Capital Rationing

A firm maximizes its shareholders' wealth by accepting every project that has a positive net present value. But this assumes that the firm can raise the funds needed to pay for these investments. This is usually a good assumption, particularly for major firms which can raise very large sums of money on fair terms and short notice. Why then does top management sometimes tell subordinates that capital is limited and that they may not exceed a specified amount of capital spending? There are two reasons.

capital rationing

Limit set on the amount of funds available for investment.

soft rationing

For many firms the limits on capital funds are "soft." By this we mean that the capital rationing is not imposed by investors. Instead the limits are imposed by top management. For example, suppose that you are an ambitious, upwardly mobile junior manager. You are keen to expand your part of the business and as a result you tend to overstate the investment opportunities. Rather than trying to determine which of your

8 There may be fewer IRRs than the number of sign changes. You may even encounter projects for which there is no IRR. For example, there is no IRR for a project that has cash flows of +$1,000 in Year 0, -$3,000 in Year 1, and +$2,500 in Year 2. If you don't believe us, try plotting NPV for different discount rates. Can such a project ever have a negative NPV?

Brealey-Myers: I II. Value I 6. Net Present Value and I I © The McGraw-Hill

Fundamentals of Corporate Other Investment Criteria Companies, 2001

Finance, Third Edition

188 part two Value many bright ideas really are worthwhile, upper management may find it simpler to impose a limit on the amount that you and other junior managers can spend. This limit forces you to set your own priorities.

Even if capital is not rationed, other resources may be. For example, very rapid growth can place considerable strains on management and the organization. A somewhat rough-and-ready response to this problem is to ration the amount of capital that the firm spends.

hard rationing

Soft rationing should never cost the firm anything. If the limits on investment become so tight that truly good projects are being passed up, then upper management should raise more money and relax the limits it has imposed on capital spending.

But what if there is "hard rationing," meaning that the firm actually cannot raise the money it needs? In that case, it may be forced to pass up positive-NPV projects.

With hard rationing you may still be interested in net present value, but you now need to select the package of projects which is within the company's resources and yet gives the highest net present value.

Let us illustrate. Suppose that the opportunity cost of capital is 10 percent, that the company has total resources of $20 million, and that it is presented with the following project proposals:

Cash Flows, Millions of Dollars

Project

C0

Ci

C2

PV at 10%

NPV

L

-3

+2.2

+2.42

$4

$1

M

-5

+2.2

+4.84

6

1

N

-7

+6.6

+4.84

10

3

O

-6

+3.3

+6.05

8

2

P

-4

+1.1

+4.84

5

Ratio of present value to initial investment.

For our five projects the profitability index is calculated as follows:

Project PV Investment NPV Profitability Index

For our five projects the profitability index is calculated as follows:

Project PV Investment NPV Profitability Index

L

$4

$3

1

1/3 = 0.33

M

6

5

1

1/5 = 0.20

N

10

7

3

3/7 = 0.43

O

8

6

2

2/6 = 0.33

P

5

4

1

1/4 = 0.25

9 Sometimes the profitability index is defined as the ratio of present value to required investment. By this definition, all the profitability indexes calculated below are increased by 1.0. For example, project L's index would be PV/investment = 4/3 = 1.33. Note that project rankings under either definition are identical.

All five projects have a positive NPV Therefore, if there were no shortage of capital, the firm would like to accept all five proposals. But with only $20 million available, the firm needs to find the package that gives the highest possible NPV within the budget.

The solution is to pick the projects that give the highest net present value per dollar of investment. The ratio of net present value to initial investment is known as the profitability index.9

initial investment

9 Sometimes the profitability index is defined as the ratio of present value to required investment. By this definition, all the profitability indexes calculated below are increased by 1.0. For example, project L's index would be PV/investment = 4/3 = 1.33. Note that project rankings under either definition are identical.

chapter 6 Net Present Value and Other Investment Criteria 189

Project N offers the highest ratio of net present value to investment (0.43) and therefore N is picked first. Next come projects L and O, which tie with a ratio of 0.33, and after them comes P. These four projects exactly use up the $10 million budget. Between them they offer shareholders the highest attainable gain in wealth.10

y self-test 6.9 Which projects should the firm accept if its capital budget is only $10 million?

pitfalls of the profitability index

The profitability index is sometimes used to rank projects even when there is no soft or hard capital rationing. In this case the unwary user may be led to favor small projects over larger projects with higher NPVs. The profitability index was designed to select the projects with the most bang per buck—the greatest NPV per dollar spent. That's the right objective when bucks are limited. When they are not, a bigger bang is always better than a smaller one, even when more bucks are spent. Self-Test 6.10 is a numerical example.

y self-test 6.10 Calculate the profitability indexes of the two pairs of mutually exclusive investments in

Self-Tests 6.7 and 6.8. Use a 7.5 percent discount rate. Does the profitability index give the right ranking in each case?

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Responses

  • wilcome baggins
    What is the rationing in which the limits are imposed by top management?
    7 months ago

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