Problem 8-13 Calculating Profitability Index [LO 6] What is the profitability in
ID: 2735794 • Letter: P
Question
Problem 8-13 Calculating Profitability Index [LO 6]
What is the profitability index for the above set of cash flows if the relevant discount rate is 9 percent? (Do not round intermediate calculations. Round your answer to 3 decimal places (e.g., 32.161).)
What is the profitability index if the discount rate is 14 percent? (Do not round intermediate calculations. Round your answer to 3 decimal places (e.g., 32.161).)
What is the profitability index if the discount rate is 21 percent? (Do not round intermediate calculations. Round your answer to 3 decimal places (e.g., 32.161).)
Problem 8-13 Calculating Profitability Index [LO 6]
Consider the following cash flows: Year Cash Flow 0 $-29,800 1 13,900 2 15,000 3 11,400 Requirement 1:What is the profitability index for the above set of cash flows if the relevant discount rate is 9 percent? (Do not round intermediate calculations. Round your answer to 3 decimal places (e.g., 32.161).)
Profitability index __________________ Requirement 2:What is the profitability index if the discount rate is 14 percent? (Do not round intermediate calculations. Round your answer to 3 decimal places (e.g., 32.161).)
Profitability index ______________ Requirement 3:What is the profitability index if the discount rate is 21 percent? (Do not round intermediate calculations. Round your answer to 3 decimal places (e.g., 32.161).)
Profitability index ________________Explanation / Answer
Answer:-
The profitability index is defined as the PV of the cash inflows divided by the PV of the cash outflows. The equation for the profitability index at a required return of 10 percent is:
PI = [$13,900/1.09 + $15,000/(1.09)2+ $11,400/(1.09)3] / $29,800 = 1.147
The equation for the profitability index at a required return of 14 percent is
PI = [$13,900/1.14 + $15,000/(1.14)2+ $11,400/(1.14)3] / $29,800 =1.054
The equation for the profitability index at a required return of 21 percent is
PI = [$13,900/1.21 + $15,000/(1.21)2+ $11,400/(1.213] / $29,800 =0.9452
We would accept the project if the required return were 9 percent or 14 percent since the PI is greater than one. We would reject the project if the required return were 21 percent since the PI is less than one.