Mulroney Corp.is considering two mutually exclusive projects.Both require an initial investment of $10,000 at t = 0.Project X has an expected life of 2 years with after-tax cash inflows of $6,000 and $7,800 at the end of Years 1 and 2,respectively.In addition,Project X can be repeated at the end of Year 2 with no changes in its cash flows.Project Y has an expected life of 4 years with after-tax cash inflows of $4,300 at the end of each of the next 4 years.Each project has a WACC of 8%.Using the replacement chain approach,what is the NPV of the most profitable project?
A)$4,242
B)$4,246
C)$4,286
D)$4,325
E)$4,433

Question

​Mulroney Corp.is considering two mutually exclusive projects.Both require an initial investment of $10,000 at t = 0.Project X has an expected life of 2 years with after-tax cash inflows of $6,000 and $7,800 at the end of Years 1 and 2,respectively.In addition,Project X can be repeated at the end of Year 2 with no changes in its cash flows.Project Y has an expected life of 4 years with after-tax cash inflows of $4,300 at the end of each of the next 4 years.Each project has a WACC of 8%.Using the replacement chain approach,what is the NPV of the most profitable project?
A)​$4,242
B)​$4,246
C)​$4,286
D)​$4,325
E)​$4,433

Quizplus · Accepted Answer

To use the replacement chain approach, we need to calculate the present value (PV) of each project over their respective lives, combine the PV of the initial project with the PV of its repeat, and then compare it to the PV of the longer project.

For Project X, the PV of the initial investment and the cash inflows at the end of Years 1 and 2 are:

PV = -$10,000 + $6,000/(1 + 0.08) + $7,800/(1 + 0.08)^2
     = -$10,000 + $5,555.56 + $6,456.70
     = $2,012.26

The PV of the repeat of Project X is simply two years of its cash inflows:

PV = $6,000/(1 + 0.08) + $7,800/(1 + 0.08)^2
     = $5,555.56 + $6,456.70
     = $12,012.26

So the total PV of Project X is:

PV = $2,012.26 + $12,012.26
     = $14,024.52

For Project Y, the PV of the initial investment and four years of cash inflows are:

PV = -$10,000 + $4,300/(1 + 0.08) + $4,300/(1 + 0.08)^2 + $4,300/(1 + 0.08)^3 + $4,300/(1 + 0.08)^4
     = -$10,000 + $3,981.48 + $3,705.19 + $3,438.11 + $3,180.74
     = $4,305.52

Therefore, the NPV of Project X is:

NPV(X) = $14,024.52 - $10,000 = $4,024.52
NPV(Y) = $4,305.52 - $10,000 = -$5,694.48

Project X is the most profitable project, with an NPV of $4,024.52. Therefore, the best choice is Project X.

​Mulroney Corp

Mulroney Corp