Question

A delivery car had a first cost of $38,000, 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 $

Answer 1

Cost of car in present value terms taking 6 year life = -38,000 -13,000*PVAF(10%, 6 years) + 7,000*PVF(10%, 6 years)

= -38,000 -13,000*4.355 +7,000*0.564

= -90,667

AW = -90,667/PVAF(10%, 6 years)

= -90,667/4.355

= -20,819

Now, let the sale value of used car at the end of year 3 be x

Present Value = -38,000 - 13,000*PVF(10%, 3 years) + x*PVF(10%, 3 years)

AW should be the same

-20,819 = (-38,000 -13,000*2.487 +x*0.751)/2.487

-51,776.85 = -70,331 + 0.751x

X = $24,705.93