Capital Exp Decisions1

7/30/2019 Capital Exp Decisions1

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Capital Expenditure Decisions


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Capital Expenditure Decisions

DiscountingNon Discounting

Evaluation Criteria

Payback

period

Accounting

Rate of Return(ARR)

Net Present

Value(NPV)

Internal

Rate ofReturn(IRR)

Profitability

Ratio/BenefitCost Ratio( PI/BCR)


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Net Present Value

( )=

+=

n

t

t

tc

k

cNPV

1

0

1

( ) ( ) ( ) ( )03

3

2

21

1

........

111c

k

c

k

c

k

c

k

cNPV

n

n

++

++

++

+=

Where,C1, C2 represent the net cash inflow in year 1,2K 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

o Acceptance Rule NPVn Accept NPV > 0n Reject NPV < 0n May accept NPV = 0

o Evaluation of NPV methodn It recognizes the time value of moneyn It uses all cash flows occurring over the entire life of

the projectn

NPVs of the projects can be addedNPV(A+B)=NPV(A)+NPV(B)-Value Additively Principle

n NPV method is consistent with the objective ofmaximizing the shareholders wealth


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Net Present Value

Y e a r A m o u n t o u t s t

b e g i n n i n g

R e t u r n o n o u

a m o u n t a t

T o t a l a m

o u t s t a n d i

R e p a y m e

c a s h a t t

B a l a n

o u t s t a

R s R s R s R s R s1 2 5 0 0 2 5 0 2 7 5 0 9 0 0 1 8 5 0

2 1 8 5 0 1 8 5 2 0 3 5 8 0 0 1 2 3 5

3 1 2 3 5 1 2 3 . 5 1 3 5 8 . 5 7 0 0 6 5 8 . 5

4 6 5 8 . 5 6 5 . 8 5 7 2 4 . 3 5 6 0 0 1 2 4 . 3

5 1 2 4 . 3 5 1 2 . 4 3 5 1 3 6 . 7 8 5 5 0 0 - 3 6 3 . 2


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Internal Rate of Return

o Acceptance Rule IRRn Accept r > kn Reject r < kn May accept r = k

o

Evaluation of IRR methodn It recognizes the time value of moneyn It uses all cash flows occurring over the entire life of

the projectn IRR method is consistent with the objective of

maximizing the shareholders wealth

( )=

+=

n

t

t

tc

r

c

1

0

10


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Internal Rate of Return

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

o IRR method can yield multiple internal rates of return

P r o j e c t C0 C1 N P V @ 1 0 % IR R %

A - 1 0 0 1 2 0 9 . 0 8 2 0 %

B - 1 5 0 1 6 8 2 . 7 1 2 1 2 %A + B - 2 5 0 2 8 8 1 1 . 7 9 2 1 5 . 2 0 %

Initial cost 0 -20,000

Net cash flow 1 90,000

Net cash flow 2 -80,000

IRR 21.9%, 228%


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Conflict in ranking

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

n Size-disparity problemn Time-disparity problemn Unequal expected lives


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Size Disparity Problem

P a r t i c u l a r s P r o j e c t A P r o j e c t B P r o j e c t

C a s h o u t l a y s - 5 0 0 0 - 7 5 0 0 - 2 5 0 0

C a s h i n f l o we n d o f t h e 6 2 5 0 9 1 5 0 2 9 0 0

I R R ( % ) 2 5 2 2 1 6

k

N P V 6 8 1 . 2 5 8 1 7 . 3 5

1 0


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Time Disparity Problem

C0 C1 C2 C3 N P V @ 9 % IR R

M - 1 6 8 0 1 4 0 0 7 0 0 4 0 0 3 0 1 2 3

N - 1 6 8 0 1 4 0 8 4 0 1 5 1 0 3 2 1 1 7

C a s h F l o w s ( R s .)

P r o j e c t

M N

Rs. Rs.

0 560 810

5 409 520

10 276 276

15 159 70

20 53 -106

25 -40 -25730 -125 -388

Discount rate %

NPV


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Unequal expected lives (Common TimeHorizon Approach)

Particular Project A Project B

Initial outlay(Rs.) 10000 20000

Year

1 8000 8000

2 7000 9000

3 Nil 7000

4 Nil 6000

Servicelife(years) 2 4

Requiredrateof return

CashInflowsafter taxes

10%

Year Cashflow(Rs.) PVfactor Total PV(Rs.)

0 -10000 1.000 -10000

1 8000 0.909 72722 7000 0.826 5782

3 -10000 0.826 -8260

3 8000 0.751 60084 7000 0.683 4781

NPV 5583

Year Cashflow(Rs.) PVfactor Total PV(Rs.)

0 -20000 1.000 -20000

1 8000 0.909 7272

2 9000 0.826 74343 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)

P r o j e c t Y e a r s C F A T ( R s )P V f a c t o r T o t a l P V ( R s )N P V ( R s )A 1 - 5 3 0 , 0 0 0 3 . 7 9 1 1 , 1 3 , 7 3 0 1 3 , 7 3 0

B 1 - 8 2 7 , 0 0 0 5 . 3 3 5 1 , 4 4 , 0 4 5 1 9 , 0 4 5

P r o j e c t N P V ( R s ) P V f a c t o r ( E A N P V ( R s )

A 1 3 , 7 3 0 3 . 7 9 1 3 6 2 1 . 7 4

B 1 9 , 0 4 5 5 . 3 3 5 3 5 6 9 . 8 2

D e t e r m in a t io n o f N P V o f P r o j e c t s A a n d B

D e t e r m in a t i o n o f E A N P V

E A N P V= N etpresent value of the project

PV of ann uity correspond ing to l ife of the project at g iven cost ocap ital


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Unequal expected lives (EquivalentAnnual Value/Cost Approach)

P V f a c t o r

M a c h i n e AM a c h i n e B M a c h i n e AM a c h i n e

0 ( I n i t i a l C o s t ) 5 0 , 0 0 0 6 5 , 0 0 0 1 5 0 , 0 0 0 6 5 , 0

( O p e r a t in g c o s t ) :1 - 6 y e a r s ( A ) 6 9 5 0 4 . 3 5 5 3 0 2 6 7 . 2 5

1 - 1 0 y e a r s ( B ) 5 7 0 0 6 . 1 4 5 3 5 0 2

8 0 2 6 7 . 2 5 1 0 0 0 2

L e s s : S a l v a g e v a l u e

6 t h y e a r ( A ) 2 0 0 0 0 . 5 6 4 1 1 2 81 0 t h y e a r ( B ) 5 0 0 0 0 . 3 8 6 1 9 3

P V o f t o t a l c o s t s 7 9 1 3 9 . 2 5 9 8 0 9

E A C 1 8 1 7 2 . 0 4 1 5 9 6 3

C o s t s ( R s ) A d j u s t e d P V ( R

E q u i v a l e n t A n n u a l C o s t s o f M a c h i n e s A a n d

P a r t i c u l a r s


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Profitability Index

o

PI = PV of cash inflowsInitial cash outlay

o Acceptance Rule PIn Accept PI > 1n Reject PI < 1n May accept PI = 1

o Evaluation of PI method

n

It recognizes the time value of moneyn It uses all cash flows occurring over the entire life of

the projectn It is a relative measure of a projects profitability


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Conflict in ranking

Y e a r P ro je c t A (R s )P ro jec t B (R

0 -5 0 ,0 0 0 -3 5 ,0 0 0

1 4 0 ,0 0 0 3 0 ,0 0 0

2 4 0 ,0 0 0 3 0 ,0 0 0

P V o f cash in f lo w ( 0 .10 ) 6 9 ,4 4 0 5 2 ,0 8 0

N P V 1 9 ,4 4 0 1 7 ,0 8 0

P I 1 .3 8 8 8 1 .4 8 8


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Capital Rationing

Project

Initial

Investment (Rs

crore) NPV ( Rs crore) PI

X 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 a

Investment (Rs

crore) NPV ( Rs crore) PIZ 2.5 1.5 1.6

W 6 1.8 1.3

Y 2 0.5 1.25X 3 0.6 1.2


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Payback Period

o

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

Annual Cash Inflow

o Acceptance Rule Payback Period

Accept Payback Period < Max. payback period set

Reject Payback Period > Max. payback period set

o Evaluation of Payback Period methodn Simple to understand, easy to calculate and focus on

riskn Fails to take account of the cash inflows earned after

payback periodP r o j e c t C0 C1 C2 C3 P a y b a c kN P V @

X - 4 0 0 0 0 4 0 0 0 2 0 0 0 2 y r s 8 0 6

Y - 4 0 0 0 2 0 0 0 2 0 0 0 0 2 y r s - 5 3 0

C a s h F l o w s ( R s )


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Payback Period

n

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

n Administrative difficulties may be faced in determining

the maximum acceptable payback periodn Not consistent with the objective of maximizing the

market value of the firms share.

P r o j e c t C0 C1 C2 C3 P a y b a c kN P V @

X - 5 0 0 0 3 0 0 0 2 0 0 0 2 0 0 0 2 y r s 8 8 1Y - 5 0 0 0 2 0 0 0 3 0 0 0 2 0 0 0 2 y r s 7 9 8

C a s h F l o w s ( R s )


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Accounting Rate of Return

ARR = Average income

Average investment

P e r i o d 1 2 3 4 5 A v e r a g e (

E B D I T 1 0 0 0 0 1 2 0 0 0 1 4 0 0 0 1 6 0 0 0 2 0 0 0 0 1 4 4

L e s s : D e p r e c i a t io n 8 0 0 0 8 0 0 0 8 0 0 0 8 0 0 0 8 0 0 0 8 0 0

E B I T 2 0 0 0 4 0 0 0 6 0 0 0 8 0 0 0 1 2 0 0 0 6 4 0

T a x e s @ 5 0 % 1 0 0 0 2 0 0 0 3 0 0 0 4 0 0 0 6 0 0 0 3 2 0

E B IT ( 1 - T ) 1 0 0 0 2 0 0 0 3 0 0 0 4 0 0 0 6 0 0 0 3 2 0

B o o k v a l u e o f In v e s t m e n t

B e g i n n i n g 4 0 0 0 0 3 2 0 0 0 2 4 0 0 0 1 6 0 0 0 8 0 0 0

E n d i n g 3 2 0 0 0 2 4 0 0 0 1 6 0 0 0 8 0 0 0 0

A v e r a g e 3 6 0 0 0 2 8 0 0 0 2 0 0 0 0 1 2 0 0 0 4 0 0 0 2 0 0

A R R 0 .1 6

C a l c u l a t i o n o f A c c o u n t in g R a t e o f R e t u r n


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Accounting Rate of Return

o Acceptance Rule ARRAccept ARR >Min. rate set

Reject ARR< Min. rate set

o Evaluation of ARR methodn It is simple to understand and usen ARR can be readily calculated from the accounting

datan

It incorporates the entire stream of income in calculatingthe projects profitabilityn It uses accounting profits and not cash flowsn The averaging of income ignores the time value of

moneyn It 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

-100 00 300 0 300 0 3 00 0 30 00

N P V @ 1 4%

N P V @ 6 .5 4 %

C0 C1 C2 C3 C4

-100 00 321 0 3434 .7 36 75 .13 39 32 .39

N P V @ 1 4% 26 6

Rea l Cash F lows (Rs )

-1258

26 6

N om ina l Cas h F lows (Rs)


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Risk in Capital Budgeting

Initial Investment (Rs) 8,000 8,000 8,000 8,000 8,000

Life of the project (Years) 10 10 10 10 10

Discount Rate 15% 15% 15% 15% 15%

Operating Level (Nos) 3,000 3,000 3,000 3,000 3,000

Selling Price falls by 5% 10% 15% 20%

Selling Price (Rs) 3.2 3.04 2.88 2.72 2.56

Revenue 9,600 9,120 8,640 8,160 7,680Variable Cost 5,400 5,400 5,400 5,400 5,400

Contribution 4,200 3,720 3,240 2,760 2,280

Fixed Costs 1,200 1,200 1,200 1,200 1,200

Depreciation 1,200 1,200 1,200 1,200 1,200

PBIT 1,800 1,320 840 360 -120

Interest ---- ---- ---- ---- ----

PBT 1,800 1,320 840 360 -120

Tax @ 40% 720 528 336 144 -48PAT 1,080 792 504 216 -72

Cash flow from Operations 2,280 1,992 1,704 1,416 1,128

PV of Cash in flows 11,443 9,997 8,552 7,107 5,661

Net Present Value at 15% 3,443 1,997 552 -893 -2,339

% fall in NPV for 1% fall in selling price -8.40%

(Figure in Rs)

Sensitivity Analysis: Sensor Corporation

Sensitivity

all in NPV for 1% fall in selling price -289


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Normal

Initial cost

increases

by 10%

Cost ofcapital

increases

by 10%

Variablecost

increases

by 10%

Fixed cost

increases

by 10%

Initial Investment (Rs) 8000 8800 8000 8000 8000


Discount Rate 15% 15% 16.50% 15% 15%

Operating Level (Nos) 3000 3000 3000 3000 3000

Selling Price (Rs) 3.2 3.2 3.2 3.2 3.2

Revenue 9600 9600 9600 9600 9600Variable Cost 5400 5400 5400 5940 5400

Contribution 4200 4200 4200 3660 4200

Fixed Costs 1200 1200 1200 1200 1320

Depreciation 1200 1320 1200 1200 1200

PBIT 1800 1680 1800 1260 1680

Interest

PBT 1800 1680 1800 1260 1680

Tax @40% 720 672 720 504 672

PAT 1080 1008 1080 756 1008Cash flow from Operations 2280 2328 2280 1956 2208

Net Present Value at 15% 3443 2884 2818 1817 3082

Change in NPV for 1%change

in variable -56 -63 -163 -36% fall in NPV for 1%fall in

selling price

-8.40% -1.62% -1.82% -4.78% -1.05%

Sensitivity


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Excellent Good Normal Bad Worst

Demand Level (no.s) 10% 5% 3000 -5% -10%

Selling Price (Rs./unit) 5% same 3.2 -5% -10%

Variable cost 10% same 5400 same 10%

Overheads 5% -5% 1200 10% 20%

Initial Investment (Rs) 8000 8000 8000 8000 8000


Discount Rate 15% 15% 15% 15% 15%

Scenario Excellent Good Normal Bad WorstOperating Level (Nos) 3300 3150 3000 2850 2700

Selling Price (Rs) 3.36 3.00 3.20 3.04 2.88

Revenue 11088 9450 9600 8664 7776

Variable Cost 5940 5400 5400 5400 5940

Contribution 5148 4050 4200 3264 1836

Fixed Costs 1260 1140 1200 1320 1440

Depreciation 1200 1200 1200 1200 1200

PBIT 2688 1710 1800 744 -804

Interest 0 0 0 0 0

PBT 2688 1710 1800 744 -804Tax @40% 1075.2 684 720 297.6 -321.6

PAT 1612.8 1026 1080 446.4 -482.4

Cash flowfromOperations 2812.8 2226 2280 1646.4 717.6

Present Value of Cash in flows 14117 11172 11443 8263 3601

Net Present Value 6117 3172 3443 263 -4399

Probability (%) 15% 20% 30% 20% 15%

Expected NPV

Standard Deviaion of NPV

Coefficient of Variation

1978

1607

0.81

Scenario Analysis: Sensonr Corporation


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Capital Exp Decisions1