Untitled-29

158 Financial Management

0 20,000 40,000 Net present Value

Probability

1.0 1.2 1.4 Probability index

Probability

A'

B

shown in Exhibit 6.17. Since profitability index is a linear transformation of net present

value, the shape of its profitability distribution is identical to that of the probability

distribution of net present value. The profitability distribution of profitability index for

our project is shown in Exhibit 6.18. It should be noted that the x-axis of this exhibit

shows the profitability index values corresponding to the net present values shown on

the axis of Exhibit 6.18.

Figure 6.18: Probability Distribution of Net Present Value

Figure 6.19: Probability Distribution of Probability Index

Having transformed the probability distribution of net present value into the probability

distribution of profitability index, we compare the dispersion of the profitability index

of the project with the maximum risk profile acceptable to management for the expected

profitability index of the project. Suppose the maximum risk profile acceptable to

management when the expected profitability index 1.20 is as shown by curve B in

Exhibit 6.18. comparing the dispersion of the profitability distributions A and B shown

in Exhibit 6.18 we find the risk of the project is less than the maximal risk acceptable

to management for the given level of expected profitability index. Hence the project

is deemed worthwile.

Note that the higher the expected value of profitability index, the greater the dispersion