A recent college grad is trying to decide whether he should keep his presently owned car or purchase a new one. A new car will cost $26,000 and have annual operation and maintenance costs of $1200 per year with an $8000 salvage value in 5 years, which is its economic service life. The presently owned car has a resale value now of $5000; 1 year from now it will be $3000, 2 years from now $2500, and 3 years from now $2200. Its operating cost is expected to be $1900 during the first year, with costs increasing by $200 per year. The presently owned car will definitely not be kept longer than 3 more years. Should the presently owned car be sold now? Use annual worth calculations at i=10% per year.

Some solution hints given :

AEC for challenger= 26000 (A/P, 10%, 5) + 1200 – 8000 (P/F, 10%, 5) = 6478.35 To find the economic service life for defender, calculate AEC for
n=1: 5000(A/P, 10%, 1) – 3000 + 1900 = 4400

n=2: 5000(A/P, 10%, 2) – 2500 (A/F, 10%, 2) + 1900 + 200 (A/G, 10%, 2) = 3685.74
n=3: 5000(A/P, 10%, 3) – 2200 (A/F, 10%, 3) + 1900 + 200 (A/G, 10%, 3) = 3433.2
AEC is minimized for the defender when n=3. The economic service life for defender is 3 years. Since 3433.2 < 6478.35, the defender must be kept. The current car should not be sold now.

The above solution provides that the current car should not be sold now. It must be kept for at least 3 years. What should be done after year 3? That is, should it be sold at the end of year 3? Or, should it be kept for one more year until the end of year 4? Conduct marginal analysis to answer this question based on the additional information given below.

• Market value of the current car at the end of year 4: $2000

• Operating cost for the current car during year 4: $6000