Question

A delivery car had a first cost of $30,000, an annual operating cost of $14,000, and an estimated $7500 salvage value after its 6-year life. Due to an economic slowdown, the car will be retained for only 4 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

Present Value of Total cost = First cost + Present value of Operating Cost - Present value of salvage value

= 30000 + 14000*(1-(1+14%)^-6)/14% - 7500/(1+14%)^6

= 81,024

AW value = Present Value of Total cost/PVA (14%,6)

AW value = 81,024/((1-(1+14%)^-6)/14%)

= 20,836

If AW value are same in case of the car will be retained for only 4 years

AW value = 20,836

Present value of Total cost in case car is held for 4 year = AW value *(1-(1+r)^-n)/r

Present value of Total cost in case car is held for 4 year = 20,836*(1-(1+14%)^-4)/14%

= 60,710

Market value of the used vehicle is determined to be = (Car Cost + Present value of Operating Cost - Present value of Total cost in case car is held for 4 year )*(1+r)^n

= (30000+14000*(1-(1+14%)^-4)/14% - 60710)*(1+14%)^4

= $17,028