Useful Lives ≠ Study Period: The Coterminated Assumption Suppose that Example 6-7 is modified such that an analysis period of six years is used (coterminated assumption) instead of 12 years, which was based on repeatability and the least common multiple of the useful lives. Perhaps the responsible

Question

Useful Lives ≠ Study Period: The Coterminated Assumption
Suppose that Example 6-7 is modified such that an analysis period of six years is used (coterminated assumption) instead of 12 years, which was based on repeatability and the least common multiple of the useful lives. Perhaps the responsible manager did not agree with the repeatability assumption and wanted a six-year analysis period because it is the planning horizon used in the company for small investment projects.

Accepted Answer

An assumption used for an investment alternative (when useful life is less than the study period) is that all cash flows will be reinvested by the firm at the MARR until the end of the study period. This assumption applies to Alternative A, which has a four-year useful life (two years less than the study period), and it is illustrated in Part 2 of Figure 6-9. We use the FW method to analyze this situation:

FW(10%)[latex]_{A}[/latex] = [−$3,500(F/P, 10%, 4) + ($1,255)(F/A, 10%, 4)](F/P, 10%, 2)
= $847,
FW(10%)[latex]_{B}[/latex] = −$5,000(F/P, 10%, 6) + ($1,480)(F/A, 10%, 6)
= $2,561.
Based on the FW of each alternative at the end of the six-year study period, we
would select Alternative B because it has the larger value ($2,561).

Question 6.8: Useful Lives ≠ Study Period: The Coterminated Assumption Su...

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