capital budgeting material

7/31/2019 Capital Budgeting Material

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Should wepursue building of

this

plant?


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Capital expenditures involve investments of significant financial resources inprojects to develop or introduce new products or services.

Capital expenditures involve investments of significant financial resources inprojects to develop or introduce new products or services.

Characteristics of capital purchases:Large capital outlays are requiredLong-term impact on earningsLack of liquidity (they cannot be readily disposed of)

Characteristics of capital purchases:Large capital outlays are required

Long-term impact on earningsLack of liquidity (they cannot be readily disposed of)


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33

Introduction

Introduction

A basicrequirement for asystematicapproach tocapital budgetingis a well-defined

set of long-rangegoals.

A basicrequirement for asystematic

approach tocapital budgetingis a well-defined

set of long-rangegoals.

An organizationshould have a well-defined business

strategy.

An organizationshould have a well-defined business

strategy.

Procedures shouldbe developed for the

review, evaluation,approval, and post-audit of capitalexpenditure

proposals.

Procedures shouldbe developed for the

review, evaluation,approval, and post-audit of capitalexpenditure

proposals.


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Money has time value if it can be invested atMoney has time value if it can be invested atsome positive returnsome positive return

Time value of money

Time value of money

Today

1.0000

Year 5

1.6105

Value of 1.00 today

Value 5 years from today

1.1000 $1.2100 1.3310 1.4641

Year 1 Year 2 Year 3 Year 4

Assume a 10% interest rate

Amounts of money received at different periods of time must beconverted to their value on a common date to be compared, added orsubtracted


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Future valueFuture value It is the amount a current sum of money earning a stated rateIt is the amount a current sum of money earning a stated rate

of interest will accumulate to at the end of the future periodof interest will accumulate to at the end of the future period

FV = PV (1 + r)FV = PV (1 + r)nn wherewherer: compound rater: compound rate

Present valuePresent value It is the current worth of a specified amount of money to beIt is the current worth of a specified amount of money to be

received at some future date at some interest rate.received at some future date at some interest rate.

PV = FV / (1 + r)PV = FV / (1 + r)nn where r: discount ratewhere r: discount rate

It is very useful to draw a time line in calculations thatIt is very useful to draw a time line in calculations thatinvolve the time value of moneyinvolve the time value of money

Time value of money

Time value of money


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AnnuitiesAnnuities An annuity is a stream of equal cash flows that occur atAn annuity is a stream of equal cash flows that occur at

equal intervals over a given period of timeequal intervals over a given period of time

2 types of annuity2 types of annuity

Ordinary annuity: Cash flows occur at the end of each yearOrdinary annuity: Cash flows occur at the end of each year Formula: PVOA = (a / r) x [1 1/(1 + r)Formula: PVOA = (a / r) x [1 1/(1 + r)nn]]

Refer to annuity tableRefer to annuity table

PVOA = Ordinary Annuity Factor (n, r) x AnnuityPVOA = Ordinary Annuity Factor (n, r) x Annuity

Annuity due: Cash flows occur at the beginning of each periodAnnuity due: Cash flows occur at the beginning of each period

Formula: PVOAD = (a / r) x [1 1/(1 + r)Formula: PVOAD = (a / r) x [1 1/(1 + r)n-1n-1] + a] + a Refer to annuity table.Refer to annuity table.

PVOAD = Ordinary Annuity Factor (n -1, r) x Annuity + AnnuityPVOAD = Ordinary Annuity Factor (n -1, r) x Annuity + Annuity

Time value of money

Time value of money


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77

Practice questions on time value of moneyPractice questions on time value of moneyDetermine the answers to each of the following situations:Determine the answers to each of the following situations:

a.a. The future value in 2 years of 1,000 deposited today in aThe future value in 2 years of 1,000 deposited today in asavings account with interest compounded annually at 8%.savings account with interest compounded annually at 8%.

b.b. The present value of 9,000 to be received in five years,The present value of 9,000 to be received in five years,discounted at 12%.discounted at 12%.

c.c. The present value of an annuity of 2,000 per year for fiveThe present value of an annuity of 2,000 per year for fiveyears discounted at 16%.years discounted at 16%.

d.d. A proposed investment of 32,010 is to be retuned in eightA proposed investment of 32,010 is to be retuned in eightequal annual payments. Determine the amount of eachequal annual payments. Determine the amount of each

payment if the interest rate is 10%.payment if the interest rate is 10%.e.e. A proposed investment will provide cash flows of 20,000;A proposed investment will provide cash flows of 20,000;

8,000; and 6,000 at the end of Years 1, 2 and 3 respectively.8,000; and 6,000 at the end of Years 1, 2 and 3 respectively.Using a discount rate of 20%, determine the present value ofUsing a discount rate of 20%, determine the present value ofthese cash flows.these cash flows.

Time value of moneyTime value of money


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Analysis of potential additions to fixed assets.Analysis of potential additions to fixed assets. Long-term decisions; involve largeLong-term decisions; involve large

expenditures.expenditures.

Very important to an organizations future.Very important to an organizations future.Capital budgeting is a process that involves theidentification of potentially desirable projects for capitalexpenditures, the subsequent evaluation of capital

expenditure proposals, and the selection of proposals thatmeet certain criteria.

Capital budgeting is a process that involves theidentification of potentially desirable projects for capitalexpenditures, the subsequent evaluation of capital

expenditure proposals, and the selection of proposals thatmeet certain criteria.


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1.1. Estimate CFs (inflows & outflows).Estimate CFs (inflows & outflows).

2.2. Assess riskiness of CFs.Assess riskiness of CFs.

3.3. Determine the appropriate cost of capital.Determine the appropriate cost of capital.4.4. Find NPV and/or IRR.Find NPV and/or IRR.

5.5. Accept if NPV > 0 and/or IRR > WACC.Accept if NPV > 0 and/or IRR > WACC.


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Relevance analysis is veryimportant in capital

budgeting because onlyrelevant information

should be included.

Relevance analysis is veryimportant in capitalbudgeting because only

relevant information

should be included.

To make a choice

between 2 alternatives,incremental relevanceanalysis often simplifies

the capital budgeting.

To make a choicebetween 2 alternatives,incremental relevance

analysis often simplifiesthe capital budgeting.


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Initial Investment costInitial Investment cost

Annual operating cash flows.Annual operating cash flows.

Terminal cash flowTerminal cash flow


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Independent projects if the cash flows ofIndependent projects if the cash flows ofone are unaffected by the acceptance ofone are unaffected by the acceptance of

the other.the other. Mutually exclusive projects if the cashMutually exclusive projects if the cash

flows of one can be adversely impacted byflows of one can be adversely impacted bythe acceptance of the other.the acceptance of the other.


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Normal cash flow stream Cost (negativeNormal cash flow stream Cost (negativeCF) followed by a series of positive cashCF) followed by a series of positive cash

inflows. One change of signs.inflows. One change of signs. Nonnormal cash flow stream Two orNonnormal cash flow stream Two or

more changes of signs. Most common:more changes of signs. Most common:Cost (negative CF), then string of positiveCost (negative CF), then string of positive

CFs, then cost to close project. NuclearCFs, then cost to close project. Nuclearpower plant, strip mine, etc.power plant, strip mine, etc.


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Capital Budgeting ModelsCapital Budgeting Models

There are two main types of CapitalBudgeting Models: Capital budgeting models that consider the

time value of money Net Present Value (NPV) Internal Rate of Return (IRR) Discounted Payback Period

Capital budgeting models that do notconsider the time value of money Payback Period Accounting Rate of Return (ARR)


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The number of years required to recoverThe number of years required to recover

a projects cost, or How long does it takea projects cost, or How long does it take

to get our money back?to get our money back? Calculated by adding projects cashCalculated by adding projects cash

inflows to its cost until the cumulativeinflows to its cost until the cumulative

cash flow for the project turns positive.cash flow for the project turns positive.


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SITUATION 1: EVEN (SAME) CASHLOWSSITUATION 1: EVEN (SAME) CASHLOWS

PAY BACKPERIODPAY BACKPERIOD= CAPITAL OUTLAY= CAPITAL OUTLAY

CASHFLOWS PER PERIODCASHFLOWS PER PERIOD

SITUATION 2: UNEVEN CASHFLOWSSITUATION 2: UNEVEN CASHFLOWS

PAY BACK PERIOD= A + B/CPAY BACK PERIOD= A + B/C

WhereWhere:: AA is the number of full years immediately before coveringis the number of full years immediately before covering

the capital outlaythe capital outlayBB is the balance remaining to cover the capital outlayis the balance remaining to cover the capital outlay

CC is the total amount that is received in the year when theis the total amount that is received in the year when the

capital outlay is fully coveredcapital outlay is fully covered


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PaybackL = 2 + / = 2.375 years

CFt -100 10 60 100

Cumulative -100 -90 0 50

0 1 2 3

=

2.4

30 80

80

-30

Project L

PaybackS = 1 + / = 1.6 years

CFt -100 70 100 20

Cumulative -100 0 20 40

0 1 2 3

=

1.6

30 50

50

-30

Project S


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Uses discounted cash flows rather thanUses discounted cash flows rather than

raw CFs.raw CFs.

Disc PaybackL = 2 + / = 2.7 years

CFt -100 10 60 80

Cumulative -100 -90.91 18.79

0 1 2 3

=

2.7

60.11

-41.32

PV of CFt -100 9.09 49.59

41.32 60.11

10%


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Net present value is thepresent value of the projects

net cash inflows from

operations...

Net present value is thepresent value of the projects

net cash inflows from

operations...

and disinvestmentless the amount of the

initial investment.

and disinvestmentless the amount of the

initial investment.


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Sum of the PVs of all cash inflows andSum of the PVs of all cash inflows andoutflows of a project:outflows of a project:

= +

=

n

0t

t

t

)k1(

CFNPV

PRESENT VALUE INTEREST FACTOR AT r%=1/(1+r)^n


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YearYear CFCFtt PVIF@10%PVIF@10% PV of CFPV of CFtt

00 -100-100 11 100100

11 1010 0.9090.909 9.099.0922 6060 0.82640.8264 49.5949.59

33 8080 0.75130.7513 60.1160.11

NPVNPVLL == 18.7918.79

NPVNPVSS = 19.98= 19.98


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NPVNPV = PV of inflows Cost= PV of inflows Cost

= Net gain in wealth= Net gain in wealth

If projects are independent, accept if theIf projects are independent, accept if the

project NPV > 0.project NPV > 0.

If projects are mutually exclusive, acceptIf projects are mutually exclusive, acceptprojects with the highest positive NPV,projects with the highest positive NPV,

those that add the most value.those that add the most value. In this example, would accept S if mutuallyIn this example, would accept S if mutually

exclusive (NPVexclusive (NPVss > NPV> NPVLL), and would), and would

accept both if independent.accept both if independent.


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1. Also called the time-adjusted rate ofreturn.

2. It is the minimum rate that could be paid forthe money invested in a project withoutlosing money.

3. It is also described as the discount rate thatresults in a projects net present valueequaling zero.


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IRR is the discount rate that forces PV ofIRR is the discount rate that forces PV ofinflows to be equal to cost, and the NPV = 0:inflows to be equal to cost, and the NPV = 0:

= +

=n

0tt

t

)IRR1(CF0


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InterpolationInterpolation Finding the discount rate that results in a zero npv.Finding the discount rate that results in a zero npv.

IRRIRR = r1 += r1 + npv1npv1 (r2-r1)(r2-r1) (npv1-npv2)(npv1-npv2)

where:where:

r1r1 discount rate that results in a positive NPVdiscount rate that results in a positive NPV

r2r2 discount rate that results in a negative NPVdiscount rate that results in a negative NPV

npv1npv1 positive NPVpositive NPV

npv2npv2 negative NPV.negative NPV.


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If IRR > WACC, the projects rate ofIf IRR > WACC, the projects rate of

return is greater than its costs.return is greater than its costs.

There is some return left over toThere is some return left over toboost stockholders returns.boost stockholders returns.


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Calculate IRR using the previousCalculate IRR using the previous

exampleexample


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If IRR > k, accept project.If IRR > k, accept project. If IRR < k, reject project.If IRR < k, reject project.

If projects are independent, acceptIf projects are independent, acceptboth projects, as both IRR > k = 10%.both projects, as both IRR > k = 10%.

If projects are mutually exclusive,If projects are mutually exclusive,accept S, because IRRaccept S, because IRRss > IRR> IRRLL..


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The higher the internalThe higher the internal

rate of return, therate of return, the

more desirable themore desirable theproject.project.

The higher the internalThe higher the internal

rate of return, therate of return, the

more desirable themore desirable theproject.project.

When using the internal rate of returnmethod to rank competing investmentprojects, the preference rule is:


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Spreadsheet ApproachSpreadsheet Approach

1. Input

A B

1 Year of cash flow Cash flow2 0 $-94,5543 1 30,0004 2 30,000

5 3 30,0006 4 30,0007 5 42,0008 IRR =IRR(B2:B7,0.08)

Internal Rate of Return (IRR)Internal Rate of Return (IRR)


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Internal Rate of Return (IRR)Internal Rate of Return (IRR)

Spreadsheet ApproachSpreadsheet Approach

2. Output

A B

1 Year of cash flow Cash flow2 0 $-94,5543 1 30,0004 2 30,0005 3 30,0006 4 30,0007 5 42,0008 IRR 0.20


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The net present value model gives explicitThe net present value model gives explicit

consideration to investment size. The internalconsideration to investment size. The internal

rate of return does not.rate of return does not. The net present value model assumes all netThe net present value model assumes all net

cash inflows are reinvested at the discountcash inflows are reinvested at the discount

rate. The internal rate of return modelrate. The internal rate of return model

assumes all net cash inflows are reinvested atassumes all net cash inflows are reinvested at

the projects internal rate of return.the projects internal rate of return.

The net present value model gives explicitThe net present value model gives explicit

consideration to investment size. The internalconsideration to investment size. The internal

rate of return does not.rate of return does not. The net present value model assumes all netThe net present value model assumes all net

cash inflows are reinvested at the discountcash inflows are reinvested at the discount

rate. The internal rate of return modelrate. The internal rate of return model

assumes all net cash inflows are reinvested atassumes all net cash inflows are reinvested atthe projects internal rate of return.the projects internal rate of return.


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Profitability IndexProfitability Index:: The profitability index, or PI, method compares theThe profitability index, or PI, method compares the

present value of future cash inflows with the initialpresent value of future cash inflows with the initialinvestment on a relative basis.investment on a relative basis.

Therefore, the PI is the ratio of the present value ofTherefore, the PI is the ratio of the present value of

cash flows (PVCF) to the initial investment of thecash flows (PVCF) to the initial investment of theproject.project.

== PVPV

Initial InvestmentInitial Investment


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Profitability Index cont:Profitability Index cont:

Decision CriterionDecision Criterion In this method, a project with a PIIn this method, a project with a PI

greater than 1 is accepted, but agreater than 1 is accepted, but a

project is rejected when its PI isproject is rejected when its PI isless than 1.less than 1.


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Average Rate of ReturnAverage Rate of Return

- Non discounting method:Non discounting method:

- ARR =ARR =Average annual profitsAverage annual profits- Average InvestmentAverage Investment

- Where average investment =Where average investment =

- (Initial outlay+scrap value)/2(Initial outlay+scrap value)/2- & Average annual profits =& Average annual profits =

- sum of annual profits/ no. of years.sum of annual profits/ no. of years.


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A graphical representation of project NPVs atA graphical representation of project NPVs atvarious different costs of capital.various different costs of capital.

kk NPVNPVLL NPVNPVSS00 5050 4040

55 3333 2929

1010 1919 2020

1515 77 1212

2020 (4)(4) 55


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-10

0

10

20

30

40

50

60

5 10 15 20 23.6

NPV($)

Discount Rate (%)

IRRL = 18.1%

IRRS = 23.6%

Crossover Point = 8.7%

SL

.

.

. ...

..

.

. .


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If projects are independent, the twoIf projects are independent, the twomethods always lead to the samemethods always lead to the same

accept/reject decisions.accept/reject decisions. If projects are mutually exclusive If projects are mutually exclusive If k > crossover point, the two methodsIf k > crossover point, the two methods

lead to the same decision and there is nolead to the same decision and there is no

conflict.conflict. If k < crossover point, the two methodsIf k < crossover point, the two methods

lead to different accept/reject decisions.lead to different accept/reject decisions.


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Size (scale) differences the smallerSize (scale) differences the smallerproject frees up funds at t = 0 forproject frees up funds at t = 0 for

investment. The higher the opportunityinvestment. The higher the opportunitycost, the more valuable these funds, socost, the more valuable these funds, so

high k favors small projects.high k favors small projects.

Timing differences the project with fasterTiming differences the project with faster

payback provides more CF in early yearspayback provides more CF in early yearsfor reinvestment. If k is high, early CFfor reinvestment. If k is high, early CF

especially good, NPVespecially good, NPVSS > NPV> NPVLL..


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A good method of investment appraisal must:A good method of investment appraisal must:

Take time value of money into account.Take time value of money into account.

Use cashflows instead of profitsUse cashflows instead of profits Use all cashflows.Use all cashflows.

Take into account cost of capital of the firm.Take into account cost of capital of the firm.


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Suppose you are asked whether or not a newSuppose you are asked whether or not a newconsumer product should be launched. Based onconsumer product should be launched. Based onprojected sales and costs, we expect that the cashprojected sales and costs, we expect that the cashflows over the five year life of the project would be E2flows over the five year life of the project would be E2000 in the first two years, E4 000 in the next two, and000 in the first two years, E4 000 in the next two, andE5 000 in the last year. It will cost E10 000 to beginE5 000 in the last year. It will cost E10 000 to beginproduction. We use a 10% discount rate to evaluateproduction. We use a 10% discount rate to evaluatenew products. Should we take on the new project?new products. Should we take on the new project?


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The projected cashflows from a proposed investment are:

PeriodCash flows

1 100

2 200

3 500

This project costs E500.-What is the payback period for this investment?-What is the discounted payback period for this investment,if the discount rate is 10%?


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A project has a total upfront cost ofA project has a total upfront cost of

E435.44 The cash flow E100 in the firstE435.44 The cash flow E100 in the first

year, E200 in the second year andyear, E200 in the second year andE300 in the third year. What is the IRR?E300 in the third year. What is the IRR?

If we require 18% return, should weIf we require 18% return, should we

take this investment?take this investment?


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The accounting rateof return is theaverage annualincrease in net

income that resultsfrom acceptance of acapital expenditure

proposal divided bythe initial investmentor the averageinvestment in the

project.

The accounting rateof return is theaverage annualincrease in net

income that resultsfrom acceptance of acapital expenditureproposal divided bythe initial investmentor the averageinvestment in the

project.

MobileYogurtShoppe

Mobile Yogurt Shoppepurchased a vehicle andequipment costing$90,554. It has adisposal value of $8,000at the end of 5 years.


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Accounting Rate of ReturnAccounting Rate of Return

Annual net cash inflow from operations 30,000Less average annual depreciation:

[90,554 - 8,000]/5) 16,511

Average annual increase in net income 13,489


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Accounting rateof return on initial

investment

Average annualincrease in net income

Initial investment

=

Accounting rateof return on initial

investment

=13,48994,554 = 0.1427


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Accounting rateof return on

averageinvestment

Average annualincrease in net income

Average investment

=

Accounting rateof return on

averageinvestment

=13,48953,277 = 0.2532

([94,554 + 12,000])/2

94,544 = initial investment,12,000 = disinvestment


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Predicted net cashinflow from operations:

Year 1 50,000 10,000

Year 2 50,000 10,000

Year 3 10,000 50,000Year 4 10,000 50,000

Total 120,000 120,000

Total depreciation -100,000 -100,000

Total net income 20,000 20,000Project life 4 years 4 years

Average annual increase in income$ 5,000$ 5,000

Project A Project B

ARR of Project A:

5,000/100,000 = 0.05

ARR of Project B:

5,000/100,000 = 0.05


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Evaluating Capital Budgeting ModelsEvaluating Capital Budgeting Models

Net present value analysis of Project A:

Predicted 12% PresentCash Year(s) Present ValueInflows of Cash Value of Cash

(Outflows) Flows Factor Flows

Initial investment (100,000) 0 1.000 (100,000)Operation 50,000 1-2 1.736 86,800

10,000 3-4 3.170-1.736 14,340

Net present value of all cash flows 1,140


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Evaluating Capital Budgeting ModelsEvaluating Capital Budgeting Models

Net present value analysis of Project B:

Predicted 12% PresentCash Year(s) Present ValueInflows of Cash Value of Cash

(Outflows) Flows Factor Flows

Initial investment (100,000) 0 1.000 (100,000)Operation 10,000 1-2 1.736 17,360

50,000 3-4 3.170-1.736 71,700

Net present value of all cash flows (10,940)


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Capital budgeting models do not makeCapital budgeting models do not make

investment decisions. They only helpinvestment decisions. They only help

managers separate capital expendituremanagers separate capital expenditureproposal that meet certain criteria fromproposal that meet certain criteria from

those that do notthose that do not

Multiple Investment CriteriaMultiple Investment Criteria Management may use a single capitalManagement may use a single capital

budgeting model or they may use multiplebudgeting model or they may use multiplemodels, including those that have not beenmodels, including those that have not been

discusseddiscussed


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5353

For example, to be accepted, a proposal mustFor example, to be accepted, a proposal must

meet the following criteria:meet the following criteria: Proposal must be in line with the organizations long-Proposal must be in line with the organizations long-

range goals and business strategyrange goals and business strategy Maximum payback period of 3 yearsMaximum payback period of 3 years

Have a net positive NPV when discounted at 14Have a net positive NPV when discounted at 14percentpercent

Have an initial investment of less than 500,000Have an initial investment of less than 500,000

If many of the criteria suggest the projectIf many of the criteria suggest the projectshould be taken, the chance is greater that theshould be taken, the chance is greater that the

project is desirableproject is desirable


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Proposal A Proposal B Proposal C

Predicted cash flows (in 000):Initial investment (26,900) (55,960) (30,560)Operation:

Year 1 10,000 20,000 20,000Year 2 10,000 20,000 20,000Year 3 10,000 20,000 0Year 4 10,000 20,000 0

Disinvestment 0 0 0


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Proposal AProposal A

Predicted cash flows (in 000):Initial investment (26,900)Operation:

Year 1 10,000Year 2 10,000Year 3 10,000Year 4 10,000

Disinvestment 0Net present value (in 000) at 12% 3,470Internal rate of return 18%


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Proposal BProposal BPredicted cash flows (in 000):

Initial investment (55,960)Operation:

Year 1 20,000Year 2 20,000Year 3 20,000Year 4 20,000

Disinvestment 0Net present value (in 000) at 12% 4,780Internal rate of return 16%

Ranking Capital Budgeting ProposalsRanking Capital Budgeting Proposals


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Proposal CProposal C

Predicted cash flows (in 000):Initial investment (30,560)Operation:

Year 1 20,000Year 2 20,000Year 3 0Year 4 0

Disinvestment 0Net present value (in 000) at 12% $3,240Internal rate of return 20%



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Ranking by investment criterion:Net present value 2 1 3Internal rate of return 2 3 1

Prop.Prop.

AAProp.Prop.

BBProp.Prop.

CC



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A frequent criticism of NPV, when it isused to rank proposals, is that it fails toadjust for the size of the proposed

investment To overcome this difficulty, managers

may rank projects on the basis of each

projects present value index, which iscomputed as the present value of theprojects subsequent cash flows dividedby the initial investment.

Present Value IndexPresent Value Index


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Present valueindex =

Present value of subsequentcash flows

Initial investment


30,370,00026,900,000

Present valueindex = 1.129

Proposal AProposal A


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Initial investment



60,675,00055,960,000

Proposal BProposal B


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Initial investment



33,800,00030,560,000

Proposal CProposal C


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Ranking by investment criterion:Net present value 2 1 3Internal rate of return 2 3 1Present value index 1 3 2

Prop.Prop.

AAProp.Prop.

BBProp.Prop.

CC



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