Another tool used to evaluate projects is called the profitability index (PI), or benefitcost ratio. This index is defined as the present value of the future cash flows divided by the initial investment. So, if a project costs $200 and the present value of its future cash flows is $220, the profitability index value would be $220/200

1.1. Notice that the NPV for this investment is $20, so it is a desirable investment. More generally, if a project has a positive NPV, then the present value of the future cash flows must be bigger than the initial investment. The profitability index would thus be bigger than 1 for a positive NPV investment and less than 1 for a negative NPV investment. How do we interpret the profitability index? In our example, the PI was 1.1. This tells us that, per dollar invested, $1.10 in value or $.10 in NPV results. The profitability index thus measures "bang for the buck," that is, the value created per dollar invested. For this reason, it is often proposed as a measure of performance for government or other not-for-profit investments. Also, when capital is scarce, it may make sense to allocate it to those projects with the highest PIs. We will return to this issue in a later chapter. The PI is obviously very similar to the NPV. However, consider an investment that costs $5 and has a $10 present value and an investment that costs $100 with a $150 present value. The first of these investments has an NPV of $5 and a PI of 2. The second has an NPV of $50 and a PI of 1.5. If these are mutually exclusive investments, then the second one is preferred even though it has a lower PI. This ranking problem is very similar to the IRR ranking problem we saw in the previous section. In all, there sems to be little reason to rely on the PI instead of the NPV. Our discussion of the PI is summarized as follows.

Questions:

a What does the profitability index measure?

b How would you state the profitability index rule?