As discussed in Section 6.2, either of the following two equations can be applied to determine the amount necessary to recover invested capital and a required return: CR 1 = ?P(A?P,i,n) + S(A?F,i,n) or CR 2 = ?[(P – S)(A/P,i,n) + S(i)] For an alternative that has a first cost of $50,000 and a salvage value of $5,000 after its 5- year life, show that the capital recovery calculated using either of these equations is exactly the same. Use an interest rate of 10% per year.
What will be an ideal response?
CR 1 = -50,000(A/P,10%,5) + 5,000(A/F,10%,5)
= -50,000(0.26380) + 5,000(0.16380)
= $-12,371
CR 2 = -[(50,000 – 5,000)(A/P,10%,5) + 5,000(0.10)]
= -[(45,000)(0.26380) + 5,000(0.10)]
= $-12,371
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