Question

A delivery car had a first cost of $26,000, an annual operating cost of $17,000, and an estimated $5000 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 14% 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 $  .

Answer 1

Case 1: Useful life=6 years

AW of Car=-26000*(A/P,0.14,6)-17000+5000*(A/F,0.14,6)

Let us calculate the interest factors

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AW of Car=-26000*0.257157-17000+5000*0.117157=-$23100.30

Case 2 : Car is sold at a salvage value of S after three years

AW of Car=-26000*(A/P,0.14,3)-17000+S*(A/F,0.14,3)

Let us calculate the interest factors

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AW of Car=-26000*0.430731-17000+S*0.290731=-$28199.01+S*0.290731

Since both AW's are equal

-28199.01+S*0.290731=-23100.30

S=(-23100.30+28199.01)/0.290731=$17537.55

Market value of car should be $17537.55