Question

A delivery car had a first cost of $30,000, an annual operating cost of $12,000, and an estimated $7500 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 9% 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

The question involves calculating the market value of a used delivery car so that its annual worth (AW) is the same over a 3-year period as it would have been if the car was retained for its full 6-year life cycle. This requires factoring in depreciation, operating costs, the salvage value, and the time value of money at a 9% interest rate.

Step-by-step explanation:

The student is asking about the determination of a used vehicle's market value, considering depreciation and opportunity cost of capital, to ensure that the vehicle's annual worth (AW) over 3 years is equivalent to what it would have been over the intended 6-year lifespan. To calculate the market value of the used vehicle, various costs and values related to vehicle ownership and operation are taken into account, and financial formulas including the concept of the time value of money are applied.

To find the equivalent market value, one commonly applies the concept of present value. This calculation would involve an estimation of total costs and salvage value over the actual and intended periods, discounted at the given interest rate, and then equating the calculated AW for both scenarios.

Without providing a specific formula or calculation here, the key concept is that the market value must be set at a point where the annualized cost (taking into account depreciation, operating costs, and interest) remains consistent, regardless of the shortened usage period.