## Profitability Index or Benefit Cost Ratio Analysis

Although individual projects might promise relatively attractive yields, combining them can create unforeseen difficulties. Undertaking a large number of projects simultaneously can require a very fast rate of expansion. Additional personnel requirements and organizational problems can arise that diminish overall rates of return. At some point in the capital budgeting process, management must decide what total volume of favorable projects the firm can successfully undertake without significantly reducing projected returns. Another reason for limiting the capital budget at some firms is the reluctance or inability to obtain external financing by issuing debt or selling stock. For example, considering the plight of firms with substantial amounts of debt during economic recession, management may simply refuse to use high levels of debt financing. Such capital rationing complicates the capital budgeting process and requires more complex tools of analysis.

A variant of NPV analysis that is often used in complex capital budgeting situations is called the profitability index (PI), or the benefit/cost ratio method. The profitability index is calculated as follows:

PV of Cash Inflows PV of Cash Outflows

The PI shows the relative profitability of any project, or the present value of benefits per dollar of cost.

In the SVCC example described in Table 15.4, NPV > 0 implies a desirable investment project and PI > 1. To see that this is indeed the case, we can use the profitability index formula, given in Equation 15.5, and the present value of cash inflows and outflows from the project, given in Equation 15.4. The profitability index for the SVCC project is

PI = PV of Cash Inflows PV of Outflows = \$27,987,141 \$20,254,820 = 1.38

This means that the SVCC capital investment project returns \$1.38 in cash inflows for each dollar of cash outflow, when both figures are expressed in present-value terms.

In PI analysis, a project with PI > 1 should be accepted and a project with PI < 1 should be rejected. Projects will be accepted provided that they return more than a dollar of discounted benefits for each dollar of cost. Thus, the PI and NPV methods always indicate the same accept/ reject decisions for independent projects, because PI > 1 implies NPV > 0 and PI < 1 implies NPV < 0. However, for alternative projects of unequal size, PI and NPV criteria can give different project rankings. This can sometimes cause problems when mutually exclusive projects are being evaluated. Before investigating the source of such conflicts, however, it is worthwhile to introduce two additional capital budgeting decision rules.

internal rate of return (IRR)

Discount rate that equates present value of cash inflows and outflows (15.6)