additional topic 6-capital rationing

7/27/2019 Additional Topic 6-Capital Rationing

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A D D I T I O N A L N O T E S F O R T O P I C 6

CAPITAL RATIONING


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Capital Rationing

Suppose that you have evaluatedfive capital investment projects for

your company.

Suppose that the VP of Finance hasgiven you a limited capital budget.

How do you decide which projectsto select?


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Capital Rationing

You could rank the projects by IRR:

IRR

5%

10%

15%

20%

25%

$

1


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Capital Rationing


IRR

5%

10%

15%

20%

25%

$

1 2


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Capital Rationing


IRR

5%

10%

15%

20%

25%

$

1 2 3


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Capital Rationing


IRR

5%

10%

15%

20%

25%

$

1 2 3 4


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Capital Rationing


IRR

5%

10%

15%

20%

25%

$

1 2 3 4 5


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Capital Rationing


IRR

5%

10%

15%

20%

25%

$

1 2 3 4 5

$X

Our budget is limited

so we accept onlyprojects 1, 2, and 3.


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Capital Rationing


IRR

5%

10%

15%

20%

25%

$

1 2 3

$X

Our budget is limited

so we accept onlyprojects 1, 2, and 3.


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Capital Rationing

Ranking projects by IRR is notalways the best way to deal witha limited capital budget.

Its better to pick the largestNPVs.


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Problems with Project Ranking

1) Mutually exclusive projects of unequalsize (the size disparityproblem)

The NPV decision may not agree withIRR or PI.

Solution: select the project with thelargest NPV.


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Size Disparity Example

Project Ayear cash flow

0 (135,000)1 60,0002 60,0003 60,000

required return = 12%IRR = 15.89%NPV = $9,110

PI = 1.07


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Project Byear cash flow

0 (30,000)1 15,0002 15,0003 15,000


PI = 1.20


0 (135,000)1 60,0002 60,0003 60,000


PI = 1.07


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Project Byear cash flow

0 (30,000)1 15,0002 15,0003 15,000


PI = 1.20


0 (135,000)1 60,0002 60,0003 60,000


PI = 1.07


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Problems with Project Ranking

2) The time disparityproblem with mutuallyexclusive projects.

NPV and PI assume cash flows are

reinvested at the required rate of return forthe project.

IRR assumes cash flows are reinvested atthe IRR.

The NPV or PI decision may not agree withthe IRR.

Solution: select the largest NPV.


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Time Disparity Example

Project Ayear cash flow0 (48,000)1 1,2002 2,400

3 39,0004 42,000

required return = 12%

IRR = 18.10%NPV = $9,436PI = 1.20


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Project Byear cash flow0 (46,500)1 36,5002 24,000

3 2,4004 2,400


IRR = 25.51%NPV = $8,455PI = 1.18


3 39,0004 42,000


IRR = 18.10%NPV = $9,436PI = 1.20


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Project Byear cash flow0 (46,500)1 36,5002 24,000

3 2,4004 2,400


IRR = 25.51%NPV = $8,455PI = 1.18


3 39,0004 42,000


IRR = 18.10%NPV = $9,436PI = 1.20


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Mutually Exclusive Investmentswith Unequal Lives

Suppose our firm is planning toexpand and we have to select oneof two machines.

They differ in terms of economiclife and capacity.

How do we decide which machine

to select?


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The after-tax cash flows are:

Year Machine 1 Machine 2

0 (45,000) (45,000)

1 20,000 12,000

2 20,000 12,000

3 20,000 12,000

4 12,000

5 12,000

6 12,000

Assume a required return of 14%.


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Step 1: Calculate NPV

NPV1 = $1,433

NPV2 = $1,664

So, does this mean #2 is better?

No! The two NPVs cant be

compared!


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Step 2: Equivalent AnnualAnnuity (EAA) method

If we assume that each project will bereplaced an infinite number of times inthe future, we can convert each NPV to an

annuity.

The projects EAAs canbe compared todetermine which is the best project!

EAA: Simply annuitize the NPV over theprojects life.


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EAA with your calculator:

Simply spread the NPV over the life of theproject

Machine 1: PV = 1433, N = 3, I = 14,

solve: PMT = -617.24.

Machine 2: PV = 1664, N = 6, I = 14,

solve: PMT = -427.91.


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EAA1 = $617

EAA2 = $428

This tells us that: NPV1 = annuity of$617 per year.

NPV2 = annuity of$428 per year.

So, weve reduced a problem withdifferent time horizons to a couple ofannuities.

Decision Rule: Select the highest EAA.We would choose machine #1.


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Step 3: Convert back toNPV

Assuming infinite replacement, theEAAs are actually perpetuities. Get thePV by dividing the EAA by the requiredrate of return.

NPV 1 = 617/.14 = $4,407

NPV 2 = 428/.14 = $3,057

This doesnt change the answer, ofcourse; it just converts EAA to an NPVthat can be compared.

additional topic 6-capital rationing

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