A delivery car had a first cost of $26,000, an annual operating cost of $13,000,

Question

A delivery car had a first cost of $26,000, an annual operating cost of $13,000, and an estimated $7000 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 10% 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 $ 23110.09 0

Explanation / Answer

Let the market value be 'M'

i = 10%

1st case : PW (cost) = 26000 + 13000/1.1 + 13000/1.12 +... + (13000 -7000)/1.16

PW = $ 78667.07

Annual cost = A

A/1.1 + .... + A/1.16 = 78667.07 (equating PV of annual costs = PW calculated earlier)

A = $ 18062.54

Case 2:

n = 3 years

PW = 26000 + 13000/1.1 + ... + (13000 - M)/1.13 = 18062.54/1.1 + 18062.54/1.12 + 18062.54/1.13

(AW remains the same for 3 years and is equated to the PW (cost) of holding the car for 3 years)

M = $ 17849

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