Introduction to Finance

profi tability index (PI)
, also called the 
benefi t/cost ratio
.
 
The PI method computes the ratio 
between
 
the present values of the infl ows and outfl ows:
PI =
Present value of future cash flows
Initial cost
=
∑
n
t
= 1
CF
t
(1 +
r
)
t
CF
0
(17-3)
The PI measures the relative benefi ts of undertaking a project; namely, the PV of benefi ts 
received for each dollar invested. A PI of 2, for example, means that the project returns a 
PV of $2 for every $1 invested. Since it would be foolish to invest in a project that returns 
less than a dollar for every dollar invested, the profi tability index has a natural decision 
rule: accept a project that has a PI greater than 1.0, and reject a project that has a PI less 
than 1.0.
profi tability index (PI) 
or
 benefi t/
cost ratio 
ratio between the present 
values of the infl ows and the 
outfl ows
12
The reason the MIRR ranks projects in the same order as the NPV method is because the MIRR is a transformation 
of the NPV calculation. The terminal value calculation in the MIRR method is equal to the FV of the PV of the 
infl ows. For example, for project A, the PV of the infl ows is $21,986.56. At the 10 percent required return, the FV of 
this amount in year fi ve is $21,986.56(1.10)
5
= $35,409.57, which, with some rounding error, is the terminal value 
we computed above.

---

17.7 Capital Budgeting Techniques—Payback Period
537
Using the data in Table 17.3, we calculate the PV of project A’s infl ows to be $21,982. 
Since its initial cost is $20,000, project A has a PI of $21,982∕$20,000, or 1.099. Project B’s 
cash infl ows have a PV of $25,988, so its PI is $25,988∕$25,000, or 1.040.
The relationship between PI and NPV should be clear. Whenever NPV is positive, PI 
exceeds 1.0. Likewise, whenever NPV is negative, PI is less than 1.0. Thus, the NPV, IRR, 
and PI always agree on which projects would enhance shareholder wealth and which would 
diminish it.
17.7
Capital Budgeting Techniques—
Payback Period
The payback period method does not consider the time value of money so it is a nondiscounted 
cash fl ow technique. So, why discuss it? We discuss it because it is simple to compute and still 
used by some fi rms. You need to know this technique and be able to explain why it should be 
avoided to make investment decisions.
The