Question

a delivery car had a first cost of $30000, an annual operating cost of $15000, and an estimated $4500 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 10% per year, what must the market value of the 2-year-old vehicle be in order for its AW value to be the same as the full 6-year life cycle?

Answer 1

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

First cost = $30,000

Annual operating cost = $15,000

Salvage value = $4,500

Time period = 6 years

Interest rate = 10%

Calculate the annual worth -

AW = -$30,000(A/P, 10%, 6) -$15,000 + $4,500(A/F, 10%, 6)

AW = (-$30,000 * 0.22961) -$15,000 + ($4,500 * 0.12961)

AW = -$6,888.3 -$15,000 + $583.24

AW = -$21,305.06

The annual worth of delivery car kept for full 6-year life cycle is -$21,305.06

Case 2 - When the delivery car is kept for only 2 years

First cost = $30,000

Annual operating cost = $15,000

Market value at the end of two years = X

Interest rate = 10%

Time period = 2 years

Calculate the annual worth -

AW = -$30,000(A/P, 10%, 2) -$15,000 + X(A/F, 10%, 2)

AW = (-$30,000 * 0.57619) -$15,000 + (X * 0.47619)

AW = -$17,285.7 -$15,000 + 0.47619X

AW = -$32,285.7 + 0.47619X

The annual worth of the delivery car when kept for 2 years is -$32,285.7 + 0.47619X

Equating the two annual worths' -

-$32,285.7 + 0.47619X = -$21,305.06

0.47619X = -$21,305.06 + $32,285.7

0.47619X = $10,980.64

X = $10,980.64/0.47619

X = $23,059.37

Thus,

The market value of the 2 year old vehicle would be $23,059.37.