A model SK-30 was purchased 2 years ago for $1600; it has been depreciated by straight-line depreciation using a 4-year life and zero salvage value. Because of recent innovations, the current price of the SK-30 is $995. An equipment firm has offered a trade-in allowance of $350 for the SK-30 on a

Question

A model SK-30 was purchased 2 years ago for $1600; it has been depreciated by straight-line depreciation using a 4-year life and zero salvage value. Because of recent innovations, the current price of the SK-30 is $995. An equipment firm has offered a trade-in allowance of $350 for the SK-30 on a new $1200 model EL-40. Some discussion revealed that without a trade-in, the EL-40 can be purchased for $1050. Thus, the originally quoted price of the EL-40 was overstated to allow a larger trade-in allowance. The true current market value of the SK-30 is probably only $200. In a replacement analysis, what value should be assigned to the SK-30?

Accepted Answer

In the example, five different dollar amounts relating to the SK-30 have been outlined:

1. Original cost: It cost $1600 2 years ago.
2. Present cost: It now sells for $995.
3. Book value: The original cost less 2 years of depreciation is 1600 − 2/4(1600 − 0) = $800.
4. Trade-in value: The offer was $350.
5. Market value: The estimate was $200.

We know that an economic analysis is based on the current situation, not on the past. We refer to past costs as sunk costs to emphasize this. These costs cannot be altered, and they are not relevant. (There is one exception: past costs may affect present or future income taxes.)

We want to use actual cash flows for each alternative. Here the question is, What value should be used in an economic analysis for the SK-30? The relevant cost is the equipment’s present market value of $200. Neither the original cost, the present cost, the book value, nor the trade-in value is relevant.

Example 13–8 illustrated that of the several different values that can be assigned to the existing asset, the correct one is the present market value less any costs to remove and to sell the asset.

Determining the first cost of a new alternative usually includes the purchase price, sales tax, installation costs, and other items that occur initially on a one-time basis. These values are usually rather straightforward to obtain. One must not arbitrarily subtract the existing asset’s salvage value from the new alternative’s first cost. This cash flow approach, can lead to an incorrect analysis.

As described in Example 13–8, the correct first cost to assign to the existing SK-30 is its $200 current market value. This is the present economic benefit that we would be forgoing if we keep the SK–30. This can be called our opportunity first cost. If we assume it is a cash benefit to the new asset, a potential error arises.

The error is using the cash flow perspective when the lives of the new and existing assets are not equal, which is usually the case.

The opportunity cost perspective will always lead to the correct answer, so it is the one that should be used.

For example, consider the SK-30 and EL-40 from Example 13–8. It is reasonable to assume that the 2-year-old SK-30 has 3 years of life left and that the new EL-40 would have a 5-year life. Assume that neither will have any salvage value at the end of its life. Compare the difference in their annual capital costs with the correct opportunity cost perspective and the incorrect cash flow perspective.

EL-40		SK-30
$1050	First cost	$200	Market value
5 years	Useful life	3 years	Remaining life

Looking at this from an opportunity cost perspective, the annual cost comparison of the first costs is

[latex]Annualized first cost_{SK-30}=\$200(A/P,10\%,3)=\$80[/latex]

[latex]Annualized first cost_{FI-40}=\$1050(A/P,10\%,5)=\$277[/latex]

The difference in annualized first cost between the SK-30 and EL-40 is

[latex]AFC_{FI-40}-AFC_{SK-30}=\$277-\$80=\$197[/latex]

Now using an incorrect cash flow perspective to look at the first costs, we can calculate the difference due to first cost between the SK-30 and EL-40.

[latex]Annualized first cost_{SK-30}=\$0(A/P,10\%,3)=\$0[/latex]

[latex]Annualized first cost_{FI-40}=(\$1050-200)(A/P,10\%,5)=\$224[/latex]

[latex]AFC_{FI-40}-AFC_{SK-30}=\$224-\$0=\$224[/latex]

When the existing asset’s remaining life (3 years) differs from the new asset’s useful life (5 years), the two perspectives yield different results. The correct difference of $197 is shown by using the opportunity cost approach.

Question 13.8: A model SK-30 was purchased 2 years ago for $1600; it has be...

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