Question

A delivery car had a first cost of $32,000, an annual operating cost of $15,000, and an estimated $6000 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. At an interest rate of 11% 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?

Answer 1

Case 1 - When delivery car is kept for its 6-year life

First cost = $32,000

Annual operating cost = $15,000

Salvage value = $6,000

Interest rate = 11%

Calculate the annual worth -

AW = -$32,000(A/P, 11%, 6) -$15,000 + $6,000(A/F, 11%, 6)

AW = (-$32,000 * 0.23638) - $15,000 + ($6,000 * 0.12638)

AW = -$7,564.16 - $15,000 + $758.28

AW = -$21,805.88

The annual worth of delivery car when kept for 6 year life is -$21,805.88

Case 2 - When car is retained for only 2 years

AW = -$32,000(A/P, 11%, 2) - $15,000 + MV(A/F, 11%, 2)

AW = (-$32,000 * 0.58393) - $15,000 + (MV * 0.47393)

AW = -$18,685.76 - $15,000 + 0.47393MV

AW = -$33,685.76 + 0.47393MV

The annual worth of car when retained for only 2 years was [-$33,685.76 + 0.47393MV].

Equating the both annual values -

-$21,805.88 = -$33,685.76 + 0.47393MV

-$21,805.88 + $33,685.76 = 0.47393MV

$11,879.88 = 0.47393MV

MV = $11,879.88/0.47393

MV = $25,066.74

The market value of the used vehicle must be $25,066.74.