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Capital Rationing

• Capital rationing occurs when a limit is placed on the dollar size of the capital budget.

• How to select: Select a set of projects with the highest NPVs – subject to the capital constraint. Using NPV may preclude accepting the highest ranked project in terms of PI or IRR.

Capital Rationing: An Example(Firm’s Cost of Capital = 12%)

• Independent projects ranked according to their IRRs:

Project Project Size IRR E $20,000 21.0% B 25,000 19.0 G 25,000 18.0 H 10,000 17.5 D 25,000 16.5 A 15,000 14.0 F 15,000 11.0 C 30,000 10.0

Capital Rationing Example (Continued)

• No Capital Rationing - Only projects F and C would be rejected. The firm’s capital budget would be $120,000.

• Capital Rationing - Suppose the capital budget is constrained to be $80,000. Using the IRR criterion, only projects E, B, G, and H, would be accepted, even though projects D and A would also add value to the firm. Also note, however, that a theoretical optimum could be reached only be evaluating all possible combinations of projects in order to determine the portfolio of projects with the highest NPV.

4

Ranking Problems

• Size Disparity

• Time Disparity

• Unequal Life

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Size Disparity• This occurs when we examine mutually

exclusive projects of unequal size.

• Example: Consider the following cash flows for one-year Project A and B, with required rates of return of 10%.– Initial Outlay: A = $200 B = $1,500– Inflow: A = $300 B = $1,900

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7

Project A Project BNPV 72.73 227.28PI 1.36 1.15IRR 50% 27%

• Ranking Conflict: – Using NPV, Project B is better; – Using PI and IRR, Project A is better.

Size Disparity

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• Which technique to use to select the better project?

• Use NPV whenever there is size disparity. If there is no capital rationing, project with the largest NPV will be selected. When capital rationing exists, select set of projects with the largest NPV.

Size Disparity

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Time Disparity Problem• Time Disparity problems arise because of

differing reinvestment assumptions made by the NPV and IRR decision criteria.

• Cash flows reinvested at:– According to NPV: Required rate of return– According to IRR: IRR

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• Example: Consider two projects, A and B, with initial outlay of $1,000, cost of capital of 10%, and following cash flows in years 1, 2, and 3:

• A: $100 $200 $2,000

• B: $650 $650 $650

Time Disparity Problem

11

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Project A Project BNPV 758.83 616.45PI 1.759 1.616IRR 35% 43%

• Ranking Conflict:– Using NPV, A is better– Using IRR, B is better

• Which technique to use to select the superior project?: – Use NPV

Time Disparity Problem

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Unequal Lives Problem• This occurs when we are comparing two

mutually exclusive projects with different life spans.

• To compare projects, we compute the Equivalent Annual Annuity (EAA)

Mutually Exclusive Investments with Mutually Exclusive Investments with Unequal LivesUnequal Lives

• Suppose our firm is planning to expand and we have to select 1 of 2 machines. They differ in terms of economic life and capacity.

• How do we decide which machine to select?

• 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%.

Step 1: Calculate NPVStep 1: Calculate NPV

NPVNPV11 = $1,432 = $1,432 NPVNPV22 = $1,664 = $1,664

So, does this mean #2 is better?So, does this mean #2 is better? No! The two NPVs can’t be compared!No! The two NPVs can’t be compared!

Step 2: Equivalent Annual Step 2: Equivalent Annual Annuity (EAA) methodAnnuity (EAA) method

• If we assume that each project will be replaced an infinite number of times in the future, we can convert each NPV to an annuity.

• The projects’ EAAs can be compared to determine which is the best project!

• EAA: Simply divide the NPV by the PVIFA for the project’s original life.

• EAA = NPV / (PVIFA i, n)

EAA = NPV / (PVIFA i, n)EAA = NPV / (PVIFA i, n)

EAAEAA11 = 1,432 / (PVIFA . = 1,432 / (PVIFA .14, 314, 3))

= 1,432 / (2.3216)= 1,432 / (2.3216)

= $617= $617 EAAEAA22 = 1,664 / (PVIFA = 1,664 / (PVIFA .14, 6.14, 6))

= 1,664 / (3.8887)= 1,664 / (3.8887)

= $428= $428

What does this tell us?What does this tell us?

• EAA1 = $617

• EAA2 = $428

• This tells us that:

• NPV1 = annuity of $617 per year.

• NPV2 = annuity of $428 per year.

• So, we’ve reduced a problem with different time horizons to a couple of annuities.

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

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The Multinational Firm: Capital-Budgeting

• The key to success in capital-budgeting is finding good projects. Finding new projects and correctly evaluating them are key to the continued success of firms.

• For many companies, finding new projects involves going overseas through joint ventures or strategic alliances or establishing subsidiaries abroad.

• Some companies generate > 50% of their revenues from sales abroad.

Keown, Martin, Petty - Chapter 9 21

Modified IRR

• Primary drawback of the IRR relative to the net present value is the reinvestment rate assumption made by the internal rate of return

• Modified IRR allows the decision maker to directly specify the appropriate reinvestment rate

• MIRR> required rate of return, accept

• MIRR< required rate of return, reject

Keown, Martin, Petty - Chapter 9 22

MIRR Example

• Project having a 3yr. Life and a required rate of return of 10% with the following cash flows:

FCF’s FCF’s

Initial Outlay

-$6,000 Year 2 $3,000

Year 1 $2,000 Year 3 $4,000

Keown, Martin, Petty - Chapter 9 23

• Step 1: Determine the PV of the project’s cash outflows. $6,000 is already at present.

• Step 2: Determine the terminal value of the project’s free cash flows. To do this use the project’s required rate of return to calculate the FV of the project’s three cash flows of the project’s cash outflows. They turn out to be $2,420 +$3,300 + $4,000 = $9,720 for the terminal value

MIRR Example

Keown, Martin, Petty - Chapter 9 24

• Step 3: Determine the discount rate that equates to the PV of the terminal value and the PV of the project’s cash outflows. MIRR= 17.446%. It is > required rate of return: Accept

MIRR Example