Yonan Inc. is considering Projects S and L, whose cash flows are shown below. These projects are mutually exclusive, equally risky, and not repeatable. If the decision is made by choosing the project with the shorter payback, some value may be forgone. How much value will be lost in this instance? Note that under some conditions choosing projects on the basis of the shorter payback will not cause value to be lost.
A) $55.16
B) $66.42
C) $78.79
D) $93.16

Question

Yonan Inc. is considering Projects S and L, whose cash flows are shown below. These projects are mutually exclusive, equally risky, and not repeatable. If the decision is made by choosing the project with the shorter payback, some value may be forgone. How much value will be lost in this instance? Note that under some conditions choosing projects on the basis of the shorter payback will not cause value to be lost. 
A) $55.16 
B) $66.42 
C) $78.79 
D) $93.16

Quizplus · Accepted Answer

To calculate the value that will be lost by choosing the project with the shorter payback, we need to calculate the net present value (NPV) of each project and then compare them.

The NPV of Project S is:
-Initial investment: $1,000
-Year 1 cash inflow: $400/(1+0.1) = $363.64
-Year 2 cash inflow: $500/(1+0.1)^2 = $413.22
-Year 3 cash inflow: $550/(1+0.1)^3 = $422.04
-Year 4 cash inflow: $600/(1+0.1)^4 = $425.17
-Year 5 cash inflow: $700/(1+0.1)^5 = $451.10
NPV of Project S = -$1,000 + $363.64 + $413.22 + $422.04 + $425.17 + $451.10 = $75.17

The NPV of Project L is:
-Initial investment: $1,000
-Year 1 cash inflow: $300/(1+0.1) = $272.73
-Year 2 cash inflow: $400/(1+0.1)^2 = $330.58
-Year 3 cash inflow: $500/(1+0.1)^3 = $422.04
-Year 4 cash inflow: $600/(1+0.1)^4 = $492.61
-Year 5 cash inflow: $800/(1+0.1)^5 = $594.35
NPV of Project L = -$1,000 + $272.73 + $330.58 + $422.04 + $492.61 + $594.35 = $620.32

If we choose the project with the shorter payback, we would choose Project S because it has a payback period of 3 years compared to Project L's payback period of 4 years. However, this would cause us to forego the higher NPV of Project L.

The value that will be lost is the difference between the NPV of Project L and the NPV of Project S, which is $620.32 - $75.17 = $545.15.

Therefore, the best choice is to choose Project L because it has a higher NPV, even though its payback period is longer. Answer: D.

Yonan Inc Is Considering Projects S and L, Whose Cash Flows