Question

Because of its age, your car costs $5,000 annually in maintenance expense. You could replace it with a newer vehicle costing $7,300 that would be expected to have a life of 8 years. If your opportunity cost of capital is 4%, by how much must maintenance expense decrease on the new vehicle to justify its purchase?

Answer 1

To justify the purchase of the new vehicle, the maintenance expense must be less than $5,580.49.

Step-by-step explanation:

To determine how much the maintenance expense must decrease on the new vehicle to justify its purchase, we need to compare the present value of the maintenance expenses for the existing car with the present value of the maintenance expenses for the new car. The formula for calculating the present value is:

Present Value = Maintenance Expense / (1 + Opportunity Cost of Capital)^n

where n is the number of years. Let's calculate the present values for both cars:

1. Existing Car: Present Value = $5,000 / (1 + 0.04)^8 = $4,103.43
2. New Car: Present Value = Maintenance Expense / (1 + 0.04)^8

To find the maintenance expense on the new vehicle that would justify its purchase, we need to solve for Maintenance Expense in the equation: $4,103.43 = Maintenance Expense / (1 + 0.04)^8. Solving for Maintenance Expense:

Maintenance Expense = $4,103.43 * (1 + 0.04)^8 = $4,103.43 * 1.3604 = $5,580.49

Therefore, the maintenance expense on the new vehicle must be less than $5,580.49 to justify its purchase.