Question

Indigo River Entertainment has a weighted-average cost of capital of 7.55 percent and is evaluating two projects: A and B. Project A involves an initial investment of 4,477 dollars and an expected cash flow of 6,939 dollars in 2 years. Project A is considered more risky than an average-risk project at Indigo River Entertainment, such that the appropriate discount rate for it is 2.04 percentage points different than the discount rate used for an average-risk project at Indigo River Entertainment. The internal rate of return for project A is 24.5 percent. Project B involves an initial investment of 5,761 dollars and an expected cash flow of 10,485 dollars in 3 years. Project B is considered less risky than an average-risk project at Indigo River Entertainment, such that the appropriate discount rate for it is 1.34 percentage points different than the discount rate used for an average-risk project at Indigo River Entertainment. The internal rate of return for project B is 22.09 percent. What is X if X equals the NPV of project A plus the NPV of project B?

Answer 1

NPV = sum of present value of cash inflows - initial investment

Present value of each cash inflow = cash inflow / (1 + discount rate)ⁿ

where n = number of years after which the cash flow occurs.

As Project A is more risky, the WACC should be adjusted upward.

Appropriate discount rate for Project A = WACC + adjustment factor

Appropriate discount rate for Project A = 7.55% + 2.04% = 9.59%

As Project B is less risky, the WACC should be adjusted downward.

Appropriate discount rate for Project A = WACC + adjustment factor

Appropriate discount rate for Project A = 7.55% - 1.34% = 6.21%

NPV of Project A = ($6,939 / (1 + 9.59%)²) - $4,477

NPV of Project A = $1,300.70

NPV of Project B = ($10,485 / (1 + 9.59%)³) - $5,761

NPV of Project B = $2,990.29

X =  $1,300.70 + $2,990.29

X =  $4,290.99