|
Profitability index (PI)(or Benefit/Cost Ratio)
the A capital-budgeting decision criterion defined as the ratio
of the present value of the future free cash flows to the initial outlay.
where
 =
the annual free cash flow in time period t
k =
the appropriate discount rate: that is, the require rate of return
or cost of capital
IO =the
initial cash outlay
n =the project's
expected lift
NPV
= PV of cash inflows - Initial Outlay
=> Accept when NPV > or = 0
PI = PV of cash inflows / Initial Outlay
=> Accept when PI > or = 1
Example:
A firm with a 10 percent required rate of return is considering
investing in a new machine with an expected life of 6 years. The after-tax
cash flows resulting from this investment are given in the Table. Discounting
the project future free cash flows back to the present yields
a present value of $53,667; dividing this value by the initial outlay
of $50,000 gives a profitability index of 1.0733, as shown in Table.
This tells us that the present value of the future benefits
accruing from this project is 1.0733 times the level of the initial
outlay. Because the profitability index is greater than 1.0, the project
should be accepted.
PI illustration of Investment in New Machinery
|
|
Free
Cash Flow
|
|
Free
Cash Flow
|
|
Initial
outlay
|
-$50,000
|
Year
4
|
12,000
|
|
Year
1
|
15,000
|
Year
5
|
14,000
|
|
Year
2
|
8,000
|
Year
6
|
16,000
|
|
Year
3
|
10,000
|
|
|
Calculation
for PI illustration of Investment in New Machinery
|
|
Free
Cash Flow
|
Present
Value Factor
at 10 Percent |
Present
Value
|
|
Initial
outlay
|
-$50,000
|
1.000
|
-$50,000
|
|
Year
1
|
15,000
|
0.909
|
13,635
|
|
Year
2
|
8,000
|
0.826
|
6,608
|
|
Year
3
|
10,000
|
0.751
|
7,510
|
|
Year
4
|
12,000
|
0.683
|
8,196
|
|
Year
5
|
14,000
|
0.621
|
8,694
|
|
Year
6
|
16,000
|
0.564
|
9,024
|
=1.0733
|
