Question

Platinum Water Aviation has a weighted-average cost of capital of 10.36 percent and is evaluating two projects: A and B. Project A involves an initial investment of 4,886 dollars and an expected cash flow of 8,404 dollars in 4 years. Project A is considered more risky than an average-risk project at Platinum Water Aviation, such that the appropriate discount rate for it is 1.01 percentage points different than the discount rate used for an average-risk project at Platinum Water Aviation. The internal rate of return for project A is 14.52 percent. Project B involves an initial investment of 6,398 dollars and an expected cash flow of 9,917 dollars in 7 years. Project B is considered less risky than an average-risk project at Platinum Water Aviation, 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 Platinum Water Aviation. The internal rate of return for project B is 6.46 percent. What is X if X equals the NPV of project A plus the NPV of project B?

Answer 1

For project A

Initial Investment = $4,886

Return in year 4 = $8,404

Average discount rate = 10.36%.

Risk adjusted discount rate for project A = 10.36% + 1.01%

= 11.37%

Risk adjusted discount rate for project A is 11.37%.

NPV of project A = [$8,404 / (1 + 11.37%) ^ 4] - $4,886

= ($8,404 / 1.5384) - $4,886

= $5,462.77 - $4,886

= $576.77

NPV of project A is $576.77.

For project B

Initial Investment = $6,398

Return in year 7 = $9,917

Average discount rate = 10.36%.

Risk adjusted discount rate for project B = 10.36% - 1.78%

= 8.58%

Risk adjusted discount rate for project B is 8.58%.

NPV of project B = [$9,917 / (1 + 8.58%) ^ 7] - $6,398

= ($8,404 / 1.7793) - $6,398

= $5,573.54 - $6,398

= -$824.46

NPV of project B is -$824.46.

Value of X = NPV of project A + NPV of project B

= $576.77 - $824.46

= -$247.69

Value of X is -$247.69.