Question

Silver Sun Entertainment has a weighted-average cost of capital of 8.22 percent and is evaluating two projects: A and B. Project A involves an initial investment of 5,756 dollars and an expected cash flow of 8,519 dollars in 6 years. Project A is considered more risky than an average-risk project at Silver Sun Entertainment, such that the appropriate discount rate for it is 0.86 percentage points different than the discount rate used for an average-risk project at Silver Sun Entertainment. The internal rate of return for project A is 6.75 percent. Project B involves an initial investment of 4,760 dollars and an expected cash flow of 8,425 dollars in 5 years. Project B is considered less risky than an average-risk project at Silver Sun Entertainment, such that the appropriate discount rate for it is 1.78 percentage points different than the discount rate used for an average-risk project at Silver Sun Entertainment. The internal rate of return for project B is 12.1 percent. What is X if X equals the NPV of project A plus the NPV of project B?

Answer 1

Calculation of NPV (Net Present Value) of Project A :

Initial Investment = $ 5,756

Expected Cash flow in 6 years = $ 8,519

Discounted rate is 0.86 percentage points different than average risk project and as the project is considered riskier than average project, the discounted rate will increase as expected return will be higher.

Therefore, Discounted rate = Weighted average Cost of Capital + Difference in percentage points

Discounted rates = 8.22 + 0.86 = 9.08 %

Net Present Value of Project A = Present Value of Cash Inflows (-) Present Value of Cash Outflows

NPV = [ 8519 * Present Value Interest factor of 9.08% for 6 years ] (-) 5756

NPV of A = 5057 (-) 5756 = $ ( 699 )

Calculation of NPV (Net Present Value) of Project B :

Initial investment = $ 4,760

Expected Cash flow in 5 years = $ 8,425

Discounted rate is 1.78 percentage points different than average risk project and as the project is considered less riskier than average project, the discounted rate will decrease as expected return will be lower.

Discounted rates = 8.22 - 1.78 = 6.44 %

Net Present Value of Project B = Present Value of Cash Outflows (-) Present Value of Cash Inflows

NPV = [ 8425 * Present Value Interest factor of 6.44% for 5 years ] (-) 4760

NPV of A = 6167 (-) 4760 = $ 1407

VALUE OF X:

X = NPV of A + NPV of B

Value of X = (699) + 1407

Therefore, X = $708