Capital Budgeting Final Ch8 IMP

8/8/2019 Capital Budgeting Final Ch8 IMP

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Chapter - 8

Capital BudgetingDecisions


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Chapter Objectives

Understand the nature and importance ofinvestment decisions.

Distinguish between discounted cash flow(DCF) and non-discounted cash flow (non-DCF)techniques of investment evaluation.

Explain the methods of calculating net presentvalue (NPV) and internal rate of return (IRR).

Show the implications of net present value(NPV) and internal rate of return (IRR).

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Chapter Objectives

Describe the non-DCF evaluation criteria:payback and accounting rate of return and

discuss the reasons for their popularity inpractice and their pitfalls. Illustrate the computation of the discounted

payback. Describe the merits and demerits of the DCF

and Non-DCF investment criteria. Compare and contrast NPV and IRR and

emphasise the superiority of NPV rule.

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Nature of Investment

Decisions The investment decisions of a firm are generally

known as the capital budgeting, or capitalexpenditure decisions.

The firms investment decisions would generallyinclude expansion,acquisition,modernisationand replacement of the long-term assets. Sale of adivision or business (divestment) is also as aninvestment decision.

Decisions like the change in the methods of salesdistribution, or an advertisement campaign or aresearch and development programme havelong-term implications for the firms expenditures andbenefits, and therefore, they should also beevaluated as investment decisions.

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Features of Long-term

Investment Decisions

The exchange of current funds for

future benefits. The funds are invested in long-term

assets (more than 1 year).

The future benefits will occur to thefirm over a series of years.

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Importance of Investment

Decisions

Growth

Risk

Funding

Irreversibility

Complexity

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Types of Investment Decisions

One classification is as follows: Expansion of existing business

Expansion of new business Replacement and modernisation

Yet another useful way to classifyinvestments is as follows: Mutually exclusive investments Independent investments

Contingent investments

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Investment Evaluation Criteria

Three steps are involved in the

evaluation of an investment: Estimation of cash flows

Estimation of the required rate of return(the opportunity cost of capital)

Application of a decision rule for makingthe choice

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Investment Decision Rule It should maximise the shareholders wealth.

It should consider all cash flows to determinethe true profitability of the project.

It should provide for an objective andunambiguous way of separating good projects

from bad projects. It should help ranking of projects according to

their true profitability.

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Investment Decision Rule It should recognise the fact that bigger cash

flows are preferable to smaller ones and early

cash flows are preferable to later ones.

It should help to choose among mutuallyexclusive projects that project which maximisesthe shareholders wealth.

It should be a criterion which is applicable toany conceivable investment projectindependent of others.

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Evaluation Criteria

A. Discounted Cash Flow (DCF) Criteria

Net Present Value (NPV) Internal Rate of Return (IRR)

Profitability Index (PI)

B. Non-discountedCash FlowCriteria

Payback Period (PB)

Discounted Payback Period (DPB)

Accounting Rate of Return (ARR)

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Net Present Value Method Cash flows of the investment project

should be forecasted based on realistic

assumptions.

Appropriate discount rate should be

identified to discount the forecasted cashflows. The appropriate discount rate isthe projects opportunity cost of capital.

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Net Present Value Method Present value of cash flows should be

calculated using the opportunity cost of capital

as the discount rate.

The project should be accepted if NPV ispositive (i.e., NPV > 0).

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Net Present Value Method Net present value should be found out by subtracting

present value of cash outflows from present value of

cash inflows. The formula for the net present valuecan be written as follows:

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31 202 3

0

1

NPV(1 ) (1 ) (1 ) (1 )

NPV(1 )

n

n

n

t

t

t

C CC CC

k k k k

CC

k!

! -

!

L


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Calculating Net Present Value Assume that Project X costs Rs 2,500 now and is

expected to generate year-end cash inflows of Rs900, Rs 800, Rs 700, Rs 600 and Rs 500 in years 1

through 5. The opportunity cost of the capital may beassumed to be 10 per cent.

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2 3 4 5

1, 0.10 2, 0.10 3, 0.10

4, 0.10 5, 0.

Rs 900 Rs 800 Rs 700 Rs 600 Rs 500Rs 2,500

(1+0.10) (1+0.10) (1+0.10) (1+0.10) (1+0.10)

[Rs 900( F ) + Rs 800( F ) + Rs 700( F )+ Rs 600( F ) + Rs 500( F

-

10)] Rs 2,500

[Rs 900 0.909 + Rs 800 0.826 + Rs 700 0.751 + Rs 600 0.683

+ Rs 500 0.620] Rs 2,500

Rs 2,725 Rs 2,500 = + Rs 225

v v v v

v


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Acceptance Rule Accept the project when NPV is positive

NPV > 0

Reject the project when NPV is negativeNPV < 0

May accept the project when NPV is zeroNPV = 0

The NPV method can be used to select betweenmutually exclusive projects; the one with the higherNPV should be selected.

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Evaluation of the NPV Method

NPV is most acceptable investment rulefor the following reasons: Time value

Measure of true profitability

Value-additivity

Shareholder value

Limitations: Involved cash flow estimation Discount rate difficult to determine

Mutually exclusive projects

Ranking of projects17


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Internal Rate of Return

Method The internal rate of return (IRR) is the rate that

equates the investment outlay with the present valueof cash inflow received over a long period. This alsoimplies that the rate of return is the discount ratewhich makes NPV = 0.

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31 20 2 3

0

1

0

1

(1 ) (1 ) (1 ) (1 )

(1 )

0(1 )

n

n

nt

t

t

n

t

t

t

r r r r

r

r

!

!

!

!

!

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Calculation of IRR Uneven Cash Flows: Calculating IRR

by Trial and Error The approach is to select any discount rate to

compute the present value of cash inflows. If thecalculated present value of the expected cash inflowis lower than the present value of cash outflows, alower rate should be tried. On the other hand, a

higher value should be tried if the present value ofinflows is higher than the present value of outflows.This process will be repeated unless the net presentvalue becomes zero.

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Calculation of IRR

Level (Equal) Cash Flows Let us assume that an investment would cost

Rs 20,000 and provide annual cash inflow ofRs 5,430 for 6 years.

The IRR of the investment can be found outas follows:

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6,

6,

6,

Rs 20,000 + Rs 5,430( AF ) = 0

Rs 20,000 Rs 5,430( AF )Rs 20,000

AF 3.683Rs 5,430

r

r

r

!

!

! !


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NPV Profile and IRR

A B C D E F G H

1 NPV Profile

2 Cash Flow

Discount

rate NPV3 -20000 0% 12,580

4 5430 5% 7,561

5 5430 10% 3,649

6 5430 15% 550

7 5430 16% 08 5430 20% (1,942)

9 5430 25% (3,974)

Figure 8.1NPVProfile

IR

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NPV Profile and IRR

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Acceptance Rule

Accept the project when r > k.

Reject the project when r < k. May accept the project when r = k.

In case of independent projects, IRR

and NPV rules will give the same resultsif the firm has no shortage of funds.

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Evaluation of IRR Method

IRR method has following merits:

Time value Profitability measure

Acceptance rule

Shareholder value

IRR method may suffer from: Multiple rates

Mutually exclusive projects

Value additivity

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Profitability Index

Profitability index is the ratio of thepresent value of cash inflows, at therequired rate of return, to the initialcash outflow of the investment.

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Profitability Index

The initial cash outlay of a project is Rs 100,000 and itcan generate cash inflow of Rs 40,000, Rs 30,000, Rs50,000 and Rs 20,000 in year 1 through 4. Assume a 10per cent rate of discount. The PV of cash inflows at 10

per cent discount rate is:

.1235.11,00,000s

1,12,350sPI

12,350s100,000s112,350sNPV

0.6820,000s0.75150,000s0.82630,000s0.90940,000s

)20,000(PVs)50,000(PVs)30,000(PVs)40,000(PVsPV 0.104,0.103,0.102,0.101,

!!

!

!

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Acceptance Rule

The following are the PI acceptance rules:

Accept the project when PI is greater than one.PI > 1

Reject the project when PI is less than one.PI < 1

May accept the project when PI is equal to one.

PI = 1 The project with positive NPV will have PI greater

than one. PI less than 1 means that the projects NPVis negative.

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Evaluation of PI Method It recognises the time value of money. It is consistent with the shareholder value

maximisation principle. A project with PI greater thanone will have positive NPV and if accepted, it willincrease shareholders wealth.

In the PI method, since the present value of cashinflows is divided by the initial cash outflow, it is arelative measure of a projects profitability.

Like NPV method, PI criterion also requirescalculation of cash flows and estimate of the discountrate. In practice, estimation of cash flows anddiscount rate pose problems.

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Payback Payback is the number of years required to recover the original

cash outlay invested in a project.

If the project generates constant annual cash inflows, the payback

period can be computed by dividing cash outlay by the annualcash inflow. That is:

Assume that a project requires an outlay of Rs 50,000 and yieldsannual cash inflow of Rs 12,500 for 7 years. The payback periodfor the project is:

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0Initial InvestmentPaybacknnual Cash Inflow

C

C

s 50,000PB 4 years

s 12,000


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Payback

Unequal cash flows In case of unequal cashinflows, the payback period can be found out by

adding up the cash inflows until the total is equal tothe initial cash outlay.

Suppose that a project requires a cash outlay of Rs20,000, and generates cash inflows of Rs

8,000; Rs 7,000; Rs 4,000; and Rs 3,000 during thenext 4 years. What is the projects payback?

3 years + 12 (1,000/3,000) months

3 years + 4 months

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Acceptance Rule The project would be accepted if its payback period

is less than the maximum or standard paybackperiod set by management.

As a ranking method, it gives highest ranking to theproject, which has the shortest payback period andlowest ranking to the project with highest payback

period.

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Evaluation of Payback

Certain virtues: Simplicity Cost effective Short-term effects Risk shield Liquidity

Serious limitations: Cash flows after payback Cash flows ignored Cash flow patterns Administrative difficulties Inconsistent with shareholder value

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Payback Reciprocal and the

Rate of Return The reciprocal of payback will be a close

approximation of the internal rate of return if

the following two conditions are satisfied:

The life of the project is large or at least twice thepayback period.

The project generates equal annual cash inflows.

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Discounted Payback Period

The discounted payback period is the number ofperiods taken in recovering the investment outlay onthe present value basis.

The discounted payback period still fails to consider the

cash flows occurring after the payback period.

3 DISCOUNTED PAYBACK I LL USTRATED

Cash Flows

(Rs)

C0 C1 C2 C3 C4

Simple

PB

Discounted

PB

NPV at

10%

-4,000 3,000 1,000 1,000 1,000 2 yrs o cash lo s -4,000 2,727 826 751 683 2.6 yrs 987

Q -4,000 0 4,000 1,000 2,000 2 yrs

o cash lo s -4,000 0 3,304 751 1,366 2.9 yrs 1,421

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Accounting Rate of Return

Method The accounting rate of return is the ratio of the average

after-tax profit divided by the average investment. The

average investment would be equal to half of theoriginal investment if it were depreciated constantly.

A variation of the ARR method is to divide averageearnings after taxes by the original cost of the projectinstead of the average cost.

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Average incomeARR

Average investment


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Acceptance Rule This method will accept all those projects whose ARR

is higher than the minimum rate established by themanagement and reject those projects which haveARR less than the minimum rate.

This method would rank a project as number one if ithas highest ARR and lowest rank would be assigned

to the project with lowest ARR.

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Evaluation of ARR Method

The ARR method may claim some merits

Simplicity

Accounting data

Accounting profitability

Serious shortcoming

Cash flows ignored Time value ignored

Arbitrary cut-off

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Conventional and Non-

conventional Cash Flows A conventional investment has cash flows the pattern of

an initial cash outlay followed by cash inflows.Conventional projects have only one change in the sign

of cash flows; for example, the initial outflow followed byinflows, i.e., + + +.

A non-conventional investment, on the other hand, hascash outflows mingled with cash inflows throughout thelife of the project. Non-conventional investments havemore than one change in the signs of cash flows; forexample, + + + ++ +.

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NPV Versus IRR

Conventional Independent Projects:

In case of conventional investments, which areeconomically independent of each other, NPVand IRR methods result in same accept-or-rejectdecision if the firm is not constrained for funds

in accepting all profitable projects.

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NPV Versus IRR

Cash Flows (Rs)

Project C0 C1 IRR NPV at 10%

X -100 120 20% 9

Y 100 -120 20% -9

Lending and borrowing-type projects:

Project with initial outflow followed by inflows is

a lending type project, and project with initialinflow followed by outflows is a borrowing typeproject, Both are conventional projects.


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Problem of Multiple IRRs

A project may have bothlending and borrowingfeatures together. IRRmethod, when used toevaluate such non-conventional investmentcan yield multiple internalrates of return because of

more than one change ofsigns in cash flows.

NPV Rs 63

-750

-500

-250

0

250

0 50 100 150 200 250

Discount Rate (%)

NPV (Rs)

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Case of Ranking Mutually

Exclusive Projects Investment projects are said to be mutually exclusive

when only one investment could be accepted andothers would have to be excluded.

Two independent projects may also be mutuallyexclusive if a financial constraint is imposed.

The NPV and IRR rules give conflicting ranking to theprojects under the following conditions: The cash flow pattern of the projects may differ. That is, the

cash flows of one project may increase over time, while thoseof others may decrease or vice-versa.

The cash outlays of the projects may differ.

The projects may have different expected lives.

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Timing of Cash Flows

Cash Flows (Rs) NPV

Project C0 C1 C2 C3 at 9% IRR

M 1,680 1,400 700 140 301 23%

N 1,680 140 840 1,510 321 17%

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Scale of Investment Cas lo ( s) V

roject C0 C1 at 10 I

A -1,000 1,500 364 50%

B -100,000 120,000 9,080 20%

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Project Life Span Cash Flows (Rs)

Project C0 C1 C2 C3 C4 C5 NPV at 10% IRR

X 10,000 12,000 908 20Y 10,000 0 0 0 0 20,120 2,495 15

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Reinvestment Assumption

The IRR method is assumed to imply that

the cash flows generated by the projectcan be reinvested at its internal rate ofreturn, whereas the NPV method isthought to assume that the cash flows

are reinvested at the opportunity cost ofcapital.

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Varying Opportunity Cost of

Capital There is no problem in using NPV method

when the opportunity cost of capital varies

over time.

If the opportunity cost of capital varies over

time, the use of the IRR rule createsproblems, as there is not a unique benchmarkopportunity cost of capital to compare withIRR.

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Project Project D

PV of cash inflows 100,000 50,000

Initial cash outflow 50,000 20,000

NPV 50,000 30,000

PI 2.00 2.50

NPV Versus PI

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A conflict may arise between the two methods if achoice between mutually exclusive projects has to

be made. Follow NPV method:


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Assignment Problems at the

Back:

1 to 20except 11, 12, 17,20

Illustrated SolvedProblems at the

Back:8.1, 8.2, 8.4, 8.5

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Capital Budgeting Final Ch8 IMP

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