Question

1. You are in the market for a new car. With gasoline prices rising, you are looking for a gas efficient car. You have narrowed down the choices to two cars.  Prima, a gas efficient car, priced at $25,000, and Malibu, a standard car, which sells for $22,000. You are planning to keep your car for six years. The manufacturer sticker on Prima states that compared to a standard car, Prima will have annual savings of $600.
   1. Assuming your opportunity cost of funds is 8 percent, which car should you purchase? Provide the relevant computations to justify your answer.
   2. Would your decision change if the interest rate is 4 percent?
   3. Would your decision in part a change if the annual savings is $500? Explain.

Answer 1

	Prima Car	Malibu Car
Initial Cost	$25,000	$22,000
Annual Savings	$600	Nil
Life	6 years	6 years

a. Assuming your opportunity cost of funds is 8 percent, which car should you purchase? Provide the relevant computations to justify your answer.

If the rate of interest is 8%, calculate the PW of Prima Car

PW = $25,000 - $600 (P/A, 8%, 6)

PW = $25,000 - $600 (4.6229) = 22,226.26

Price of Malibu Car is $22,000, which less than the PW of Prima car. Therefore, Malibu Car should be purchased.

b. Would your decision change if the interest rate is 4 percent?

If interest rate is 4%, again calculate the PW of Prima Car

PW = $25,000 - $600 (P/A, 4%, 6)

PW = $25,000 - $600 (5.2421) = $21,854.74

Now, it is better to purchase the Prima Car, because their cost is less than of the Malibu Car. The price of Malibu Car is 22,000 but after compensating the savings, the price of Prima Car is $21,854.74. Therefore, Prima Car should be purchased.

c. Would your decision in part a change if the annual savings is $500? Explain.

If the savings becomes $500 and rate of interest is 8%, then the PW of Prima Car will be

PW = $25,000 - $500 (P/A, 8%, 6)

PW = $25,000 - $500 (4.6229) = 22,688.55

Price of Malibu Car is $22,000, which again less than the PW of Prima car. Therefore, Malibu Car should be purchased. Decision in the part (a) does not change. Even if the annual savings is 500, Malibu Car should be purchased.