Question

an asset with a first cost of $250,000 is expected to have a maximum useful life of 10 years and a market value that decreases $25,000 each year. the annual operating cost is expected to be constant at $25,000 per year for first 5 years and to increase at a substantial rate of 25% per year thereafter. the interest rate is 4% per year. calculate the economic service life of the asset.

Answer 1

To calculate the economic service life of an asset with given first costs, market value depreciation, operating cost changes, and interest rate, compare the present worth of costs for each potential year of service. Apply the present value formula using a 4% interest rate to find when additional years are no longer economically advantageous.

Step-by-step explanation:

The question relates to determining the economic service life of an asset, where various financial factors such as initial cost, market value depreciation, operating costs, and interest rates are considered. To calculate the economic service life, the method involves comparing the present worth of keeping the asset for each possible life span, factoring in depreciation, operating costs, and the time value of money using a 4% interest rate.

The asset's initial cost is $250,000, and its market value decreases by $25,000 each year. The annual operating cost is constant at $25,000 for the first 5 years and increases by 25% each year afterward. These costs are summed for each year and discounted back to present value using the formula for present value, considering a 4% interest rate. The economic service life is the year in which this calculated present worth is the lowest, indicating that any additional year would not be economically beneficial.