Question

You are analyzing a project and have prepared the following data:

Year Cash flow
0 -$169,000
1 $ 46,200
2 $ 87,300
3 $ 41,000
4 $ 39,000
Required payback period 2.5 years
Required AAR 7.25 percent
Required return 8.50 percent
C-1 What is the payback period? Should you accept the project?
C-2 What is the profitability index of the project? Should you accept the project?
C-3 What is the NPV of the project?

Answer 1

The payback period for the project is 3 years. The profitability index is -1.04, indicating that the project should not be accepted. The NPV of the project is $146,666, suggesting that the project should be accepted.

Step-by-step explanation:

C-1 The payback period is the length of time it takes for an investment to recover its initial cost. To calculate the payback period, you need to add up the cash flows until they equal or exceed the initial investment. In this case, the initial investment is -$169,000, and the cash flows in years 1-3 are $46,200, $87,300, and $41,000 respectively. Adding these up, we get $46,200 + $87,300 + $41,000 = $174,500. Since this amount is greater than the initial investment, the payback period is less than 4 years, specifically 3 years.

C-2 The profitability index is a measure of the profitability of an investment. It is calculated by dividing the present value of the cash inflows by the initial investment. In this case, the present value of the cash inflows can be calculated using the required return of 8.50 percent. The present value of the cash inflows in years 1-4 are $42,780, $73,494, $31,936, and $28,351 respectively. Adding these up, we get $42,780 + $73,494 + $31,936 + $28,351 = $176,561. Dividing this by the initial investment of -$169,000, we get a profitability index of -$176,561 / -$169,000 = -1.04. Since the profitability index is less than 1, the project should not be accepted.

C-3 The NPV (Net Present Value) of a project is the difference between the present value of cash inflows and the present value of cash outflows. To calculate the NPV, you need to discount each cash flow at the required return of 8.50 percent and then sum them up. The discounted cash flows in years 1-4 are $42,780 / (1 + 8.50%)^1, $73,494 / (1 + 8.50%)^2, $31,936 / (1 + 8.50%)^3, and $28,351 / (1 + 8.50%)^4 respectively. Calculating these values, we get $39,455, $61,954, $24,603, and $20,654. Summing these up, we get $39,455 + $61,954 + $24,603 + $20,654 = $146,666. Since the NPV is positive, the project should be accepted.