# 1.24 The Capital Rationing Problem

There are two reasons why competing projects may be mutually exclusive:

1. There is inadequate space to build two building or house large equipment.
2. There is insufficient financial resources to finance both. We refer to this problem as a âCapital Rationing Problem.â

The PI is used to determine which competing projects should be accepted and which rejected. Assume a firm has only finite sources with which to finance some, none, or all potential projects. Those that are accepted provide the highest PI, ranked from highest to lowest.

In the following example, we will assume that the firm has \$10,000 of capital to invest.

 ProjectÂ InvestmentÂ NPV PI A 3,000 2,000 1.5 B 5,000 2,300 1.4 C \$2,000 \$600 1.3 D 2,500 400 1.2 E 4,000 600 1.1

Projects A, B, And C should be accepted since they have the highest PIs, the highest aggregate NPVs, and exhaust the firmâs available investment capital.

Suppose instead, we assume that Project D has a higher NPV than originally assumed â equal to \$800 with a PI of 1.35.

 ProjectÂ InvestmentÂ NPV PI A 3,000 2,000 1.5 B 5,000 2,300 1.4 C \$2,000 \$600 1.3 D 2,500 800 1.35 E 4,000 600 1.1

The PI still directs us to select A, B, and C; however, if we assume that the firmâs objective is to maximize wealth, as defined by the projectsâ NPVs, we should choose A, B, and D. This combination would put the firm over its capital limitation. Clearly, in the presence of limited capital, the PI method is not necessarily consistent with the notion of wealth maximization, which is paramount (to most corporate executives).

In order to maximize the firmâs wealth by choosing investment projects with high NPVs, the firm would want to add on more projects if the chosen highest PI project, or projects, do not exhaust the available investment capital. For instance, if the firm has \$1,000 to invest and has chosen a projectÂ with the highest PI and an investment cost of \$900, there is clearly little left to invest. The firm may then choose another project whose cost is, say \$100 (i.e., if there is such an opportunity), but has a far lower ranking on the PI range, leaving more desirable projects, in terms of PI rank, âon the table.â