Question

Suppose your firm is considering two mutually exclusive, required projects with the cash flows shown below. The required rate of return on projects of both of their risk class is 12 percent, and that the maximum allowable payback and discounted payback statistic for the projects are 2 and 3 years, respectively.

Time: 0 1 2 3

Project A Cash Flow -39,000 29,000 49,000 20,000

Project B Cash Flow -49,000 29,000 39,000 69,000

Use the PI decision rule to evaluate these projects; accept the project with the higher PI value.

a. accept both a and b

b. accept neither a nor b

c. reject a, accept b

d. accept a, reject b

Answer 1

Project A

Profitability Index is a ratio of the discounted cash flow to the initial cash flow of the project. It is calculated using the below formula:

Profitability Index= NPV + Initial investment/ Initial investment

Net present value can be solved using a financial calculator. The steps to solve on the financial calculator:

• Press the CF button.
• CF0= -$39,000. Indicate the initial cash flow by a negative sign since it is a cash outflow.  
• Cash flow for each year should be entered.
• Press Enter and down arrow after inputting each cash flow.
• After entering the last cash flow cash flow, press the NPV button and enter the required rate of return of 12%.
• Press enter after that. Press the down arrow and CPT buttons to get the net present value.  

Net present value at 12% required rate of return is $40,190.96.

Profitability Index= $40,190.96 + $39,000/ $39,000

= $79,190.96 / $39,000

= 2.03.

Project B

Profitability Index is a ratio of the discounted cash flow to the initial cash flow of the project. It is calculated using the below formula:

Profitability Index= NPV + Initial investment/ Initial investment

Net present value can be solved using a financial calculator. The steps to solve on the financial calculator:

• Press the CF button.
• CF0= -$49,000. Indicate the initial cash flow by a negative sign since it is a cash outflow.  
• Cash flow for each year should be entered.
• Press Enter and down arrow after inputting each cash flow.
• After entering the last cash flow cash flow, press the NPV button and enter the required rate of return of 12%.
• Press enter after that. Press the down arrow and CPT buttons to get the net present value.  

Net present value at 12% required rate of return is $57,096.26.

Profitability Index= $57,096.26 + $49,000/ $49,000

= $106,096.26 / $49,000

= 2.17.

Using the PI decision rule, the firm should accept Project B since it has the highest profitability index.

Hence, the answer is option c.

In case of any query, kindly comment on the solution.