Question

an asset has an initial cost of $10 000. its maintenance costs are $300 in the first year, and go up by 20% per year thereafter. its salvage value declines by straight-line depreciation over ten years. if your marr is 10%, what is its economic life?

Answer 1

The economic life of an asset is the period over which the present worth of the asset's costs are minimized, factoring in depreciation, maintenance costs, and salvage value, discounted at the MARR of 10%.

Step-by-step explanation:

In this question, we are asked to calculate the economic life of an asset which has an initial cost of $10,000, with maintenance costs increasing and salvage value decreasing over time. To determine economic life, one needs to consider the time at which the asset's cost, including its maintenance and operation less the salvage value, is minimal when discounted at the Minimum Acceptable Rate of Return (MARR). Since MARR is given as 10%, one would need to calculate the annual cost of the asset including depreciation, the increasing maintenance costs, and then discount these costs back to their present value. The year at which this cost is the lowest would then be regarded as the asset's economic life.

Depreciation is calculated using straight-line depreciation, which would mean the asset loses an equal amount of value each year over the 10-year span. For maintenance costs that increase by 20% each year, a geometric series can be used to represent the escalation in costs. The economic life, therefore, is found when the present worth of the sum of the depreciation costs and the escalated maintenance costs, minus the salvage value, is at its minimum.