Question

A delivery car had a first cost of $30,000, an annual operating cost of $16,000, and an estimated $7500 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 9% 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

MARR = 9%

Initial cost = 30000

Annual operating cost = 16000

salvage value = 7500

AW when life is 6 years = -30000*(A/P, 9%, 6) -16000 + 7500 *(A/F,9%,6)

= -30000*0.22291978 -16000 + 7500 *0.13291978

= -21690.695

Now due to economic slowdown vehcile has to be sold in three years

Let market value be M, then

AW when kept for 3 years = -30000*(A/P, 9%, 3) -16000 + M *(A/F,9%,3)

= -30000*0.3950547 -16000 + M *0.3050547

= -27851.641 + M *0.3050547

As per the condition given in ques,

AW when kept for 3 years = AW when life is 6 years

-27851.641 + M *0.3050547 = -21690.695

M = (27851.641 - 21690.695) / 0.3050547

M = 20196.20