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A delivery car had a first cost of $40,000, an annual operating cost of $15,000, and...

A delivery car had a first cost of $40,000, an annual operating cost of $15,000, and an estimated $5500 salvage value after its 6-year life. Due to an economic slowdown, the car will be retained for only 3 years and must be sold now as a used vehicle. At an interest rate of 8% per year, what must the market value of the used vehicle be in order for its AW value to be the same as the AW if it had been kept for its full life cycle?

The market value of the used vehicle is determined to be $  .

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Answer #1
(i) Annual Worth if the vehicle is kept for its full life cycle -
PV of Vehicle = 40000 + 15000 x PVAF(8%,6) - 5500/(1.08^6)
40000 + 15000 x 4.6229 - 3465.93
40000 + 69343.19 - 3465.93
105877.3
AW = PV / PVAF(8%,6)
105877.3/4.6229
22902.88
(ii) Let the Market value be MV -
PV if Vehicle is kept for 3 years = 40000 + 15000 x PVAF(8%,3) - MV/(1.08^3)
40000 + 15000 x 2.5771 - 0.7938 MV
40000 + 69343.19 - 3465.93
78656.45 - 0.7938 MV
AW = PV / PVAF(8%,3)
22902.88 = 78656.45 - 0.7938 MV / 2.5771
78656.45 - 0.7938 MV = 22902.88 x 2.5771
78656.45 - 0.7938 MV = 59022.95
MV = (78656.45-59022.95)/0.7938
24732.57
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