Capital Exp Decisions

7/28/2019 Capital Exp Decisions

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Capital Expenditure Decisions

DiscountingNon Discounting

Evaluation Criteria

Payback period Accounting

Rate of Return(ARR)

Net PresentValue(NPV)

InternalRate of Return(IRR)

ProfitabilityRatio/BenefitCost Ratio( PI/BCR)



Net Present Value

n

t t

t ck

c NPV

1

01

03

3

2

21

1........

111c

k

c

k

c

k

c

k

c NPV

n

n

Where,C1, C2… represent the net cash inflow in year 1, 2… K is the opportunity cost of CapitalC0 is the initial cost of investmentn is the expected life of investment



Net Present Value

Acceptance Rule NPVAccept NPV > 0Reject NPV < 0May accept NPV = 0

Evaluation of NPV methodIt recognizes the time value of moneyIt uses all cash flows occurring over the entire life of the projectNPVs of the projects can be addedNPV(A+B)=NPV(A)+NPV(B)-Value Additively PrincipleNPV method is consistent with the objective of maximizing the shareholders wealth



Net Present Value

Year Amount outstanding in the

beginningReturn on outstanding

amount at 10%Total amount

outstanding flowsRepayment fromcash at the end

Balanceoutstanding

Rs Rs Rs Rs Rs1 2500 250 2750 900 1850

2 1850 185 2035 800 1235

3 1235 123.5 1358.5 700 658.5

4 658.5 65.85 724.35 600 124.35

5 124.35 12.435 136.785 500 -363.215



Internal Rate of Return

Acceptance Rule IRRAccept r > kReject r < kMay accept r = k

Evaluation of IRR method

It recognizes the time value of moneyIt uses all cash flows occurring over the entire life of the projectIRR method is consistent with the objective of maximizing the shareholders wealth

n

t

t

t cr

c

1

01

0



Internal Rate of Return

Unlike in the case of NPV method, the value additivityprinciple does not hold.

IRR method can yield multiple internal rates of return

Project C0 C1 NPV @ 10% IRR %A -100 120 9.08 20%

B -150 168 2.712 12%A+B -250 288 11.792 15.20%

Initial cost 0 -20,000Net cash flow 1 90,000Net cash flow 2 -80,000IRR 21.9%, 228%



Conflict in ranking

Different rankings given by the NPV and IRRmethods can be illustrated under the followingheads:

Size-disparity problemTime-disparity problemUnequal expected lives



Size Disparity Problem

Particulars Project A Project B Pro

Cash outlays -5000 -7500 -2500

Cash inflows at theend of the year, 1 6250 9150 2900

IRR (%) 25 22 16

kNPV 681.25 817.35

10



Time Disparity Problem

C0 C1 C2 C3 NPV @ 9% IRRM -1680 1400 700 400 301 23%

N -1680 140 840 1510 321 17%

Cash Flows (Rs.)

Project

M N

Rs. Rs.

0 560 810

5 409 520

10 276 276

15 159 70

20 53 -106

25 -40 -257

30 -125 -388

Discount rate %

NPV



Unequal expected lives ( Common TimeHorizon Approach)

Particular Project A Project BInitial outlay (Rs.) 10000 20000

Year 1 8000 8000

2 7000 9000

3 Nil 7000

4 Nil 6000

Service life (years) 2 4

Required rate of return

Cash Inflows after taxes

10%

Year Cash flow (Rs.) PV factor Total PV (Rs.)0 -10000 1.000 -10000

1 8000 0.909 7272

2 7000 0.826 5782

3 -10000 0.826 -8260

3 8000 0.751 6008

4 7000 0.683 4781

NPV 5583

Year Cash flow (Rs.) PV factor Total PV (Rs.)0 -20000 1.000 -20000

1 8000 0.909 7272

2 9000 0.826 7434

3 7000 0.751 5257

4 6000 0.683 4098

NPV 4061

Project A

Project B



Unequal expected lives (EquivalentAnnual Value/Cost Approach)

Project Years CFAT(Rs) PV factor (0.10) Total PV(Rs) NPV(A 1-5 30,000 3.791 1,13,730 13,730B 1-8 27,000 5.335 1,44,045 19,045

Project NPV(Rs) PV factor (0.10) EANPV(Rs)A 13,730 3.791 3621.74B 19,045 5.335 3569.82

Determination of NPV of Projects A and B

Determination of EANPV

EANPV = Net present value of the projectPV of annuity corresponding to life of the project at given cost of capital



Unequal expected lives (EquivalentAnnual Value/Cost Approach)

PV factor (0.10)Machine A Machine B Machine A Machin

0 (Initial Cost) 50,000 65,000 1 50,000 65,

(Operating cost):1-6 years (A) 6950 4.355 30267.251-10 years (B) 5700 6.145 35026.5

80267.25 100026.5Less: Salvage value

6th year (A) 2000 0.564 112810th year (B) 5000 0.386 1930PV of total costs 79139.25 98096.5EAC 18172.04 15963.63

Costs (Rs) Adjusted PV(Rs)Equivalent Annual Costs of Machines A and B

Particulars



Profitability IndexPI = PV of cash inflows

Initial cash outlay

Acceptance Rule PIAccept PI > 1Reject PI < 1May accept PI = 1

Evaluation of PI methodIt recognizes the time value of moneyIt uses all cash flows occurring over the entire life of the projectIt is a relative measure of a project’s profitability



Conflict in ranking

Year Project A (Rs) Project B (Rs)0 -50,000 -35,0001 40,000 30,0002 40,000 30,000

PV of cash inflow(0.10) 69,440 52,080NPV 19,440 17,080

PI 1.3888 1.488



Capital Rationing

Project

InitialInvestment (Rs

crore) NPV ( Rs crore) PIX 3 0.6 1.2

Y 2 0.5 1.25

Z 2.5 1.5 1.6

W 6 1.8 1.3

Project

n aInvestment (Rs

crore) NPV ( Rs crore) PIZ 2.5 1.5 1.6

W 6 1.8 1.3

Y 2 0.5 1.25

X 3 0.6 1.2



Payback Period

Payback Period (Constant annual cash inflows)Payback = Initial Investment

Annual Cash Inflow

Acceptance Rule Payback PeriodAccept Payback Period < Max. payback period setReject Payback Period > Max. payback period set

Evaluation of Payback Period methodSimple to understand, easy to calculate and focus onriskFails to take account of the cash inflows earned afterpayback period

Project C0 C1 C2 C3 Payback NPV @ 10%X -4000 0 4000 2000 2 yrs 806Y -4000 2000 2000 0 2yrs -530

Cash Flows (Rs)



Payback Period

Fails to consider the pattern of cash flows i.e. magnitudeand timing of cash flows

Administrative difficulties may be faced in determiningthe maximum acceptable payback period

Not consistent with the objective of maximizing themarket value of the firm’s share.

Project C0 C1 C2 C3 Payback NPV @ 10%

X -5000 3000 2000 2000 2 yrs Y -5000 2000 3000 2000 2yrs 7

Cash Flows (Rs)



Accounting Rate of Return

ARR = Average incomeAverage investment

Period 1 2 3 4 5 Average (Rs)EBDIT 10000 12000 14000 16000 20000 14400Less : Depreciation 8000 8000 8000 8000 8000 8000EBIT 2000 4000 6000 8000 12000 6400Taxes @ 50% 1000 2000 3000 4000 6000 3200EBIT (1-T) 1000 2000 3000 4000 6000 3200

Book value of InvestmentBeginning 40000 32000 24000 16000 8000Ending 32000 24000 16000 8000 0Average 36000 28000 20000 12000 4000 20000ARR 0.16

Calculation of Accounting Rate of Return



Accounting Rate of Return

Acceptance Rule ARR Accept ARR >Min. rate setReject ARR< Min. rate set

Evaluation of ARR method It is simple to understand and useARR can be readily calculated from the accounting dataIt incorporates the entire stream of income incalculating the project’s profitability

It uses accounting profits and not cash flowsThe averaging of income ignores the time value of moneyIt uses an arbitrary cut-off yardstick



Investment decisions under inflation

Discount nominal cash flows at nominal discount rate ordiscount real cash flows at real discount rate.

(1+Nominal rate) = (1+Real rate)(1+inflation rate)

C0 C1 C2 C3 C4

-10000 3000 3000 3000 3000NPV @ 14%NPV @ 6.54%

C0 C1 C2 C3 C4

-10000 3210 3434.7 3675.13 3932.39NPV @ 14% 266

Real Cash Flows (Rs)

-1258266

Nominal Cash Flows (Rs)

Documents

Capital Exp Decisions