Five years ago, a company invested in equipment having a 10-year technological l
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Question
Five years ago, a company invested in equipment having a 10-year technological life and before-tax cash flows (gross income less expenses) given below. Sales were not as good as projected, and the company is considering terminating the project. The equipment has been depreciated using MACRS with a GDS property class of 7 years. The state in which the firm operates imposes a 10% corporate income tax. The firm has federal taxable income in the $10,000,000 to $15,000,000 bracket and uses a 10% MARR hurdle rate for investments. Determine by annual cash flow analysis the net present worth of terminating the project at the end of year 5. Year Before-tax cash flow 0 -$1,250,000 Initial cost 1 $ 472,700 Actual 2 $ 541,400 Actual 3 $ 537,200 Actual 4 $ 447,700 Actual 5 $ 435,800 Actual $ 350,000 Equipment Market value 6 $ 267,750 Estimated 7 $ 199,700 Estimated 8 $ 199,700 Estimated 9 $ 172,750 Estimated 10 $ 150,000 Estimated $ 50,000 Equipment Salvage valueExplanation / Answer
Here is some notation we will use:
Computed quantities:
EUAC = Equivalent Uniform Annual Cost
EUAB = Equivalent Uniform Annual Benefit
EUAW or EUAV = Equivalent Uniform Annual Worth or Value
Cash flow elements:
P = Asset initial cost
SV = Asset salvage value end of life
R = Rebuild
Rev = Revenue in a year
O&M = Annual Operating and Maintenance costs in a year
In this section we determine the equivalent uniform annual cash flows for costs and benefits in contrast to the equivalent present value of the cash flows calculated in the previous chapter.
We can calculate separately the EUAC or EUAB, or we can calculate the composite which can be called the EUAW or EUAV—different names for the same quantity.
Each of the cash flow elements above is either a uniform annual value or it must be converted to an annual value. For example, if we are given a constant (uniform) annual revenue, we use it as it is. On the other hand, the initial cost of an asset, P, is specified at a particular time; therefore we must calculate its EUAV. Another possibility would be when a cost is described as an arithmetic gradient; this must be converted to its EUAV. We learned how to do this in earlier chapters.
The initial cost of an asset is the cost to purchase and install it, as well as any ancillary costs, such as surveys or taxes associated with the acquisition of the asset.
When we write any equation solely for cost, our convention makes a negative cash flow a positive cost. This is because it is the custom in the United States not to say, for example, that a new car costs negative $30,000. We say the car costs $30,000. Similarly, when we write any equation solely for benefits, a negative cash flow is a negative cost.
It is often useful to work with annual cash flows, so we must find the EUAC to purchase and install an asset. Therefore, the EUAC for capital asset cost = P (A/P,i%,n)
Example 1: An asset with an initial cost of $10,000, including installation, has an estimated 5-year life. Using a MARR of 15%, what is the equivalent uniform annual cost of owning this asset, not including O&M costs?
P = $10,000
n = 5 years
If the MARR were zero, then the annualized capital cost would be [ (P / n ] or $2,000 per year. With a MARR greater than zero, however, the annualized cost will be greater than $2,000 because the money tied up in this asset for five years could presumably be earning interest at the MARR rate.
EUAC for asset initial cost = P (A/P,i%,n)
= 10,000(A/P,15%,5)
= (10,000) (0.2983)
= $2,983 per year
Other expenses that occur at fixed times (rather than annually) are treated similarly. A fixed amount at the end of the life, the salvage value, is a negative cost since it is income. A fixed amount to rebuild an asset is apositive cost at some intermediate time.
The simplest approach to these cash flows is to determine the present worth (PW) of each and then calculate the annualized equivalent, EUAW.
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