Question

2) Your friend Tom is deciding whether to buy a new car. The Honda that he wants will cost $25,000, with annual costs of $1,000 per year, with an estimated salvage value of $5,000 ten years from now. His current used car could be sold for $5,000 today, with the salvage value decreasing by $1,000 for each additional year. Annual costs are currently $2,000, but are expected to increase by $500 per year. Tom anticipates that his old car could be maintained for at most three years. You can assume that Tom's minimum acceptable rate of return is 15%. a. What is the economic service life of Tom's current used car -- one, two, or three years? b. At the end of his car's economic service life, should he buy a similar used car, or buy the Honda that he is currently eyeing? c. If the annual equivalent cost of the Honda will be less than the annual equivalent cost of his old used car, when would be the best time for him to sell his old car and buy a Honda?

Answer 1

a.

Economic service life analysis of old car

EUAC for 1 yr = 5000 * (A/P, 15%,1) + 2000 - 4000 *(A/F, 15%,1)

= 5000 * 1.15 + 2000 - 4000

= 3750

EUAC for 2 yrs = 5000 * (A/P, 15%,2) + 2000 + 500 * (A/G, 15%,2) - 3000 *(A/F, 15%,2)

= 5000 * 0.615116 + 2000 + 500 * 0.465116 - 3000 *0.465116

= 3912.79

EUAC for 3 yrs = 5000 * (A/P, 15%,3) + 2000 + 500 * (A/G, 15%,3) - 2000 *(A/F, 15%,3)

= 5000 * 0.437977 + 2000 + 500 * 0.907127 - 2000 * 0.287977

= 4067.49

As EUAC is minimum in year 1, therefore economic service life is 1 yr

b.

EUAC of Honda = 25000 * (A/P, 15%,10) + 1000 - 5000 * (A/F, 15%,10)

= 25000 * 0.199252 + 1000 - 5000 * 0.049252

= 5735.04

As EUAC of Honda is more than the maximum EUAC of used car, therefore, he should but a similar used car

c. As EUAC of Honda is more than the EUAC of used car for three years, therefore, he should buy the new car only after 3 yrs