Final answer:
The equivalent uniform annual cost (EUAC) of a tractor considering its initial cost, salvage value after 10 years, and annual maintenance can be estimated by accounting for depreciation and maintenance costs, ignoring taxes and other potential costs or income. However, to accurately calculate EUAC, the present value and future value formulas must be applied to account for the 12% interest rate over the 10 years.
Step-by-step explanation:
To determine the equivalent uniform annual cost (EUAC) of a tractor, we must consider the initial cost, salvage value, operating costs, and the discount rate due to the interest rate over the life span of the tractor. The initial cost of the tractor is $7500, and after 10 years, it has a salvage value of $5000. The maintenance costs are $500 per year. The interest rate given is 12%. To simplify, the EUAC includes the annualized initial cost, annualized salvage value, and the maintenance cost adjusted for the interest rate.
First, we need to calculate the annualized initial cost using the formula for the present value of an annuity, and then adjust for the salvage value which will reduce the annual cost. Afterward, we'll add the annual maintenance costs to determine the full EUAC. However, it's important to note that an exact calculation requires more information such as the method of annualizing (e.g., whether to use a sinking fund factor or capital recovery factor) and may require the use of financial calculators or software to find the precise answer.
Given the information provided and assuming straight-line depreciation as well as ignoring taxes and other potential costs or income, as a simplified example, the EUAC could be estimated as follows:
- Depreciation = (Initial cost - Salvage value) / Life span of the tractor = ($7500 - $5000) / 10 = $250 per year
- Maintenance costs = $500 per year.
- EUAC (without considering the interest factor for simplicity) = Depreciation + Maintenance costs = $250 + $500 = $750 per year.
This number does not account for the time value of money and assumes an equal distribution of costs over the 10-year period. To accurately account for the interest rate, we would apply the present value and future value formulas to factor in the 12% interest rate over the 10 years.