capital exp decisions
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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)
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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
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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
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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
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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
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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%
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Conflict in ranking
Different rankings given by the NPV and IRRmethods can be illustrated under the followingheads:
Size-disparity problemTime-disparity problemUnequal expected lives
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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
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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
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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
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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
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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
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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
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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
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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
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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)
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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)
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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
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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
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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)