Question

Blue Eagle Recycling has a weighted-average cost of capital of 7.27 percent and is evaluating two projects: A and B. Project A involves an initial investment of 5,062 dollars and an expected cash flow of 7,745 dollars in 8 years. Project A is considered more risky than an average-risk project at Blue Eagle Recycling, such that the appropriate discount rate for it is 1.1 percentage points different than the discount rate used for an average-risk project at Blue Eagle Recycling. The internal rate of return for project A is 5.46 percent. Project B involves an initial investment of 5,615 dollars and an expected cash flow of 7,861 dollars in 9 years. Project B is considered less risky than an average-risk project at Blue Eagle Recycling, such that the appropriate discount rate for it is 0.95 percentage points different than the discount rate used for an average-risk project at Blue Eagle Recycling. The internal rate of return for project B is 3.81 percent. What is X if X equals the NPV of project A plus the NPV of project B?

Answer 1

Solution) For Project A:

Initial Investment = $5,062

Expected cash flow in 8 years = $7,745

Weighted-average cost of capital of company = 7.27%

Since, Project A is more risky than an average-risk project of the company, thus, the appropriate discount rate for it is 1.1 percentage points higher than the discount rate used for an average-risk project of the company.

Thus, discouint rate for project A = 7.27% + 1.1% = 8.37%

Net Present Value of project A = Present value of future cash flow - Initial Investment

Present Value = Future Cash Flow/(1 + discount rate)^n

= 7,745/(1 + 8.37%)^8 - 5,062

= 4,071.447 - 5,062

= -$990.5525

For Project B:

Initial Investment = $5,615

Expected cash flow in 9 years = $7,861

Weighted-average cost of capital of company = 7.27%

Since, Project B is less risky than an average-risk project of the company, thus, the appropriate discount rate for it is 0.95 percentage points lower than the discount rate used for an average-risk project of the company.

Thus, discouint rate for project B = 7.27% - 0.95% = 6.32%

Net Present Value of project B = Present value of future cash flow - Initial Investment

Present Value = Future Cash Flow/(1 + discount rate)^n

= 7,861/(1 + 6.32%)^9 - 5,615

= 4,528.382 - 5,615

= -$1,086.618

X = Net Present Value of project A + Net Present Value of project B

X = - 990.5525 - 1,086.618

X = -$2,077.17

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