Question

A present asset (defender) has a current market value of $85,000 (year 0 dollars). Estimated market values at the end of the next three years, expressed in year 0 dollars, are MV1 =$73,000, MV2 =$60,000, MV3 =$40,000. The annual expenses (expressed in year 0 dollars) are $15,000 and are expected to increase at 4.5% per year. The before-tax nominal MARR is 15\% per year. The best challenger has an economic life of five years and its associated EUAC is $39,100. Market values are expected to increase at the rate of inflation which is 3% per year. Based on this information and a before-tax analysis, what are the marginal costs of the defender each year and when should you plan to replace the defender with the challenger?

Answer 1

The marginal costs of the defender are $27,000 in year 1, $28,000 in year 2, and $35,000 in year 3. The defender should be replaced with the challenger at the end of year 3.

Step-by-step explanation:

To calculate the marginal costs of the defender each year, we need to consider the annual expenses and the change in market value. In year 1, the expenses are $15,000, and the change in market value is $85,000 - $73,000 = $12,000. Thus, the marginal cost in year 1 is $15,000 + $12,000 = $27,000. Similarly, in year 2, the expenses are $15,000, and the change in market value is $73,000 - $60,000 = $13,000. So, the marginal cost in year 2 is $15,000 + $13,000 = $28,000. In year 3, the expenses are $15,000, and the change in market value is $60,000 - $40,000 = $20,000. Therefore, the marginal cost in year 3 is $15,000 + $20,000 = $35,000.

To determine when to replace the defender with the challenger, we need to compare the annual EUAC of the challenger with the marginal costs of the defender. The EUAC of the challenger is given as $39,100. By comparing the EUAC with the marginal costs, we can determine the year in which the EUAC of the challenger is less than the marginal costs of the defender. In this case, the EUAC of the challenger is less than the marginal costs of the defender starting from year 3. Therefore, the defender should be replaced with the challenger at the end of year 3.

Answer 2

The marginal costs of the defender each year can be calculated by subtracting the annual expenses from the market values of the defender. To determine when to replace the defender with the challenger, compare the present value of the defender's remaining cash flows to the EUAC of the challenger.

Step-by-step explanation:

In order to determine the marginal costs of the defender each year, we need to calculate the annual cash flows for each year and then discount them to the present value. The annual cash flows will consist of the market values of the defender minus the annual expenses.

For each year:

• Year 1: $73,000 - $15,000 = $58,000
• Year 2: $60,000 - $15,000 = $45,000
• Year 3: $40,000 - $15,000 = $25,000

Next, we need to discount these cash flows to the present value using the MARR. The present value of each cash flow will be:

• Year 1: $58,000 / (1 + 0.15) = $50,434.78
• Year 2: $45,000 / (1 + 0.15)^2 = $34,695.65
• Year 3: $25,000 / (1 + 0.15)^3 = $15,936.67

The marginal costs of the defender each year are equal to the present value of the cash flows for that year.

To determine when to replace the defender with the challenger, we need to compare the present value of the cash flows for the defender over its remaining economic life (3 years) to the EUAC of the challenger. The present value of the remaining cash flows for the defender is:

• $50,434.78 + $34,695.65 + $15,936.67 = $101,067.10

Since the present value of the remaining cash flows for the defender is greater than the EUAC of the challenger ($101,067.10 > $39,100), it is not yet time to replace the defender with the challenger.