Under capital rationing, we need a method of selecting the portfolio of projects that yields the highest possible present value within available funds.
Consider a simple situation where a company has the following investment opportunities and has a cost of capital of 10%. If the firm has no capital rationing constraints, it should undertake all three projects because they all have possible net present values. Suppose there is a capital constraint and the company can spend only $50,000 in year zero, what should the company do? If the company strictly follows the NPV rule and starts with the highest individual NPV, it will accept the highest NPV project L, which will exhaust the entire budget. However, we can see that projects M and N together have a higher net present value ($15,870) than project L ($12,940), and their outlays are within the budget limit. Therefore, the firm should undertake M and N instead of L to obtain the highest possible net present value. It should be noted that the firm would not be able to select projects solely on the basis of individual net present values when funds are limited. The business must intend to make the most of the available funds. That is, those projects that give the highest relationship between the present value and the initial disbursement should be selected. This ratio is the rate of return. In the example, M has the highest rate of return followed by N and L. If the budget limit is $50,000, we should choose M and N following the rate of return rule.
The capital budgeting procedure under the simple capital rationing situation can be summarized as follows:
• That rule should be modified when choosing between capital-constrained projects. The objective should be to maximize the net present value per rupee of capital rather than to maximize the net present value. Projects must be ranked by their rate of return, with the highest ranked projects being undertaken until funds are exhausted.
Limitations of the Profitability Index
The capital budgeting procedure described above does not always work. It fails in two situations:
• Capital restrictions of many periods
• Indivisibility of the project
Restrictions of many periods
The serious limitation in the use of the rate of return rule is caused by the many-period restrictions. In the example in the previous post, there is also a budget cap of $50,000 in year 1 and the company is anticipating a 0 investment opportunity since the minimum is year 1.
Indivisibility of the project
The rate-of-return rule of selecting projects under capital rationing can also fail due to project invisibility. It may be more desirable to accept many similar lower-ranking projects than a single large project. The acceptance of a single large project, which may be world-class, precludes the possibility of accepting small projects, which may have a higher total net present value.
Suppose the company has a budget ceiling of $10 million. Following the profitability index ranking, the company would choose A and C. These projects spend $850,000 of the total budget and have a total net present value of $180,000. The next best project E needs an investment of $200,000, while the company only has $150,000. If we examine the various combinations of projects that satisfy the budget limit, we find that the bundle of C, E, and D is the best. They use up the entire budget and have a total net present value of $189,000. Therefore, the company can choose two lower-rated small projects, E and D, instead of the higher-rated large project A. of profitable projects.
• Our discussion has shown that the rate of return can be used to choose projects under a simple one-period capital constraint situation. It is broken in the case of capital constraints of many periods. It will also not work when any other restrictions are imposed, or when mutually exclusive projects or dependent projects are being considered.