Financial ManagementFinancial Management

Unit 3 Capital Budgeting:Unit 3 Capital Budgeting:Meaning, Definition and types of evaluating the project on the Meaning, Definition and types of evaluating the project on the

basis of payback period, NPV, IRR, PI, ARR (8+2)basis of payback period, NPV, IRR, PI, ARR (8+2)

IntroductionIntroduction Capital expenditures involve investments of significant financial resources in Capital expenditures involve investments of significant financial resources in

projects to develop or introduce new products or services.projects to develop or introduce new products or services. A basic requirement for a systematic approach to capital budgeting is a well-A basic requirement for a systematic approach to capital budgeting is a well-

defined set of long-range goalsdefined set of long-range goals An organization should have a well-defined business strategy.An organization should have a well-defined business strategy. Procedures should be developed for the review, evaluation, approval, and post-Procedures should be developed for the review, evaluation, approval, and post-

audit of capital expenditure proposals.audit of capital expenditure proposals. Characteristics of capital purchases:Characteristics of capital purchases: Large capital outlays are requiredLarge capital outlays are required Long-term impact on earningsLong-term impact on earnings Lack of liquidity (they cannot be readily disposed of)Lack of liquidity (they cannot be readily disposed of)

WHAT IS CAPITAL BUDGETING?WHAT IS CAPITAL BUDGETING? Capital budgeting is a required managerial tool. One duty Capital budgeting is a required managerial tool. One duty

of a financial manager is to choose investments with of a financial manager is to choose investments with satisfactory cash flows and rates of return. Therefore, a satisfactory cash flows and rates of return. Therefore, a financial manager must be able to decide whether an financial manager must be able to decide whether an investment is worth undertaking and be able to choose investment is worth undertaking and be able to choose intelligently between two or more alternatives. To do this, a intelligently between two or more alternatives. To do this, a sound procedure to evaluate, compare, and select projects is sound procedure to evaluate, compare, and select projects is needed. This procedure is called needed. This procedure is called capital budgetingcapital budgeting..

Capital budgeting is investment decision-making as to Capital budgeting is investment decision-making as to whether a project is worth undertaking. Capital budgeting whether a project is worth undertaking. Capital budgeting is basically concerned with the justification of capital is basically concerned with the justification of capital expenditures.expenditures.

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Time value of MoneyTime value of Money Money has time value if it can be invested at some Money has time value if it can be invested at some

positive returnpositive return

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 be converted to their value on a common date to be compared, added or subtracted

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Time value of MoneyTime value of Money Future valueFuture value

– It is the amount a current sum of money earning a stated rate of It is the amount a current sum of money earning a stated rate of interest will accumulate to at the end of the future periodinterest will accumulate to at the end of the future period

– FV = PV (1 + r)FV = PV (1 + r)n n wherewhere r: compound rater: compound rate Present valuePresent value

– It is the current worth of a specified amount of money to be It 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 rate where r: discount rate It is very useful to draw a time line in calculations that It is very useful to draw a time line in calculations that

involve the time value of moneyinvolve the time value of money

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Time value of MoneyTime value of Money

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

intervals over a given period of timeintervals 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

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Time value of MoneyTime value of MoneyPractice 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 a savings The future value in 2 years of $1,000 deposited today in a savings account with interest compounded annually at 8%.account with interest compounded annually at 8%.

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

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

d.d. A proposed investment of $32,010 is to be retuned in eight equal A proposed investment of $32,010 is to be retuned in eight equal annual payments. Determine the amount of each payment if the annual payments. Determine the amount of each payment if the interest rate is 10%.interest rate is 10%.

e.e. A proposed investment will provide cash flows of $20,000; $8,000; 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. Using a and $6,000 at the end of Years 1, 2 and 3 respectively. Using a discount rate of 20%, determine the present value of these cash discount rate of 20%, determine the present value of these cash flows.flows.

What is capital budgeting?What is capital budgeting?

Analysis of potential additions to fixed assets.Analysis of potential additions to fixed assets. Long-term decisions; involve large expenditures.Long-term decisions; involve large expenditures. Very important to an organization’s future.Very important to an organization’s future. Capital budgeting is a process that involves the Capital budgeting is a process that involves the

identification of potentially desirable projects for identification of potentially desirable projects for capital expenditures, the subsequent evaluation of capital expenditures, the subsequent evaluation of capital expenditure proposals, and the selection of capital expenditure proposals, and the selection of proposals that meet certain criteriaproposals that meet certain criteria ..

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Steps to capital budgetingSteps to capital budgeting

1.1. Estimate Cash Flows (inflows & outflows).Estimate Cash Flows (inflows & outflows).2.2. Assess riskiness of Cash Flows .Assess riskiness of Cash Flows .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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Relevancy in Capital BudgetingRelevancy in Capital Budgeting

Relevance analysis is very important in Relevance analysis is very important in capital budgeting because only relevant capital budgeting because only relevant information should be included.information should be included.

To make a choice between 2 alternatives, To make a choice between 2 alternatives, incremental relevance analysis often incremental relevance analysis often simplifies the capital budgetingsimplifies the capital budgeting..

RELEVANT CASHFLOWS IN RELEVANT CASHFLOWS IN CAPITAL BUDGETINGCAPITAL BUDGETING

Initial Investment costInitial Investment cost Annual operating cash flows.Annual operating cash flows. Terminal cash flowTerminal cash flow

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What is the difference between independent and What is the difference between independent and mutually exclusive projects?mutually exclusive projects?

Independent projects – if the cash flows of one Independent projects – if the cash flows of one are unaffected by the acceptance of the other.are unaffected by the acceptance of the other.

Mutually exclusive projects – if the cash flows Mutually exclusive projects – if the cash flows of one can be adversely impacted by the of one can be adversely impacted by the acceptance of the other.acceptance of the other.

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What is the difference between normal and What is the difference between normal and non-normal cash flow streams?non-normal cash flow streams?

Normal cash flow stream – Cost (negative CF) Normal cash flow stream – Cost (negative CF) followed by a series of positive cash inflows. followed by a series of positive cash inflows. One change of signs.One change of signs.

Non-normal cash flow stream – Two or more Non-normal cash flow stream – Two or more changes of signs. Most common: Cost changes of signs. Most common: Cost (negative CF), then string of positive CFs, then (negative CF), then string of positive CFs, then cost to close project. Nuclear power plant, strip cost to close project. Nuclear power plant, strip mine, etc.mine, etc.

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Capital Budgeting Models There are two main types of Capital Budgeting 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 not consider the time value of money Payback Period Accounting Rate of Return (ARR)

What is theWhat is the PaybackPayback period?period?

The number of years required to recover a The number of years required to recover a project’s cost, or “How long does it take to project’s cost, or “How long does it take to get our money back?”get our money back?”

Calculated by adding project’s cash inflows Calculated by adding project’s cash inflows to its cost until the cumulative cash flow for to its cost until the cumulative cash flow for the project turns positive.the project turns positive.

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PAYBACK PERIODPAYBACK PERIOD SITUATION 1: EVEN (SAME) CASHLOWSSITUATION 1: EVEN (SAME) CASHLOWS

PAY BACKPERIODPAY BACKPERIOD= CAPITAL OUTLAY= CAPITAL OUTLAYCASHFLOWS PER PERIODCASHFLOWS PER PERIOD

SITUATION 2: UNEVEN CASHFLOWSSITUATION 2: UNEVEN CASHFLOWS

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

Where: A is the number of full years immediately before covering the Where: A is the number of full years immediately before covering the capital outlaycapital outlay

B is the balance remaining to cover the capital outlayB is the balance remaining to cover the capital outlayC is the total amount that is received in the year when the C is the total amount that is received in the year when the

capital outlay is fully coveredcapital outlay is fully covered1616

CalculatingCalculating PaybackPayback

PaybackL = 2 + / = 2.375 years

CFt -100 10 60 100Cumulative -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 20Cumulative -100 0 20 40

0 1 2 3

=

1.6

30 50

50-30

Project S

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Strengths &weaknesses of Strengths &weaknesses of PaybackPayback

StrengthsStrengths– Provides an indication of a project’s risk and Provides an indication of a project’s risk and

liquidity.liquidity.– Easy to calculate and understand.Easy to calculate and understand.

WeaknessesWeaknesses– Ignores the time value of money.Ignores the time value of money.– Ignores Cash Flows occurring after the payback Ignores Cash Flows occurring after the payback

period.period.

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Discounted payback periodDiscounted payback period

Uses discounted cash flows rather than raw Uses discounted cash flows rather than raw CFs.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 ValueNet Present Value

Net present value is the present value of the Net present value is the present value of the project’s net cash inflows from operations...project’s net cash inflows from operations...and disinvestment less the amount of the and disinvestment less the amount of the

initial investment.initial investment.

Net Present Value (NPV)Net Present Value (NPV)

Sum of the PVs of all cash inflows and outflows Sum of the PVs of all cash inflows and outflows of a project:of a project:

n

0tt

t

)k 1 (CF NPV

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

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What is Project L’s NPV?What is Project L’s NPV?

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

00 -100-100 11 -$100 -$100 11 10 10 0.909 0.909 9.099.09 22 60 60 0.8264 0.8264 49.5949.59 33 80 80 0.7513 0.7513 60.1160.11 NPVNPVLL = = Rs.18.79 Rs.18.79

NPVNPVSS = Rs.19.98 = Rs.19.98

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Rationale for the NPV methodRationale for the NPV method

NPVNPV = PV of inflows – Cost= PV of inflows – Cost= Net gain in wealth= Net gain in wealth

If projects are independent, accept if the If projects are independent, accept if the project NPV > 0.project NPV > 0.

If projects are mutually exclusive, accept If projects are mutually exclusive, accept projects with the highest positive NPV, those projects with the highest positive NPV, those that add the most value.that add the most value.

In this example, would accept S if mutually In this example, would accept S if mutually exclusive (NPVexclusive (NPVss > NPV > NPVLL), and would accept ), and would accept both if independent.both if independent.

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

1. Also called the time-adjusted rate of return.2. It is the minimum rate that could be paid for the

money invested in a project without losing money.

3. It is also described as the discount rate that results in a project’s net present value equaling zero.

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

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

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n

0tt

t) IRR 1 (

CF 0

Rationale for the IRR methodRationale for the IRR method

If IRR > WACC, the project’s rate of If IRR > WACC, the project’s rate of return is greater than its costs. There is return is greater than its costs. There is some return left over to boost some return left over to boost stockholders’ returns.stockholders’ returns.

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Calculate IRR – using the Calculate IRR – using the previous exampleprevious example

Calculate IRR – using the previous exampleCalculate IRR – using the previous example

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IRR Acceptance CriteriaIRR Acceptance Criteria

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

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

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

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The higher the internal rate of return, the more desirable

the project.

When using the internal rate of return method to rank competing investment projects, the preference rule is:

Internal Rate of Return MethodInternal Rate of Return Method

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Internal Rate of Return (IRR)Internal Rate of Return (IRR)Spreadsheet ApproachSpreadsheet Approach

1. Input A B1 Year of cash flow Cash flow2 0 Rs.-94,5543 1 30,0004 2 30,0005 3 30,0006 4 30,0007 5 42,0008 IRR =IRR(B2:B7,0.08)

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2. Output

A B1 Year of cash flow Cash flow2 0 Rs.-94,5543 1 30,0004 2 30,0005 3 30,0006 4 30,0007 5 42,0008 IRR 0.20

Internal Rate of Return (IRR)Internal Rate of Return (IRR)Spreadsheet ApproachSpreadsheet Approach

Differences Between Net Present Value and Differences Between Net Present Value and the Internal Rate of Return Modelsthe Internal Rate of Return Models

The net present value model gives explicit The net present value model gives explicit consideration to investment size. The internal consideration to investment size. The internal rate of return does not.rate of return does not.

The net present value model assumes all net The net present value model assumes all net cash inflows are reinvested at the discount rate. cash inflows are reinvested at the discount rate. The internal rate of return model assumes all The internal rate of return model assumes all net cash inflows are reinvested at the project’s net cash inflows are reinvested at the project’s internal rate of return.internal rate of return.

Other Capital budgeting Techniques:Other Capital budgeting Techniques:

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

value of future cash inflows with the initial investment on a value of future cash inflows with the initial investment on a relative basis. relative basis.

Therefore, the PI is the ratio of the present value of cash Therefore, the PI is the ratio of the present value of cash flows (PVCF) to the initial investment of the project.flows (PVCF) to the initial investment of the project.– == PV PV

Initial InvestmentInitial Investment

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Capital budgeting Techniques:Capital budgeting Techniques:

Profitability Index cont…:Profitability Index cont…: Decision CriterionDecision Criterion In this method, a project with a PI In this method, a project with a PI

greater than 1 is accepted, but a project greater than 1 is accepted, but a project is rejected when its PI is less than 1. is rejected when its PI is less than 1.

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Capital budgeting Techniques:Capital budgeting Techniques:

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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NPV ProfilesNPV Profiles A graphical representation of project NPVs at A graphical representation of project NPVs at

various different costs of capital.various different costs of capital.

k k NPVNPVLL NPVNPVSS

00 $50$50 $40$40 55 33 33 29 291010 19 19 20 201515 7 7 12 122020 (4) (4) 5 5

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Drawing NPV profilesDrawing NPV profiles

-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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Comparing the NPV and IRR Comparing the NPV and IRR methodsmethods

If projects are independent, the two methods If projects are independent, the two methods always lead to the same accept/reject decisions.always lead to the same accept/reject decisions.

If projects are mutually exclusive …If projects are mutually exclusive …– If k > crossover point, the two methods lead to the If k > crossover point, the two methods lead to the

same decision and there is no conflict.same decision and there is no conflict.– If k < crossover point, the two methods lead to If k < crossover point, the two methods lead to

different accept/reject decisions.different accept/reject decisions.

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Reasons Why NPV profiles crossReasons Why NPV profiles cross

Size (scale) differences – the smaller project Size (scale) differences – the smaller project frees up funds at t = 0 for investment. The higher frees up funds at t = 0 for investment. The higher the opportunity cost, the more valuable these the opportunity cost, the more valuable these funds, so high k favors small projects.funds, so high k favors small projects.

Timing differences – the project with faster Timing differences – the project with faster payback provides more CF in early years for payback provides more CF in early years for reinvestment. If k is high, early CF especially reinvestment. If k is high, early CF especially good, NPVgood, NPVSS > NPV > NPVLL..

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Capital Budgeting Techniques:Capital Budgeting Techniques:

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 cash flows instead of profitsUse cash flows instead of profits Use all cash flows.Use all cash flows. Take into account cost of capital of the firm.Take into account cost of capital of the firm.

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Accounting Rate of ReturnAccounting Rate of Return

The The accounting rate of returnaccounting rate of return is the average is the average annual increase in net income that results annual increase in net income that results from acceptance of a capital expenditure from acceptance of a capital expenditure proposal divided by the initial investment or proposal divided by the initial investment or the average investment in the project.the average investment in the project.

Accounting Rate of ReturnAccounting Rate of Return

Cake Shoppe purchased a vehicle and equipment Cake Shoppe purchased a vehicle and equipment costing Rs.90,554. It has a disposal value of costing Rs.90,554. It has a disposal value of Rs.8,000 at the end of 5 years.Rs.8,000 at the end of 5 years.

Annual net cash inflow from operationsAnnual net cash inflow from operationsRs.30,000Rs.30,000

Less average annual depreciation:Less average annual depreciation: [Rs.90,554 – Rs.8,000]/5)[Rs.90,554 – Rs.8,000]/5) 16,51116,511 Average annual increase in net incomeAverage annual increase in net income

Rs.13,489Rs.13,489

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Accounting rate of return on initial

investment

Average annual increase in net income

Initial investment=

Accounting rate of return on initial

investment=

Rs.13,489Rs.94,554 = 0.1427

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Accounting rate of return on average

investment

Average annual increase in net income

Average investment=

Accounting rate of return on average

investment=

13,48953,277 = 0.2532

([94,554 + 12,000])/2Rs.94,544 = initial investment, Rs.12,000 = disinvestment

Present value indexPresent value index

– A frequent criticism of NPV, when it is used to A frequent criticism of NPV, when it is used to rank proposals, is that it fails to adjust for the rank proposals, is that it fails to adjust for the size of the proposed investmentsize of the proposed investment

– To overcome this difficulty, managers may rank To overcome this difficulty, managers may rank projects on the basis of each project’s present projects on the basis of each project’s present value index, which is computed as the present value index, which is computed as the present value of the project’s subsequent cash flows value of the project’s subsequent cash flows divided by the initial investment.divided by the initial investment.

Present value indexPresent value index

Present value index =Present value index =

Present value of subsequent cash flowsPresent value of subsequent cash flows Initial investmentInitial investment