Superior Project Comparison and NPV Calculation | CFA® Level 1 Exam Prep

Which Project is Superior According to Common Life Approach? Find Out Now!

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Question

Foundation Systems, a software engineering company, is considering the acceptance of two mutually exclusive projects. Assume the following information:

Project A -

Initial cash outlay ($40,000)

t1: $8,000

t2: $14,000

t3: $13,000

t4: $12,000

t5: $11,000

t6: $10,000

cost of capital is 11.5%

Project B -

Initial cash outlay ($20,000)

t1: $7,000

t2: $13,000

t3 $12,000

cost of capital is 11.5%

Assuming no taxes, a $0.00 salvage value at the end of each project, and the fact that both projects can be replicated identically at the end of their lives, which is the superior project according to the Common Life approach? Additionally, what is the NPV of the superior project over the common life?

Answers

A. Project A, NPV $7,165.11

B. Project A, NPV $9,280.90

C. The Common Life approach cannot be applied to these two projects, due to the fact that the projects share unequal lives.

D. Project B, NPV $9,280.90

E. Project B, NPV $5,391.49

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Explanations

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A. B. C. D. E.

The Common Life, or "Replacement Chain" approach is a method which allows two projects with differing lives to be compared on the basis of NPV or IRR. In analyzing two or more projects using theCommon Life approach, the two projects are multiplied in such a way that each comprises the same amount of time periods. In this example, you are provided with one project that is three periods long, and another which is six periods. By multiplying the three-period project by two, then we are able to formulate a situation in which both projects share a "common life." The calculation of the NPV for Project B assumes the following series of cash flows: t0: ($20,000) t1: $7,000 t2: $13,000 t3: [$12,000 + ($20,000)]= ($8,000) t4: $7,000 t5: $13,000 t6: $12,000

During t3, the project is "replaced," and the $12,000 inflow is offset by the ($20,000) required to implement the project once again. Incorporating this series of cash flows into your calculator will yield a NPV of $9,280.90 for project B, and this is higher than the NPV of $7,165.11 for project A.

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