 Swaps 109
Definitions 111 How swaps save money 114 Advantages of swaps 115
Terminating interest rate swaps 116 Implicit credit risk 117 Worked single currency swap 117 Valuation 119 Cross currency swap 120 Worked example 121 Swaptions 122 Exercise 124 Summary 124
9 Forward interest rates 125
Definitions 127 Example forward rates 127 Hedging principles 130 Forward rate agreement 131 Yield curves 134 Exercise 138 Summary 138
10 Futures 139
Futures market 141 Terminology 142 Benefits 143 Clearinghouse operation 144 Bond futures 145 Hedging mechanisms 145 Hedging example one 147
Hedging example two 149 Exercise 152 Summary 152
11 Foreign exchange 153
Risk 155 Spot rates 157 Longer dates 161 Equivalence 162
Comparisons and arbitrage 164 Exercise 165 Summary 165
Contents
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 917
12 Options 167
Description 169 Terminology 170 Underlying asset 172
Call options 172 Put options 176 Example 178 Covered call 180 Insurance using a stock and a long put 182 Pricing models 182 Black Scholes model 184 Call put parity 187 Greeks 188
Binomial models 191 Comparison to Black Scholes 194 Exercise 198 Summary 198
13 Real options 199
Real options 201 Black Scholes model 202 Binomial model 203
Exercise 205 Summary 205
14 Valuation 207
Valuation methods 209 Assets 210 Market methods 211 Multi-period dividend discount models 213 Free cash flow valuation 215
Adjusted present value 224 Economic profit 227 Exercise 229 Summary 230
15 Leasing 231
Economics of leasing 233 Interest rates 235 Classification 236
Amortization 241 Accounting 242 Settlements 243
viii
Contents
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1017
Lessor evaluation 246 Lessee evaluation 250 Exercise 252 Summary 253
16 Basic statistics 255
Methods 257 Descriptive statistics 257 Probability distributions 270 SamplingCentral Limit Theorem 277 Hypothesis testing 282 Correlation and regression 293 LINEST function 302
Exercise 304 Summary 304
Appendices 307
1 Exercise answers functions list software installation and licence 309
2 An introduction to Microsoftreg Office 2007 (Office 12) 345
Index 359
ix
Contents
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1117
Acknowledgements
I would like to thank Angela Matthew and Frances for their support
and assistance with the completion of this book In addition Christopher
Cudmore Martina OrsquoSullivan and Laura Blake of Pearson Education have
provided valuable support and backing for this project
x
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1217
xi
About the author
Alastair Day has worked in the finance industry for more than 25 yearsin treasury and marketing functions and was formerly a director of avendor leasing company specializing in the IT and technology indus-
tries After rapid growth the directors sold the enterprise to a publiccompany and he established Systematic Finance as a consultancy special-izing in
983119 financial modelling ndash review design build and audit
983119 training in financial modelling corporate finance leasing and credit
analysis on an in-house and public basis throughout Europe Middle East
Africa and America
983119 finance and operating lease structuring as a consultant and lessor
Alastair is author of three modelling books published by FT Prentice Hall Mastering Financial Modelling Mastering Risk Modelling and Mastering
Financial Mathematics in Excel apart from other books and publications on
financial analysis and leasing
Alastair has a degree in Economics and German from LondonUniversity and an MBA from the Open University Business School
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1317
xii
Conventions
983119 The main part of the text is set in AGaramond whereas entries are set in
Courier For example
Enter the Scenario Name as Base Case
983119 Items on the menu bars also shown in Courier For example
Select Tools Goal Seek
983119 The names of functions are in Courier capitals This is the payment
function which requires inputs for the interest rate number of periods
present value and future value
=PMT(INTNPERPVFVTYPE)
983119 Cell formulas are also shown in Courier For example
=IF($C$75=1IF($B25gtC$22$B25-C$22-C$23-
C$23)IF($B25ltC$22C$22-$B25-C$23-C$23))
983119 Equations are formed with the equation editor and shown in normal
notation For example net present value
(CashFlow) N
NPV = ndashndashndashndashndashndashndashndashndashndash (1 + r) N
983119 Genders The use of lsquohersquo or lsquohimrsquo refers to masculine or feminine and this
is used for simplicity to avoid repetition
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1417
xiii
Overview
WHO NEEDS THIS BOOK
More than 20 years ago I used a Hewlett Packard 38C to calculate interest
rates and analyse cash flows and then progressed to an HP 41C with a printer
magnetic strip reader and plug-in finance and mathematics packs This wasan early alphanumeric calculator which gave me the opportunity to program
lease versus purchase or lessor lease evaluation cash flows and structure more
complex lease structures This is before IBM launched the personal compu-
ter in the early 1980s Since that time I have progressed through calculators
such as the HP 12C HP 17BII HP 19B or TI BAII Plus which all provide
dedicated user screens and allow you to undertake financial mathematics
While calculators are much easier than tables or earlier methods they can
be difficult to use without errors When I run training courses on the basic
financial calculations the main drawback is only too obvious you cannot see
your inputs or check the interim calculations and therefore delegates always
want to see a map of the variables to understand the answer
While I have continued to use financial calculators which have now been
augmented with other programs on mobile phones using Windows Mobile
or a selection of applications on Apple iPhones and have in the past created
programs in Basic the most comprehensive medium for financial mathe-
matics has grown to be Microsoftreg Excel I first used Lotus in 1988 and
Excel 30 in 1990 and through various upgrades Excel grew into Microsoftreg
Office 2007 which remains little changed in the core financial functions
through to todayrsquos versions Given that almost everybody in finance has Excel on their desks and
increasingly on their laptops phones or pocket computers the objective
of this book is to explain the basic calculations for mathematical finance
backed up by simple templates for further use and development together
with examples and exercises If you work through each of the chapters in the
book and try the exercises you will improve your Excel skills and obtain a
better grasp of the underlying financial concepts
My other modelling books published by FT Prentice Hall Mastering
Financial Modelling and Mastering Risk Modelling provide complete modelsfor some of the topics in this book and combine finance with model design
using ideas of best practice coupled with methods of auditing and testing
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1517
xiv
This book adheres to systematic spreadsheet best practice and adopts the
same colour scheme method and layout
The key objectives for this book are to
983119 provide explanation of key financial formulas and subject areas
983119 show the use of the formulas using straightforward Excel templates
983119 introduce examples and exercises for extension work
983119 provide a library of basic templates for further development
This book aims to assist two key groups
983119 practitioners who want a manual of financial mathematics from which
they can gain immediate use and payback
983119 business students who need a textbook which is more geared to Excel
solutions than some college manualsThe areas of responsibility where the book should be of interest are
983119 CFOs and finance directors
983119 financial controllers
983119 financial analysts and executives
983119 accountants
983119 corporate finance specialists
983119
treasury managers 983119 risk managers
983119 academics business and MBA students
Therefore people interested in this book range from a company accountant
who wants a reference book to academics and business students who need a
financial mathematics manual in Excel The book has an international bias
and will provide examples which are relevant to the UK and overseas
HOW TO USE THIS BOOK
983119 Install the Excel application templates using the simple SETUP com-
mand The files will install automatically together with a program group
and icons There is a key to the file names on page 343
983119 Work through each of the chapters and the examples
983119 Use the manual spreadsheets and templates as a reference guide for fur-
ther work
983119 Practise develop and improve your efficiency and competence with Excel
Alastair L Day
Email adaysystemcouk or Internet wwwfinancial-modelscom
Overview
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1617
xv
Warranty and disclaimer
The financial models used in the book have not been formally audited and
no representation warranty or undertaking (express or implied) is made and
no responsibility is taken or accepted by Systematic Finance and its direc-
tors as to the adequacy accuracy completeness or reasonableness of the
financial models and the company excludes liability thereof
In particular no responsibility is taken or accepted by the company and
all liability is excluded by the company for the accuracy of the computations
comprised therein and the assumptions upon which such computations are
based In addition the reader receives and uses the financial models entirely
at his own risk and no responsibility is taken or accepted by the Company
and accordingly all liability is excluded by the company for any losses which
may result from the use of the financial models whether as a direct or indi-
rect consequence of a computer virus or otherwise
Microsoft Microsoft Excel Windows and Windows XP are either re-
gistered trademarks or trademarks of Microsoft Corporation in the United
States andor other countries Screen shots reprinted by permission from
Microsoft Corporation
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1717
1
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 717
vi
4 Bonds calculations 43
Description 45 Cash flows 48 Zero coupons 50
Yield 51 Yield to call 51 Price and yield relationship 53 Yield curve pricing 53 Other yield measures 55 Yield measures 57 Exercise 59 Summary 59
5 Bonds risks61
Risks 63 Duration 66 Convexity 70 Comparison 75 Exercise 77 Summary 77
6 Floating rate securities 79
Floating rates 81 Characteristics of interest rate securities 82 Yield evaluation 84 Coupon stripping 89 Exercise 90 Summary 91
7 Amortization and depreciation 93
Amortization 95
Full amortization 97 Delayed payments 97 Sum of digits 100 Straight line and declining balance depreciation 101 UK declining balance method 103 Double declining balance depreciation 104 French depreciation 105 Exercise 107 Summary 108
Contents
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 817
vii
8 Swaps 109
Definitions 111 How swaps save money 114 Advantages of swaps 115
Terminating interest rate swaps 116 Implicit credit risk 117 Worked single currency swap 117 Valuation 119 Cross currency swap 120 Worked example 121 Swaptions 122 Exercise 124 Summary 124
9 Forward interest rates 125
Definitions 127 Example forward rates 127 Hedging principles 130 Forward rate agreement 131 Yield curves 134 Exercise 138 Summary 138
10 Futures 139
Futures market 141 Terminology 142 Benefits 143 Clearinghouse operation 144 Bond futures 145 Hedging mechanisms 145 Hedging example one 147
Hedging example two 149 Exercise 152 Summary 152
11 Foreign exchange 153
Risk 155 Spot rates 157 Longer dates 161 Equivalence 162
Comparisons and arbitrage 164 Exercise 165 Summary 165
Contents
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 917
12 Options 167
Description 169 Terminology 170 Underlying asset 172
Call options 172 Put options 176 Example 178 Covered call 180 Insurance using a stock and a long put 182 Pricing models 182 Black Scholes model 184 Call put parity 187 Greeks 188
Binomial models 191 Comparison to Black Scholes 194 Exercise 198 Summary 198
13 Real options 199
Real options 201 Black Scholes model 202 Binomial model 203
Exercise 205 Summary 205
14 Valuation 207
Valuation methods 209 Assets 210 Market methods 211 Multi-period dividend discount models 213 Free cash flow valuation 215
Adjusted present value 224 Economic profit 227 Exercise 229 Summary 230
15 Leasing 231
Economics of leasing 233 Interest rates 235 Classification 236
Amortization 241 Accounting 242 Settlements 243
viii
Contents
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1017
Lessor evaluation 246 Lessee evaluation 250 Exercise 252 Summary 253
16 Basic statistics 255
Methods 257 Descriptive statistics 257 Probability distributions 270 SamplingCentral Limit Theorem 277 Hypothesis testing 282 Correlation and regression 293 LINEST function 302
Exercise 304 Summary 304
Appendices 307
1 Exercise answers functions list software installation and licence 309
2 An introduction to Microsoftreg Office 2007 (Office 12) 345
Index 359
ix
Contents
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1117
Acknowledgements
I would like to thank Angela Matthew and Frances for their support
and assistance with the completion of this book In addition Christopher
Cudmore Martina OrsquoSullivan and Laura Blake of Pearson Education have
provided valuable support and backing for this project
x
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1217
xi
About the author
Alastair Day has worked in the finance industry for more than 25 yearsin treasury and marketing functions and was formerly a director of avendor leasing company specializing in the IT and technology indus-
tries After rapid growth the directors sold the enterprise to a publiccompany and he established Systematic Finance as a consultancy special-izing in
983119 financial modelling ndash review design build and audit
983119 training in financial modelling corporate finance leasing and credit
analysis on an in-house and public basis throughout Europe Middle East
Africa and America
983119 finance and operating lease structuring as a consultant and lessor
Alastair is author of three modelling books published by FT Prentice Hall Mastering Financial Modelling Mastering Risk Modelling and Mastering
Financial Mathematics in Excel apart from other books and publications on
financial analysis and leasing
Alastair has a degree in Economics and German from LondonUniversity and an MBA from the Open University Business School
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1317
xii
Conventions
983119 The main part of the text is set in AGaramond whereas entries are set in
Courier For example
Enter the Scenario Name as Base Case
983119 Items on the menu bars also shown in Courier For example
Select Tools Goal Seek
983119 The names of functions are in Courier capitals This is the payment
function which requires inputs for the interest rate number of periods
present value and future value
=PMT(INTNPERPVFVTYPE)
983119 Cell formulas are also shown in Courier For example
=IF($C$75=1IF($B25gtC$22$B25-C$22-C$23-
C$23)IF($B25ltC$22C$22-$B25-C$23-C$23))
983119 Equations are formed with the equation editor and shown in normal
notation For example net present value
(CashFlow) N
NPV = ndashndashndashndashndashndashndashndashndashndash (1 + r) N
983119 Genders The use of lsquohersquo or lsquohimrsquo refers to masculine or feminine and this
is used for simplicity to avoid repetition
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1417
xiii
Overview
WHO NEEDS THIS BOOK
More than 20 years ago I used a Hewlett Packard 38C to calculate interest
rates and analyse cash flows and then progressed to an HP 41C with a printer
magnetic strip reader and plug-in finance and mathematics packs This wasan early alphanumeric calculator which gave me the opportunity to program
lease versus purchase or lessor lease evaluation cash flows and structure more
complex lease structures This is before IBM launched the personal compu-
ter in the early 1980s Since that time I have progressed through calculators
such as the HP 12C HP 17BII HP 19B or TI BAII Plus which all provide
dedicated user screens and allow you to undertake financial mathematics
While calculators are much easier than tables or earlier methods they can
be difficult to use without errors When I run training courses on the basic
financial calculations the main drawback is only too obvious you cannot see
your inputs or check the interim calculations and therefore delegates always
want to see a map of the variables to understand the answer
While I have continued to use financial calculators which have now been
augmented with other programs on mobile phones using Windows Mobile
or a selection of applications on Apple iPhones and have in the past created
programs in Basic the most comprehensive medium for financial mathe-
matics has grown to be Microsoftreg Excel I first used Lotus in 1988 and
Excel 30 in 1990 and through various upgrades Excel grew into Microsoftreg
Office 2007 which remains little changed in the core financial functions
through to todayrsquos versions Given that almost everybody in finance has Excel on their desks and
increasingly on their laptops phones or pocket computers the objective
of this book is to explain the basic calculations for mathematical finance
backed up by simple templates for further use and development together
with examples and exercises If you work through each of the chapters in the
book and try the exercises you will improve your Excel skills and obtain a
better grasp of the underlying financial concepts
My other modelling books published by FT Prentice Hall Mastering
Financial Modelling and Mastering Risk Modelling provide complete modelsfor some of the topics in this book and combine finance with model design
using ideas of best practice coupled with methods of auditing and testing
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1517
xiv
This book adheres to systematic spreadsheet best practice and adopts the
same colour scheme method and layout
The key objectives for this book are to
983119 provide explanation of key financial formulas and subject areas
983119 show the use of the formulas using straightforward Excel templates
983119 introduce examples and exercises for extension work
983119 provide a library of basic templates for further development
This book aims to assist two key groups
983119 practitioners who want a manual of financial mathematics from which
they can gain immediate use and payback
983119 business students who need a textbook which is more geared to Excel
solutions than some college manualsThe areas of responsibility where the book should be of interest are
983119 CFOs and finance directors
983119 financial controllers
983119 financial analysts and executives
983119 accountants
983119 corporate finance specialists
983119
treasury managers 983119 risk managers
983119 academics business and MBA students
Therefore people interested in this book range from a company accountant
who wants a reference book to academics and business students who need a
financial mathematics manual in Excel The book has an international bias
and will provide examples which are relevant to the UK and overseas
HOW TO USE THIS BOOK
983119 Install the Excel application templates using the simple SETUP com-
mand The files will install automatically together with a program group
and icons There is a key to the file names on page 343
983119 Work through each of the chapters and the examples
983119 Use the manual spreadsheets and templates as a reference guide for fur-
ther work
983119 Practise develop and improve your efficiency and competence with Excel
Alastair L Day
Email adaysystemcouk or Internet wwwfinancial-modelscom
Overview
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1617
xv
Warranty and disclaimer
The financial models used in the book have not been formally audited and
no representation warranty or undertaking (express or implied) is made and
no responsibility is taken or accepted by Systematic Finance and its direc-
tors as to the adequacy accuracy completeness or reasonableness of the
financial models and the company excludes liability thereof
In particular no responsibility is taken or accepted by the company and
all liability is excluded by the company for the accuracy of the computations
comprised therein and the assumptions upon which such computations are
based In addition the reader receives and uses the financial models entirely
at his own risk and no responsibility is taken or accepted by the Company
and accordingly all liability is excluded by the company for any losses which
may result from the use of the financial models whether as a direct or indi-
rect consequence of a computer virus or otherwise
Microsoft Microsoft Excel Windows and Windows XP are either re-
gistered trademarks or trademarks of Microsoft Corporation in the United
States andor other countries Screen shots reprinted by permission from
Microsoft Corporation
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1717
1
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 817
vii
8 Swaps 109
Definitions 111 How swaps save money 114 Advantages of swaps 115
Terminating interest rate swaps 116 Implicit credit risk 117 Worked single currency swap 117 Valuation 119 Cross currency swap 120 Worked example 121 Swaptions 122 Exercise 124 Summary 124
9 Forward interest rates 125
Definitions 127 Example forward rates 127 Hedging principles 130 Forward rate agreement 131 Yield curves 134 Exercise 138 Summary 138
10 Futures 139
Futures market 141 Terminology 142 Benefits 143 Clearinghouse operation 144 Bond futures 145 Hedging mechanisms 145 Hedging example one 147
Hedging example two 149 Exercise 152 Summary 152
11 Foreign exchange 153
Risk 155 Spot rates 157 Longer dates 161 Equivalence 162
Comparisons and arbitrage 164 Exercise 165 Summary 165
Contents
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 917
12 Options 167
Description 169 Terminology 170 Underlying asset 172
Call options 172 Put options 176 Example 178 Covered call 180 Insurance using a stock and a long put 182 Pricing models 182 Black Scholes model 184 Call put parity 187 Greeks 188
Binomial models 191 Comparison to Black Scholes 194 Exercise 198 Summary 198
13 Real options 199
Real options 201 Black Scholes model 202 Binomial model 203
Exercise 205 Summary 205
14 Valuation 207
Valuation methods 209 Assets 210 Market methods 211 Multi-period dividend discount models 213 Free cash flow valuation 215
Adjusted present value 224 Economic profit 227 Exercise 229 Summary 230
15 Leasing 231
Economics of leasing 233 Interest rates 235 Classification 236
Amortization 241 Accounting 242 Settlements 243
viii
Contents
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1017
Lessor evaluation 246 Lessee evaluation 250 Exercise 252 Summary 253
16 Basic statistics 255
Methods 257 Descriptive statistics 257 Probability distributions 270 SamplingCentral Limit Theorem 277 Hypothesis testing 282 Correlation and regression 293 LINEST function 302
Exercise 304 Summary 304
Appendices 307
1 Exercise answers functions list software installation and licence 309
2 An introduction to Microsoftreg Office 2007 (Office 12) 345
Index 359
ix
Contents
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1117
Acknowledgements
I would like to thank Angela Matthew and Frances for their support
and assistance with the completion of this book In addition Christopher
Cudmore Martina OrsquoSullivan and Laura Blake of Pearson Education have
provided valuable support and backing for this project
x
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1217
xi
About the author
Alastair Day has worked in the finance industry for more than 25 yearsin treasury and marketing functions and was formerly a director of avendor leasing company specializing in the IT and technology indus-
tries After rapid growth the directors sold the enterprise to a publiccompany and he established Systematic Finance as a consultancy special-izing in
983119 financial modelling ndash review design build and audit
983119 training in financial modelling corporate finance leasing and credit
analysis on an in-house and public basis throughout Europe Middle East
Africa and America
983119 finance and operating lease structuring as a consultant and lessor
Alastair is author of three modelling books published by FT Prentice Hall Mastering Financial Modelling Mastering Risk Modelling and Mastering
Financial Mathematics in Excel apart from other books and publications on
financial analysis and leasing
Alastair has a degree in Economics and German from LondonUniversity and an MBA from the Open University Business School
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1317
xii
Conventions
983119 The main part of the text is set in AGaramond whereas entries are set in
Courier For example
Enter the Scenario Name as Base Case
983119 Items on the menu bars also shown in Courier For example
Select Tools Goal Seek
983119 The names of functions are in Courier capitals This is the payment
function which requires inputs for the interest rate number of periods
present value and future value
=PMT(INTNPERPVFVTYPE)
983119 Cell formulas are also shown in Courier For example
=IF($C$75=1IF($B25gtC$22$B25-C$22-C$23-
C$23)IF($B25ltC$22C$22-$B25-C$23-C$23))
983119 Equations are formed with the equation editor and shown in normal
notation For example net present value
(CashFlow) N
NPV = ndashndashndashndashndashndashndashndashndashndash (1 + r) N
983119 Genders The use of lsquohersquo or lsquohimrsquo refers to masculine or feminine and this
is used for simplicity to avoid repetition
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1417
xiii
Overview
WHO NEEDS THIS BOOK
More than 20 years ago I used a Hewlett Packard 38C to calculate interest
rates and analyse cash flows and then progressed to an HP 41C with a printer
magnetic strip reader and plug-in finance and mathematics packs This wasan early alphanumeric calculator which gave me the opportunity to program
lease versus purchase or lessor lease evaluation cash flows and structure more
complex lease structures This is before IBM launched the personal compu-
ter in the early 1980s Since that time I have progressed through calculators
such as the HP 12C HP 17BII HP 19B or TI BAII Plus which all provide
dedicated user screens and allow you to undertake financial mathematics
While calculators are much easier than tables or earlier methods they can
be difficult to use without errors When I run training courses on the basic
financial calculations the main drawback is only too obvious you cannot see
your inputs or check the interim calculations and therefore delegates always
want to see a map of the variables to understand the answer
While I have continued to use financial calculators which have now been
augmented with other programs on mobile phones using Windows Mobile
or a selection of applications on Apple iPhones and have in the past created
programs in Basic the most comprehensive medium for financial mathe-
matics has grown to be Microsoftreg Excel I first used Lotus in 1988 and
Excel 30 in 1990 and through various upgrades Excel grew into Microsoftreg
Office 2007 which remains little changed in the core financial functions
through to todayrsquos versions Given that almost everybody in finance has Excel on their desks and
increasingly on their laptops phones or pocket computers the objective
of this book is to explain the basic calculations for mathematical finance
backed up by simple templates for further use and development together
with examples and exercises If you work through each of the chapters in the
book and try the exercises you will improve your Excel skills and obtain a
better grasp of the underlying financial concepts
My other modelling books published by FT Prentice Hall Mastering
Financial Modelling and Mastering Risk Modelling provide complete modelsfor some of the topics in this book and combine finance with model design
using ideas of best practice coupled with methods of auditing and testing
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1517
xiv
This book adheres to systematic spreadsheet best practice and adopts the
same colour scheme method and layout
The key objectives for this book are to
983119 provide explanation of key financial formulas and subject areas
983119 show the use of the formulas using straightforward Excel templates
983119 introduce examples and exercises for extension work
983119 provide a library of basic templates for further development
This book aims to assist two key groups
983119 practitioners who want a manual of financial mathematics from which
they can gain immediate use and payback
983119 business students who need a textbook which is more geared to Excel
solutions than some college manualsThe areas of responsibility where the book should be of interest are
983119 CFOs and finance directors
983119 financial controllers
983119 financial analysts and executives
983119 accountants
983119 corporate finance specialists
983119
treasury managers 983119 risk managers
983119 academics business and MBA students
Therefore people interested in this book range from a company accountant
who wants a reference book to academics and business students who need a
financial mathematics manual in Excel The book has an international bias
and will provide examples which are relevant to the UK and overseas
HOW TO USE THIS BOOK
983119 Install the Excel application templates using the simple SETUP com-
mand The files will install automatically together with a program group
and icons There is a key to the file names on page 343
983119 Work through each of the chapters and the examples
983119 Use the manual spreadsheets and templates as a reference guide for fur-
ther work
983119 Practise develop and improve your efficiency and competence with Excel
Alastair L Day
Email adaysystemcouk or Internet wwwfinancial-modelscom
Overview
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1617
xv
Warranty and disclaimer
The financial models used in the book have not been formally audited and
no representation warranty or undertaking (express or implied) is made and
no responsibility is taken or accepted by Systematic Finance and its direc-
tors as to the adequacy accuracy completeness or reasonableness of the
financial models and the company excludes liability thereof
In particular no responsibility is taken or accepted by the company and
all liability is excluded by the company for the accuracy of the computations
comprised therein and the assumptions upon which such computations are
based In addition the reader receives and uses the financial models entirely
at his own risk and no responsibility is taken or accepted by the Company
and accordingly all liability is excluded by the company for any losses which
may result from the use of the financial models whether as a direct or indi-
rect consequence of a computer virus or otherwise
Microsoft Microsoft Excel Windows and Windows XP are either re-
gistered trademarks or trademarks of Microsoft Corporation in the United
States andor other countries Screen shots reprinted by permission from
Microsoft Corporation
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1717
1
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 917
12 Options 167
Description 169 Terminology 170 Underlying asset 172
Call options 172 Put options 176 Example 178 Covered call 180 Insurance using a stock and a long put 182 Pricing models 182 Black Scholes model 184 Call put parity 187 Greeks 188
Binomial models 191 Comparison to Black Scholes 194 Exercise 198 Summary 198
13 Real options 199
Real options 201 Black Scholes model 202 Binomial model 203
Exercise 205 Summary 205
14 Valuation 207
Valuation methods 209 Assets 210 Market methods 211 Multi-period dividend discount models 213 Free cash flow valuation 215
Adjusted present value 224 Economic profit 227 Exercise 229 Summary 230
15 Leasing 231
Economics of leasing 233 Interest rates 235 Classification 236
Amortization 241 Accounting 242 Settlements 243
viii
Contents
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1017
Lessor evaluation 246 Lessee evaluation 250 Exercise 252 Summary 253
16 Basic statistics 255
Methods 257 Descriptive statistics 257 Probability distributions 270 SamplingCentral Limit Theorem 277 Hypothesis testing 282 Correlation and regression 293 LINEST function 302
Exercise 304 Summary 304
Appendices 307
1 Exercise answers functions list software installation and licence 309
2 An introduction to Microsoftreg Office 2007 (Office 12) 345
Index 359
ix
Contents
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1117
Acknowledgements
I would like to thank Angela Matthew and Frances for their support
and assistance with the completion of this book In addition Christopher
Cudmore Martina OrsquoSullivan and Laura Blake of Pearson Education have
provided valuable support and backing for this project
x
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1217
xi
About the author
Alastair Day has worked in the finance industry for more than 25 yearsin treasury and marketing functions and was formerly a director of avendor leasing company specializing in the IT and technology indus-
tries After rapid growth the directors sold the enterprise to a publiccompany and he established Systematic Finance as a consultancy special-izing in
983119 financial modelling ndash review design build and audit
983119 training in financial modelling corporate finance leasing and credit
analysis on an in-house and public basis throughout Europe Middle East
Africa and America
983119 finance and operating lease structuring as a consultant and lessor
Alastair is author of three modelling books published by FT Prentice Hall Mastering Financial Modelling Mastering Risk Modelling and Mastering
Financial Mathematics in Excel apart from other books and publications on
financial analysis and leasing
Alastair has a degree in Economics and German from LondonUniversity and an MBA from the Open University Business School
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1317
xii
Conventions
983119 The main part of the text is set in AGaramond whereas entries are set in
Courier For example
Enter the Scenario Name as Base Case
983119 Items on the menu bars also shown in Courier For example
Select Tools Goal Seek
983119 The names of functions are in Courier capitals This is the payment
function which requires inputs for the interest rate number of periods
present value and future value
=PMT(INTNPERPVFVTYPE)
983119 Cell formulas are also shown in Courier For example
=IF($C$75=1IF($B25gtC$22$B25-C$22-C$23-
C$23)IF($B25ltC$22C$22-$B25-C$23-C$23))
983119 Equations are formed with the equation editor and shown in normal
notation For example net present value
(CashFlow) N
NPV = ndashndashndashndashndashndashndashndashndashndash (1 + r) N
983119 Genders The use of lsquohersquo or lsquohimrsquo refers to masculine or feminine and this
is used for simplicity to avoid repetition
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1417
xiii
Overview
WHO NEEDS THIS BOOK
More than 20 years ago I used a Hewlett Packard 38C to calculate interest
rates and analyse cash flows and then progressed to an HP 41C with a printer
magnetic strip reader and plug-in finance and mathematics packs This wasan early alphanumeric calculator which gave me the opportunity to program
lease versus purchase or lessor lease evaluation cash flows and structure more
complex lease structures This is before IBM launched the personal compu-
ter in the early 1980s Since that time I have progressed through calculators
such as the HP 12C HP 17BII HP 19B or TI BAII Plus which all provide
dedicated user screens and allow you to undertake financial mathematics
While calculators are much easier than tables or earlier methods they can
be difficult to use without errors When I run training courses on the basic
financial calculations the main drawback is only too obvious you cannot see
your inputs or check the interim calculations and therefore delegates always
want to see a map of the variables to understand the answer
While I have continued to use financial calculators which have now been
augmented with other programs on mobile phones using Windows Mobile
or a selection of applications on Apple iPhones and have in the past created
programs in Basic the most comprehensive medium for financial mathe-
matics has grown to be Microsoftreg Excel I first used Lotus in 1988 and
Excel 30 in 1990 and through various upgrades Excel grew into Microsoftreg
Office 2007 which remains little changed in the core financial functions
through to todayrsquos versions Given that almost everybody in finance has Excel on their desks and
increasingly on their laptops phones or pocket computers the objective
of this book is to explain the basic calculations for mathematical finance
backed up by simple templates for further use and development together
with examples and exercises If you work through each of the chapters in the
book and try the exercises you will improve your Excel skills and obtain a
better grasp of the underlying financial concepts
My other modelling books published by FT Prentice Hall Mastering
Financial Modelling and Mastering Risk Modelling provide complete modelsfor some of the topics in this book and combine finance with model design
using ideas of best practice coupled with methods of auditing and testing
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1517
xiv
This book adheres to systematic spreadsheet best practice and adopts the
same colour scheme method and layout
The key objectives for this book are to
983119 provide explanation of key financial formulas and subject areas
983119 show the use of the formulas using straightforward Excel templates
983119 introduce examples and exercises for extension work
983119 provide a library of basic templates for further development
This book aims to assist two key groups
983119 practitioners who want a manual of financial mathematics from which
they can gain immediate use and payback
983119 business students who need a textbook which is more geared to Excel
solutions than some college manualsThe areas of responsibility where the book should be of interest are
983119 CFOs and finance directors
983119 financial controllers
983119 financial analysts and executives
983119 accountants
983119 corporate finance specialists
983119
treasury managers 983119 risk managers
983119 academics business and MBA students
Therefore people interested in this book range from a company accountant
who wants a reference book to academics and business students who need a
financial mathematics manual in Excel The book has an international bias
and will provide examples which are relevant to the UK and overseas
HOW TO USE THIS BOOK
983119 Install the Excel application templates using the simple SETUP com-
mand The files will install automatically together with a program group
and icons There is a key to the file names on page 343
983119 Work through each of the chapters and the examples
983119 Use the manual spreadsheets and templates as a reference guide for fur-
ther work
983119 Practise develop and improve your efficiency and competence with Excel
Alastair L Day
Email adaysystemcouk or Internet wwwfinancial-modelscom
Overview
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1617
xv
Warranty and disclaimer
The financial models used in the book have not been formally audited and
no representation warranty or undertaking (express or implied) is made and
no responsibility is taken or accepted by Systematic Finance and its direc-
tors as to the adequacy accuracy completeness or reasonableness of the
financial models and the company excludes liability thereof
In particular no responsibility is taken or accepted by the company and
all liability is excluded by the company for the accuracy of the computations
comprised therein and the assumptions upon which such computations are
based In addition the reader receives and uses the financial models entirely
at his own risk and no responsibility is taken or accepted by the Company
and accordingly all liability is excluded by the company for any losses which
may result from the use of the financial models whether as a direct or indi-
rect consequence of a computer virus or otherwise
Microsoft Microsoft Excel Windows and Windows XP are either re-
gistered trademarks or trademarks of Microsoft Corporation in the United
States andor other countries Screen shots reprinted by permission from
Microsoft Corporation
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1717
1
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1017
Lessor evaluation 246 Lessee evaluation 250 Exercise 252 Summary 253
16 Basic statistics 255
Methods 257 Descriptive statistics 257 Probability distributions 270 SamplingCentral Limit Theorem 277 Hypothesis testing 282 Correlation and regression 293 LINEST function 302
Exercise 304 Summary 304
Appendices 307
1 Exercise answers functions list software installation and licence 309
2 An introduction to Microsoftreg Office 2007 (Office 12) 345
Index 359
ix
Contents
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1117
Acknowledgements
I would like to thank Angela Matthew and Frances for their support
and assistance with the completion of this book In addition Christopher
Cudmore Martina OrsquoSullivan and Laura Blake of Pearson Education have
provided valuable support and backing for this project
x
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1217
xi
About the author
Alastair Day has worked in the finance industry for more than 25 yearsin treasury and marketing functions and was formerly a director of avendor leasing company specializing in the IT and technology indus-
tries After rapid growth the directors sold the enterprise to a publiccompany and he established Systematic Finance as a consultancy special-izing in
983119 financial modelling ndash review design build and audit
983119 training in financial modelling corporate finance leasing and credit
analysis on an in-house and public basis throughout Europe Middle East
Africa and America
983119 finance and operating lease structuring as a consultant and lessor
Alastair is author of three modelling books published by FT Prentice Hall Mastering Financial Modelling Mastering Risk Modelling and Mastering
Financial Mathematics in Excel apart from other books and publications on
financial analysis and leasing
Alastair has a degree in Economics and German from LondonUniversity and an MBA from the Open University Business School
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1317
xii
Conventions
983119 The main part of the text is set in AGaramond whereas entries are set in
Courier For example
Enter the Scenario Name as Base Case
983119 Items on the menu bars also shown in Courier For example
Select Tools Goal Seek
983119 The names of functions are in Courier capitals This is the payment
function which requires inputs for the interest rate number of periods
present value and future value
=PMT(INTNPERPVFVTYPE)
983119 Cell formulas are also shown in Courier For example
=IF($C$75=1IF($B25gtC$22$B25-C$22-C$23-
C$23)IF($B25ltC$22C$22-$B25-C$23-C$23))
983119 Equations are formed with the equation editor and shown in normal
notation For example net present value
(CashFlow) N
NPV = ndashndashndashndashndashndashndashndashndashndash (1 + r) N
983119 Genders The use of lsquohersquo or lsquohimrsquo refers to masculine or feminine and this
is used for simplicity to avoid repetition
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1417
xiii
Overview
WHO NEEDS THIS BOOK
More than 20 years ago I used a Hewlett Packard 38C to calculate interest
rates and analyse cash flows and then progressed to an HP 41C with a printer
magnetic strip reader and plug-in finance and mathematics packs This wasan early alphanumeric calculator which gave me the opportunity to program
lease versus purchase or lessor lease evaluation cash flows and structure more
complex lease structures This is before IBM launched the personal compu-
ter in the early 1980s Since that time I have progressed through calculators
such as the HP 12C HP 17BII HP 19B or TI BAII Plus which all provide
dedicated user screens and allow you to undertake financial mathematics
While calculators are much easier than tables or earlier methods they can
be difficult to use without errors When I run training courses on the basic
financial calculations the main drawback is only too obvious you cannot see
your inputs or check the interim calculations and therefore delegates always
want to see a map of the variables to understand the answer
While I have continued to use financial calculators which have now been
augmented with other programs on mobile phones using Windows Mobile
or a selection of applications on Apple iPhones and have in the past created
programs in Basic the most comprehensive medium for financial mathe-
matics has grown to be Microsoftreg Excel I first used Lotus in 1988 and
Excel 30 in 1990 and through various upgrades Excel grew into Microsoftreg
Office 2007 which remains little changed in the core financial functions
through to todayrsquos versions Given that almost everybody in finance has Excel on their desks and
increasingly on their laptops phones or pocket computers the objective
of this book is to explain the basic calculations for mathematical finance
backed up by simple templates for further use and development together
with examples and exercises If you work through each of the chapters in the
book and try the exercises you will improve your Excel skills and obtain a
better grasp of the underlying financial concepts
My other modelling books published by FT Prentice Hall Mastering
Financial Modelling and Mastering Risk Modelling provide complete modelsfor some of the topics in this book and combine finance with model design
using ideas of best practice coupled with methods of auditing and testing
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1517
xiv
This book adheres to systematic spreadsheet best practice and adopts the
same colour scheme method and layout
The key objectives for this book are to
983119 provide explanation of key financial formulas and subject areas
983119 show the use of the formulas using straightforward Excel templates
983119 introduce examples and exercises for extension work
983119 provide a library of basic templates for further development
This book aims to assist two key groups
983119 practitioners who want a manual of financial mathematics from which
they can gain immediate use and payback
983119 business students who need a textbook which is more geared to Excel
solutions than some college manualsThe areas of responsibility where the book should be of interest are
983119 CFOs and finance directors
983119 financial controllers
983119 financial analysts and executives
983119 accountants
983119 corporate finance specialists
983119
treasury managers 983119 risk managers
983119 academics business and MBA students
Therefore people interested in this book range from a company accountant
who wants a reference book to academics and business students who need a
financial mathematics manual in Excel The book has an international bias
and will provide examples which are relevant to the UK and overseas
HOW TO USE THIS BOOK
983119 Install the Excel application templates using the simple SETUP com-
mand The files will install automatically together with a program group
and icons There is a key to the file names on page 343
983119 Work through each of the chapters and the examples
983119 Use the manual spreadsheets and templates as a reference guide for fur-
ther work
983119 Practise develop and improve your efficiency and competence with Excel
Alastair L Day
Email adaysystemcouk or Internet wwwfinancial-modelscom
Overview
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1617
xv
Warranty and disclaimer
The financial models used in the book have not been formally audited and
no representation warranty or undertaking (express or implied) is made and
no responsibility is taken or accepted by Systematic Finance and its direc-
tors as to the adequacy accuracy completeness or reasonableness of the
financial models and the company excludes liability thereof
In particular no responsibility is taken or accepted by the company and
all liability is excluded by the company for the accuracy of the computations
comprised therein and the assumptions upon which such computations are
based In addition the reader receives and uses the financial models entirely
at his own risk and no responsibility is taken or accepted by the Company
and accordingly all liability is excluded by the company for any losses which
may result from the use of the financial models whether as a direct or indi-
rect consequence of a computer virus or otherwise
Microsoft Microsoft Excel Windows and Windows XP are either re-
gistered trademarks or trademarks of Microsoft Corporation in the United
States andor other countries Screen shots reprinted by permission from
Microsoft Corporation
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1717
1
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1117
Acknowledgements
I would like to thank Angela Matthew and Frances for their support
and assistance with the completion of this book In addition Christopher
Cudmore Martina OrsquoSullivan and Laura Blake of Pearson Education have
provided valuable support and backing for this project
x
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1217
xi
About the author
Alastair Day has worked in the finance industry for more than 25 yearsin treasury and marketing functions and was formerly a director of avendor leasing company specializing in the IT and technology indus-
tries After rapid growth the directors sold the enterprise to a publiccompany and he established Systematic Finance as a consultancy special-izing in
983119 financial modelling ndash review design build and audit
983119 training in financial modelling corporate finance leasing and credit
analysis on an in-house and public basis throughout Europe Middle East
Africa and America
983119 finance and operating lease structuring as a consultant and lessor
Alastair is author of three modelling books published by FT Prentice Hall Mastering Financial Modelling Mastering Risk Modelling and Mastering
Financial Mathematics in Excel apart from other books and publications on
financial analysis and leasing
Alastair has a degree in Economics and German from LondonUniversity and an MBA from the Open University Business School
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1317
xii
Conventions
983119 The main part of the text is set in AGaramond whereas entries are set in
Courier For example
Enter the Scenario Name as Base Case
983119 Items on the menu bars also shown in Courier For example
Select Tools Goal Seek
983119 The names of functions are in Courier capitals This is the payment
function which requires inputs for the interest rate number of periods
present value and future value
=PMT(INTNPERPVFVTYPE)
983119 Cell formulas are also shown in Courier For example
=IF($C$75=1IF($B25gtC$22$B25-C$22-C$23-
C$23)IF($B25ltC$22C$22-$B25-C$23-C$23))
983119 Equations are formed with the equation editor and shown in normal
notation For example net present value
(CashFlow) N
NPV = ndashndashndashndashndashndashndashndashndashndash (1 + r) N
983119 Genders The use of lsquohersquo or lsquohimrsquo refers to masculine or feminine and this
is used for simplicity to avoid repetition
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1417
xiii
Overview
WHO NEEDS THIS BOOK
More than 20 years ago I used a Hewlett Packard 38C to calculate interest
rates and analyse cash flows and then progressed to an HP 41C with a printer
magnetic strip reader and plug-in finance and mathematics packs This wasan early alphanumeric calculator which gave me the opportunity to program
lease versus purchase or lessor lease evaluation cash flows and structure more
complex lease structures This is before IBM launched the personal compu-
ter in the early 1980s Since that time I have progressed through calculators
such as the HP 12C HP 17BII HP 19B or TI BAII Plus which all provide
dedicated user screens and allow you to undertake financial mathematics
While calculators are much easier than tables or earlier methods they can
be difficult to use without errors When I run training courses on the basic
financial calculations the main drawback is only too obvious you cannot see
your inputs or check the interim calculations and therefore delegates always
want to see a map of the variables to understand the answer
While I have continued to use financial calculators which have now been
augmented with other programs on mobile phones using Windows Mobile
or a selection of applications on Apple iPhones and have in the past created
programs in Basic the most comprehensive medium for financial mathe-
matics has grown to be Microsoftreg Excel I first used Lotus in 1988 and
Excel 30 in 1990 and through various upgrades Excel grew into Microsoftreg
Office 2007 which remains little changed in the core financial functions
through to todayrsquos versions Given that almost everybody in finance has Excel on their desks and
increasingly on their laptops phones or pocket computers the objective
of this book is to explain the basic calculations for mathematical finance
backed up by simple templates for further use and development together
with examples and exercises If you work through each of the chapters in the
book and try the exercises you will improve your Excel skills and obtain a
better grasp of the underlying financial concepts
My other modelling books published by FT Prentice Hall Mastering
Financial Modelling and Mastering Risk Modelling provide complete modelsfor some of the topics in this book and combine finance with model design
using ideas of best practice coupled with methods of auditing and testing
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1517
xiv
This book adheres to systematic spreadsheet best practice and adopts the
same colour scheme method and layout
The key objectives for this book are to
983119 provide explanation of key financial formulas and subject areas
983119 show the use of the formulas using straightforward Excel templates
983119 introduce examples and exercises for extension work
983119 provide a library of basic templates for further development
This book aims to assist two key groups
983119 practitioners who want a manual of financial mathematics from which
they can gain immediate use and payback
983119 business students who need a textbook which is more geared to Excel
solutions than some college manualsThe areas of responsibility where the book should be of interest are
983119 CFOs and finance directors
983119 financial controllers
983119 financial analysts and executives
983119 accountants
983119 corporate finance specialists
983119
treasury managers 983119 risk managers
983119 academics business and MBA students
Therefore people interested in this book range from a company accountant
who wants a reference book to academics and business students who need a
financial mathematics manual in Excel The book has an international bias
and will provide examples which are relevant to the UK and overseas
HOW TO USE THIS BOOK
983119 Install the Excel application templates using the simple SETUP com-
mand The files will install automatically together with a program group
and icons There is a key to the file names on page 343
983119 Work through each of the chapters and the examples
983119 Use the manual spreadsheets and templates as a reference guide for fur-
ther work
983119 Practise develop and improve your efficiency and competence with Excel
Alastair L Day
Email adaysystemcouk or Internet wwwfinancial-modelscom
Overview
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1617
xv
Warranty and disclaimer
The financial models used in the book have not been formally audited and
no representation warranty or undertaking (express or implied) is made and
no responsibility is taken or accepted by Systematic Finance and its direc-
tors as to the adequacy accuracy completeness or reasonableness of the
financial models and the company excludes liability thereof
In particular no responsibility is taken or accepted by the company and
all liability is excluded by the company for the accuracy of the computations
comprised therein and the assumptions upon which such computations are
based In addition the reader receives and uses the financial models entirely
at his own risk and no responsibility is taken or accepted by the Company
and accordingly all liability is excluded by the company for any losses which
may result from the use of the financial models whether as a direct or indi-
rect consequence of a computer virus or otherwise
Microsoft Microsoft Excel Windows and Windows XP are either re-
gistered trademarks or trademarks of Microsoft Corporation in the United
States andor other countries Screen shots reprinted by permission from
Microsoft Corporation
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1717
1
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1217
xi
About the author
Alastair Day has worked in the finance industry for more than 25 yearsin treasury and marketing functions and was formerly a director of avendor leasing company specializing in the IT and technology indus-
tries After rapid growth the directors sold the enterprise to a publiccompany and he established Systematic Finance as a consultancy special-izing in
983119 financial modelling ndash review design build and audit
983119 training in financial modelling corporate finance leasing and credit
analysis on an in-house and public basis throughout Europe Middle East
Africa and America
983119 finance and operating lease structuring as a consultant and lessor
Alastair is author of three modelling books published by FT Prentice Hall Mastering Financial Modelling Mastering Risk Modelling and Mastering
Financial Mathematics in Excel apart from other books and publications on
financial analysis and leasing
Alastair has a degree in Economics and German from LondonUniversity and an MBA from the Open University Business School
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1317
xii
Conventions
983119 The main part of the text is set in AGaramond whereas entries are set in
Courier For example
Enter the Scenario Name as Base Case
983119 Items on the menu bars also shown in Courier For example
Select Tools Goal Seek
983119 The names of functions are in Courier capitals This is the payment
function which requires inputs for the interest rate number of periods
present value and future value
=PMT(INTNPERPVFVTYPE)
983119 Cell formulas are also shown in Courier For example
=IF($C$75=1IF($B25gtC$22$B25-C$22-C$23-
C$23)IF($B25ltC$22C$22-$B25-C$23-C$23))
983119 Equations are formed with the equation editor and shown in normal
notation For example net present value
(CashFlow) N
NPV = ndashndashndashndashndashndashndashndashndashndash (1 + r) N
983119 Genders The use of lsquohersquo or lsquohimrsquo refers to masculine or feminine and this
is used for simplicity to avoid repetition
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1417
xiii
Overview
WHO NEEDS THIS BOOK
More than 20 years ago I used a Hewlett Packard 38C to calculate interest
rates and analyse cash flows and then progressed to an HP 41C with a printer
magnetic strip reader and plug-in finance and mathematics packs This wasan early alphanumeric calculator which gave me the opportunity to program
lease versus purchase or lessor lease evaluation cash flows and structure more
complex lease structures This is before IBM launched the personal compu-
ter in the early 1980s Since that time I have progressed through calculators
such as the HP 12C HP 17BII HP 19B or TI BAII Plus which all provide
dedicated user screens and allow you to undertake financial mathematics
While calculators are much easier than tables or earlier methods they can
be difficult to use without errors When I run training courses on the basic
financial calculations the main drawback is only too obvious you cannot see
your inputs or check the interim calculations and therefore delegates always
want to see a map of the variables to understand the answer
While I have continued to use financial calculators which have now been
augmented with other programs on mobile phones using Windows Mobile
or a selection of applications on Apple iPhones and have in the past created
programs in Basic the most comprehensive medium for financial mathe-
matics has grown to be Microsoftreg Excel I first used Lotus in 1988 and
Excel 30 in 1990 and through various upgrades Excel grew into Microsoftreg
Office 2007 which remains little changed in the core financial functions
through to todayrsquos versions Given that almost everybody in finance has Excel on their desks and
increasingly on their laptops phones or pocket computers the objective
of this book is to explain the basic calculations for mathematical finance
backed up by simple templates for further use and development together
with examples and exercises If you work through each of the chapters in the
book and try the exercises you will improve your Excel skills and obtain a
better grasp of the underlying financial concepts
My other modelling books published by FT Prentice Hall Mastering
Financial Modelling and Mastering Risk Modelling provide complete modelsfor some of the topics in this book and combine finance with model design
using ideas of best practice coupled with methods of auditing and testing
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1517
xiv
This book adheres to systematic spreadsheet best practice and adopts the
same colour scheme method and layout
The key objectives for this book are to
983119 provide explanation of key financial formulas and subject areas
983119 show the use of the formulas using straightforward Excel templates
983119 introduce examples and exercises for extension work
983119 provide a library of basic templates for further development
This book aims to assist two key groups
983119 practitioners who want a manual of financial mathematics from which
they can gain immediate use and payback
983119 business students who need a textbook which is more geared to Excel
solutions than some college manualsThe areas of responsibility where the book should be of interest are
983119 CFOs and finance directors
983119 financial controllers
983119 financial analysts and executives
983119 accountants
983119 corporate finance specialists
983119
treasury managers 983119 risk managers
983119 academics business and MBA students
Therefore people interested in this book range from a company accountant
who wants a reference book to academics and business students who need a
financial mathematics manual in Excel The book has an international bias
and will provide examples which are relevant to the UK and overseas
HOW TO USE THIS BOOK
983119 Install the Excel application templates using the simple SETUP com-
mand The files will install automatically together with a program group
and icons There is a key to the file names on page 343
983119 Work through each of the chapters and the examples
983119 Use the manual spreadsheets and templates as a reference guide for fur-
ther work
983119 Practise develop and improve your efficiency and competence with Excel
Alastair L Day
Email adaysystemcouk or Internet wwwfinancial-modelscom
Overview
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1617
xv
Warranty and disclaimer
The financial models used in the book have not been formally audited and
no representation warranty or undertaking (express or implied) is made and
no responsibility is taken or accepted by Systematic Finance and its direc-
tors as to the adequacy accuracy completeness or reasonableness of the
financial models and the company excludes liability thereof
In particular no responsibility is taken or accepted by the company and
all liability is excluded by the company for the accuracy of the computations
comprised therein and the assumptions upon which such computations are
based In addition the reader receives and uses the financial models entirely
at his own risk and no responsibility is taken or accepted by the Company
and accordingly all liability is excluded by the company for any losses which
may result from the use of the financial models whether as a direct or indi-
rect consequence of a computer virus or otherwise
Microsoft Microsoft Excel Windows and Windows XP are either re-
gistered trademarks or trademarks of Microsoft Corporation in the United
States andor other countries Screen shots reprinted by permission from
Microsoft Corporation
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1717
1
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1317
xii
Conventions
983119 The main part of the text is set in AGaramond whereas entries are set in
Courier For example
Enter the Scenario Name as Base Case
983119 Items on the menu bars also shown in Courier For example
Select Tools Goal Seek
983119 The names of functions are in Courier capitals This is the payment
function which requires inputs for the interest rate number of periods
present value and future value
=PMT(INTNPERPVFVTYPE)
983119 Cell formulas are also shown in Courier For example
=IF($C$75=1IF($B25gtC$22$B25-C$22-C$23-
C$23)IF($B25ltC$22C$22-$B25-C$23-C$23))
983119 Equations are formed with the equation editor and shown in normal
notation For example net present value
(CashFlow) N
NPV = ndashndashndashndashndashndashndashndashndashndash (1 + r) N
983119 Genders The use of lsquohersquo or lsquohimrsquo refers to masculine or feminine and this
is used for simplicity to avoid repetition
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1417
xiii
Overview
WHO NEEDS THIS BOOK
More than 20 years ago I used a Hewlett Packard 38C to calculate interest
rates and analyse cash flows and then progressed to an HP 41C with a printer
magnetic strip reader and plug-in finance and mathematics packs This wasan early alphanumeric calculator which gave me the opportunity to program
lease versus purchase or lessor lease evaluation cash flows and structure more
complex lease structures This is before IBM launched the personal compu-
ter in the early 1980s Since that time I have progressed through calculators
such as the HP 12C HP 17BII HP 19B or TI BAII Plus which all provide
dedicated user screens and allow you to undertake financial mathematics
While calculators are much easier than tables or earlier methods they can
be difficult to use without errors When I run training courses on the basic
financial calculations the main drawback is only too obvious you cannot see
your inputs or check the interim calculations and therefore delegates always
want to see a map of the variables to understand the answer
While I have continued to use financial calculators which have now been
augmented with other programs on mobile phones using Windows Mobile
or a selection of applications on Apple iPhones and have in the past created
programs in Basic the most comprehensive medium for financial mathe-
matics has grown to be Microsoftreg Excel I first used Lotus in 1988 and
Excel 30 in 1990 and through various upgrades Excel grew into Microsoftreg
Office 2007 which remains little changed in the core financial functions
through to todayrsquos versions Given that almost everybody in finance has Excel on their desks and
increasingly on their laptops phones or pocket computers the objective
of this book is to explain the basic calculations for mathematical finance
backed up by simple templates for further use and development together
with examples and exercises If you work through each of the chapters in the
book and try the exercises you will improve your Excel skills and obtain a
better grasp of the underlying financial concepts
My other modelling books published by FT Prentice Hall Mastering
Financial Modelling and Mastering Risk Modelling provide complete modelsfor some of the topics in this book and combine finance with model design
using ideas of best practice coupled with methods of auditing and testing
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1517
xiv
This book adheres to systematic spreadsheet best practice and adopts the
same colour scheme method and layout
The key objectives for this book are to
983119 provide explanation of key financial formulas and subject areas
983119 show the use of the formulas using straightforward Excel templates
983119 introduce examples and exercises for extension work
983119 provide a library of basic templates for further development
This book aims to assist two key groups
983119 practitioners who want a manual of financial mathematics from which
they can gain immediate use and payback
983119 business students who need a textbook which is more geared to Excel
solutions than some college manualsThe areas of responsibility where the book should be of interest are
983119 CFOs and finance directors
983119 financial controllers
983119 financial analysts and executives
983119 accountants
983119 corporate finance specialists
983119
treasury managers 983119 risk managers
983119 academics business and MBA students
Therefore people interested in this book range from a company accountant
who wants a reference book to academics and business students who need a
financial mathematics manual in Excel The book has an international bias
and will provide examples which are relevant to the UK and overseas
HOW TO USE THIS BOOK
983119 Install the Excel application templates using the simple SETUP com-
mand The files will install automatically together with a program group
and icons There is a key to the file names on page 343
983119 Work through each of the chapters and the examples
983119 Use the manual spreadsheets and templates as a reference guide for fur-
ther work
983119 Practise develop and improve your efficiency and competence with Excel
Alastair L Day
Email adaysystemcouk or Internet wwwfinancial-modelscom
Overview
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1617
xv
Warranty and disclaimer
The financial models used in the book have not been formally audited and
no representation warranty or undertaking (express or implied) is made and
no responsibility is taken or accepted by Systematic Finance and its direc-
tors as to the adequacy accuracy completeness or reasonableness of the
financial models and the company excludes liability thereof
In particular no responsibility is taken or accepted by the company and
all liability is excluded by the company for the accuracy of the computations
comprised therein and the assumptions upon which such computations are
based In addition the reader receives and uses the financial models entirely
at his own risk and no responsibility is taken or accepted by the Company
and accordingly all liability is excluded by the company for any losses which
may result from the use of the financial models whether as a direct or indi-
rect consequence of a computer virus or otherwise
Microsoft Microsoft Excel Windows and Windows XP are either re-
gistered trademarks or trademarks of Microsoft Corporation in the United
States andor other countries Screen shots reprinted by permission from
Microsoft Corporation
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1717
1
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1417
xiii
Overview
WHO NEEDS THIS BOOK
More than 20 years ago I used a Hewlett Packard 38C to calculate interest
rates and analyse cash flows and then progressed to an HP 41C with a printer
magnetic strip reader and plug-in finance and mathematics packs This wasan early alphanumeric calculator which gave me the opportunity to program
lease versus purchase or lessor lease evaluation cash flows and structure more
complex lease structures This is before IBM launched the personal compu-
ter in the early 1980s Since that time I have progressed through calculators
such as the HP 12C HP 17BII HP 19B or TI BAII Plus which all provide
dedicated user screens and allow you to undertake financial mathematics
While calculators are much easier than tables or earlier methods they can
be difficult to use without errors When I run training courses on the basic
financial calculations the main drawback is only too obvious you cannot see
your inputs or check the interim calculations and therefore delegates always
want to see a map of the variables to understand the answer
While I have continued to use financial calculators which have now been
augmented with other programs on mobile phones using Windows Mobile
or a selection of applications on Apple iPhones and have in the past created
programs in Basic the most comprehensive medium for financial mathe-
matics has grown to be Microsoftreg Excel I first used Lotus in 1988 and
Excel 30 in 1990 and through various upgrades Excel grew into Microsoftreg
Office 2007 which remains little changed in the core financial functions
through to todayrsquos versions Given that almost everybody in finance has Excel on their desks and
increasingly on their laptops phones or pocket computers the objective
of this book is to explain the basic calculations for mathematical finance
backed up by simple templates for further use and development together
with examples and exercises If you work through each of the chapters in the
book and try the exercises you will improve your Excel skills and obtain a
better grasp of the underlying financial concepts
My other modelling books published by FT Prentice Hall Mastering
Financial Modelling and Mastering Risk Modelling provide complete modelsfor some of the topics in this book and combine finance with model design
using ideas of best practice coupled with methods of auditing and testing
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1517
xiv
This book adheres to systematic spreadsheet best practice and adopts the
same colour scheme method and layout
The key objectives for this book are to
983119 provide explanation of key financial formulas and subject areas
983119 show the use of the formulas using straightforward Excel templates
983119 introduce examples and exercises for extension work
983119 provide a library of basic templates for further development
This book aims to assist two key groups
983119 practitioners who want a manual of financial mathematics from which
they can gain immediate use and payback
983119 business students who need a textbook which is more geared to Excel
solutions than some college manualsThe areas of responsibility where the book should be of interest are
983119 CFOs and finance directors
983119 financial controllers
983119 financial analysts and executives
983119 accountants
983119 corporate finance specialists
983119
treasury managers 983119 risk managers
983119 academics business and MBA students
Therefore people interested in this book range from a company accountant
who wants a reference book to academics and business students who need a
financial mathematics manual in Excel The book has an international bias
and will provide examples which are relevant to the UK and overseas
HOW TO USE THIS BOOK
983119 Install the Excel application templates using the simple SETUP com-
mand The files will install automatically together with a program group
and icons There is a key to the file names on page 343
983119 Work through each of the chapters and the examples
983119 Use the manual spreadsheets and templates as a reference guide for fur-
ther work
983119 Practise develop and improve your efficiency and competence with Excel
Alastair L Day
Email adaysystemcouk or Internet wwwfinancial-modelscom
Overview
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1617
xv
Warranty and disclaimer
The financial models used in the book have not been formally audited and
no representation warranty or undertaking (express or implied) is made and
no responsibility is taken or accepted by Systematic Finance and its direc-
tors as to the adequacy accuracy completeness or reasonableness of the
financial models and the company excludes liability thereof
In particular no responsibility is taken or accepted by the company and
all liability is excluded by the company for the accuracy of the computations
comprised therein and the assumptions upon which such computations are
based In addition the reader receives and uses the financial models entirely
at his own risk and no responsibility is taken or accepted by the Company
and accordingly all liability is excluded by the company for any losses which
may result from the use of the financial models whether as a direct or indi-
rect consequence of a computer virus or otherwise
Microsoft Microsoft Excel Windows and Windows XP are either re-
gistered trademarks or trademarks of Microsoft Corporation in the United
States andor other countries Screen shots reprinted by permission from
Microsoft Corporation
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1717
1
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1517
xiv
This book adheres to systematic spreadsheet best practice and adopts the
same colour scheme method and layout
The key objectives for this book are to
983119 provide explanation of key financial formulas and subject areas
983119 show the use of the formulas using straightforward Excel templates
983119 introduce examples and exercises for extension work
983119 provide a library of basic templates for further development
This book aims to assist two key groups
983119 practitioners who want a manual of financial mathematics from which
they can gain immediate use and payback
983119 business students who need a textbook which is more geared to Excel
solutions than some college manualsThe areas of responsibility where the book should be of interest are
983119 CFOs and finance directors
983119 financial controllers
983119 financial analysts and executives
983119 accountants
983119 corporate finance specialists
983119
treasury managers 983119 risk managers
983119 academics business and MBA students
Therefore people interested in this book range from a company accountant
who wants a reference book to academics and business students who need a
financial mathematics manual in Excel The book has an international bias
and will provide examples which are relevant to the UK and overseas
HOW TO USE THIS BOOK
983119 Install the Excel application templates using the simple SETUP com-
mand The files will install automatically together with a program group
and icons There is a key to the file names on page 343
983119 Work through each of the chapters and the examples
983119 Use the manual spreadsheets and templates as a reference guide for fur-
ther work
983119 Practise develop and improve your efficiency and competence with Excel
Alastair L Day
Email adaysystemcouk or Internet wwwfinancial-modelscom
Overview
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1617
xv
Warranty and disclaimer
The financial models used in the book have not been formally audited and
no representation warranty or undertaking (express or implied) is made and
no responsibility is taken or accepted by Systematic Finance and its direc-
tors as to the adequacy accuracy completeness or reasonableness of the
financial models and the company excludes liability thereof
In particular no responsibility is taken or accepted by the company and
all liability is excluded by the company for the accuracy of the computations
comprised therein and the assumptions upon which such computations are
based In addition the reader receives and uses the financial models entirely
at his own risk and no responsibility is taken or accepted by the Company
and accordingly all liability is excluded by the company for any losses which
may result from the use of the financial models whether as a direct or indi-
rect consequence of a computer virus or otherwise
Microsoft Microsoft Excel Windows and Windows XP are either re-
gistered trademarks or trademarks of Microsoft Corporation in the United
States andor other countries Screen shots reprinted by permission from
Microsoft Corporation
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1717
1
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1617
xv
Warranty and disclaimer
The financial models used in the book have not been formally audited and
no representation warranty or undertaking (express or implied) is made and
no responsibility is taken or accepted by Systematic Finance and its direc-
tors as to the adequacy accuracy completeness or reasonableness of the
financial models and the company excludes liability thereof
In particular no responsibility is taken or accepted by the company and
all liability is excluded by the company for the accuracy of the computations
comprised therein and the assumptions upon which such computations are
based In addition the reader receives and uses the financial models entirely
at his own risk and no responsibility is taken or accepted by the Company
and accordingly all liability is excluded by the company for any losses which
may result from the use of the financial models whether as a direct or indi-
rect consequence of a computer virus or otherwise
Microsoft Microsoft Excel Windows and Windows XP are either re-
gistered trademarks or trademarks of Microsoft Corporation in the United
States andor other countries Screen shots reprinted by permission from
Microsoft Corporation
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1717
1
7172019 Mastering Financial Mathematics in Microsoft Excel Contents
httpslidepdfcomreaderfullmastering-financial-mathematics-in-microsoft-excel-contents 1717
1