A delivery car had a first cost of $30,000, an annual operating cost of $12,000, and an estimated $4000 salvage value after its 6-year life. Due to an economic slowdown, the car will be retained for only 2 years and must be sold now as a used vehicle. (a) At an interest rate of 10% per year, what must the market value of the 2-year-old vehicle be in order for its AW value to be the same as the AW for a full 6-year life cycle? (b) Compare your answer in (a) with the first cost and expected salvage after 6 years. Is the required market value a reasonable one, in your opinion?
What will be an ideal response?
(a) AW4 = -30,000(A/P,10%,6) – 12,000 + 4000(A/F,10%,6)
= -30,000(0.22961) – 12,000 + 4000(0.12961)
= $-18,370
-18,370 = -30,000(A/P,10%,2) – 12,000 + S(A/F,10%,2)
-18,370 = -30,000(0.57619) – 12,000 + S(0.47619)
0.47619S = 10,916
S = $22,923
(b) S = $22,923 is very high for a used delivery car; this market value is over 5.7 times the estimated salvage of $4000.
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