Use of Profitability Index in Capital Rationing

Russell M. Angelo

Under capital rationing, we need a method of selecting that portfolio of projects which yields highest possible present value within the available funds.

Let us consider a simple situation where a firm has the following investment opportunities and has a 10% cost of capital. If the firm has no capital rationing constraint, if should undertake all three projects because they all have possible net present values. Suppose there is a capital constraint and the firm can spend only 50000$ in year zero, what should the firm do? If the firm strictly follows the net present value rule and starts with the highest individual net present value, it will accept the highest net present value project L, which will exhaust the entire budget. We can, however, see that projects M and N together have higher net present value (15870 $) than project L (12940 $) and their outlays are within the budget ceiling. The firm should, therefore, undertake M and N rather than L to obtain highest possible net present value. It should be noted that the firm could not select projects solely on the basis of individual net present values when funds are limited. The firm should intend to get the largest benefit for the available funds. That is, those projects should be selected that give the highest ratio of present value to initial outlay. This ratio is the profitability index. In the example, M has the highest profitability index followed by N and L. If the budget limit is 50000 $, we should choose M and N following the profitability index rule.

The capital budgeting procedure under the simple situation of capital rationing may be summarized as follows:

• That rule should be modified while choosing among projects under capital constraint. The objective should be to maximize net present value per rupee of capital rather than to maximize net present value. Projects should be ranked by their profitability index, and top-ranked projects should be undertaken until funds are exhausted.

Limitations of Profitability Index

The capital budgeting procedure described above does not always work. It fails in two situations:

• Many-period capital constraints

• Project indivisibility

Many-period constraints

The serious limitation in using the profitability index rule is caused by the many-period constraints. In the above post example, there is a budget limit of 50000$ year 1 also and the firm is anticipating an investment opportunity 0 as in low is year 1.

Project indivisibility

The profitability index rule of selecting projects under capital rationing can also fail because of project invisibility. It may be more desirable to accept many lower ranked similar projects than a single large project. The acceptance of a single large project, which may be top-ranked, excludes the possibility of accepting small projects, which may have higher total net present value.

Suppose that the firm has budget ceiling of 10$ million. Following the ranking by profitability index, the firm would choose A and C. These projects spend 850000$ of the total a budget and have a total net present value of 180000$. The next best project E needs an investment of 200000$, while the firm has only 150000$. If we examine the various combinations of projects satisfying the budget limit, we find the package of C, E and D as the best. They exhaust the entire budget and have a total net present value of 189000$. Thus, the firm can choose two lower ranked, small projects, E and D, in place of the higher ranked, large project, A. This section procedure will become very unwieldy if the firm has chosen the best package of projects from a large number of profitable projects.

• Our discussion has shown that the profitability index can be used to choose projects under simple, one-period, capital constraint situation. It breaks down in the case of many-period capital constraints. It will also not work when any other constraint is imposed, or when mutually exclusive projects, or dependent projects are being considered.

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