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A delivery car had a first cost of $34,000, an annual operating cost of $18,000, and...

A delivery car had a first cost of $34,000, an annual operating cost of $18,000, and an estimated $6500 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?

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Answer #1
Annual worth for full life:
Annual operating cost -18000
Annuity factor for 6 yrs at 8% 4.6229
Present wrth of AOC -83212.2
Add: Investment -34000
less: Present value of Salvage 4096.3
($ 6500*0.6302)
Present worth of Full life -113116
Divide: Annuity factor 4.6229
Annual Worth    -24468.6
Same annual worth for 3 years -24468.6
Present worth for 3 years -73405.9
($ 24468.6*3)
Less: Initial Investment 34000
Less: Present value of AOC for 3 yrs 46387.8
($18000*2.5771)
Present value of salvage 6982
Divide: Present value factor of Yr-3 0.7938
Salvage value at the end of yr-3 8796
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