Question

A delivery car had a first cost of $32,000, an annual operating cost of $19,000, and an estimated $3500 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 12% 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

Answer is 20,149.33 Present Value of total costfirst cost + present Value of operating cost -Present Value of salvage Present Value of total cost 32000 (19000 x 4.11407) (3500 x 0.506631) 0.892857 Year 1 108,344 0.797194 Year 2 0.71178 Year 3 Aw Value-Present Value of total cost /PVA( 12%, 6Years) 0.635518 Year 4 -108344/4.1114 0.567427 Year 5 26,351.93 0.506631 Year 6 4.111407 Present value of total cost if held for only 3years 32000 +(19000 x 4.11407) (3500 x 0.506631) 26.351.93 x (PVA 12%, 3Years) 0.892857 Year 1 - 26.351.93 x 2.4018 0.797194 Year 2 0.71178 Year 3 63,292.90 2.401831 Market value of the used vehicle $ 32,000.00 First cost Add :present Value of operating cost ( 19000 x 2.4018) 45,634.79 $ (63,292.90) $ 14,341.90 Less : present value of Car at 3rd year A+ B-C Discounting Factor @ 12%, 3rd Year Market value of the used vehicle D/ E 0.71178 20,149.33