Question

Suppose your firm is considering investing in a project with the cash flows shown below, that the required rate of return on projects of this risk class is 8 percent, and that the maximum allowable payback and discounted payback statistics for the project are 3.5 and 4.5 years, respectively.

Time:	0	1	2	3	4	5	6
Cash flow:	–$5,000	$1,200	$2,400	$1,600	$1,600	$1,400	$1,200

Use the PI decision rule to evaluate this project. (Do not round intermediate calculations and round your final answer to 2 decimal places.)

Should it be accepted or rejected?

• rejected

• accepted

Answer 1

Profitability Index (PI) decision rule to evaluate the project

-The Project’s Profitability Index (PI) is the ratio of discounted annual cash inflows divided by it’s initial investment cost.

-The Profitability Index (PI) is calculated by dividing the present value of benefits by present value of costs

-It considers the relative size of the initial investment costs.

-Based on Profitability Index Analysis method, the Investment should be selected if the Profitability Index is greater than 1, else the Project should be rejected.

-If the Profitability Index (PI) is greater than 1, then the Project should be accepted.

-If the Profitability Index (PI) is less than 1, then the Project should be rejected.

-The Profitability Index is the ratio of discounted annual cash inflows divided by it’s initial investment cost. The Profitability Index (PI) is calculated by dividing the present value of benefits by present value of costs. It considers the relative size of the initial investment costs.

Profitability Index (PI) for the Project

Year	Annual cash flows ($)	Present Value factor at 8%	Present Value of Annual cash flows ($)
1	1,200	0.925926	1,111.11
2	2,400	0.857339	2,057.61
3	1,600	0.793832	1,270.13
4	1,600	0.735030	1,176.05
5	1,400	0.680583	952.82
6	1,200	0.630170	756.20
TOTAL			7,323.92

Profitability Index = Present Value of annual cash inflows / Initial Investment

= $7,323.92 / $5,000

= 1.46

DECISION

The Project “SHOULD BE ACCEPTED”, Since the Profitability Index (PI) for the Project is greater than 1 (1.46).

NOTE

The formula for calculating the Present Value Inflow Factor (PVIF) is [1 / (1 + r)ⁿ], where “r” is the Discount Rate/Cost of capital and “n” is the number of years.