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Before moving on to the analysis of this capital investment, I should mention that there would be several incentives to invest in the cash registers. As already stated, the new cash registers would eliminate data entry errors by cashiers and would prevent cashiers from deliberately entering low prices for their friends and relatives. Employee fraud is a common and expensive problem, unfortunately. Also, the company may anticipate that it will be increasingly difficult to hire qualified employees over the next several years. Furthermore, the new cash registers would enable the company to collect marketing data on a real-time basis, which it cannot do at present. In short, there are several good reasons for buying the cash registers. However, the following discussion focuses on the financial aspects of the investment decision.

Analyzing the Investment: First Comments

The first step is to make a ballpark estimate of how much the future returns would have to be for the investment. The business has to recover the capital invested in the cash registers, which is $500,000 in the example. The business has five years to recover this amount of capital. But clearly, future returns of just $100,000 per year for five years is not enough.

This amount of yearly return would not cover the company’s cost of capital each year. So to start the ball rolling, an annual return of $160,000 is used in the analysis, which might seem to be adequate to cover the company’s cost of capital. But is $160,000 per year actually enough?

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First Pass at Analyzing the Investment

Figure 14.2 presents a spreadsheet analysis of the investment in the new cash registers. (In the old days before personal computers, this two-dimensional layout was called a
worksheet.
) This is only a first pass to see whether $160,000

annual returns on the investment would be sufficient. The analysis may seem complex at first glance, but it is quite straightforward. The method begins with the return for each year and makes demands on the cash return.

The demands are four in number: (1) interest on debt capital, (2) income tax, (3) ROE (return on equity), and (4) recovery of capital invested in the assets. The first three amounts must be calculated by fixed formulas each year. The fourth is a free-floater; these amounts can follow any pattern year to year. But their total over the five years must add to $500,000, which is the amount of capital invested in the assets.

I’ll walk down the first-year column in some detail; the other four years are simply repeats of the first year. The first claim on the annual return (in this example, the labor cost savings for the year) is for interest. For year 1, the interest claim is $14,000 ($175,000 debt balance at start of year ×

8.0% interest rate = $14,000 annual interest). The second demand is for income tax. The annual labor cost savings increase the company’s taxable income each year. Income tax each year depends on the interest for the year, which is deductible and on the depreciation method used for calculating income tax. As shown in Figure 14.2 the straight-line depreciation method is used, which gives a $100,000 depreciation deduction each year for five years using a zero salvage value at the end of five years. (The accelerated depreciation method could be used instead.)

The bottom layer in Figure 14.2 shows the calculation of income tax for each year attributable to the investment. The income tax for the year is entered above as the second takeout from the annual labor cost savings. The third takeout from the annual return is for earnings on equity capital (see Figure 14.2). The deduction for ROE is based on the ROE goal of 18.0

percent per year. ROE for year 1 equals $58,500 ($325,000

equity capital at start of year × 18.0% ROE = $58,500 net income).

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Interest rate

8.0%

ROE

18.0%

Cost-of-capital factors

Income tax rate

40.0%

Debt % of capital

35.0%

Equity % of capital

65.0%

Year 1

Year 2

Year 3

Year 4

Year 5

Annual Returns

Labor cost savings $160,000

$160,000

$160,000

$160,000

$160,000

Distribution of Returns

For interest

($ 14,000) ($ 12,065) ($ 9,872) ($ 7,384) ($ 4,564) For income tax

($ 18,400) ($ 19,174) ($ 20,051) ($ 21,046) ($ 22,174) For ROE

($ 58,500) ($ 50,415) ($ 41,249) ($ 30,856) ($ 19,072) Equals capital

recovery

$ 69,100

$ 78,346

$ 88,828

$100,713

$114,189

Cumulative capital

recovery at

end of year

$ 69,100

$147,446

$236,274

$336,987

$451,176

Capital Invested at Beginning of Year

Debt

$175,000

$150,815

$123,394

$ 92,304

$ 57,054

Equity

$325,000

$280,085

$229,160

$171,422

$105,958

Total

$500,000

$430,900

$352,554

$263,726

$163,013

Income Tax

EBIT increase

$160,000

$160,000

$160,000

$160,000

$160,000

Interest expense ($ 14,000)

($12,065) ($ 9,872) ($ 7,384) ($ 4,564)

Depreciation

($100,000) ($100,000) ($100,000) ($100,000) ($100,000) Taxable income

$ 46,000

$ 47,935

$ 50,128

$ 52,616

$ 55,436

Income tax

$ 18,400

$ 19,174

$ 20,051

$ 21,046

$ 22,174

FIGURE 14.2
Analysis of investment in cash registers, assuming $160,000

annual returns.

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As mentioned, the $160,000 annual cash returns amount used in Figure 14.2 is just the starting point in the analysis.

This amount may not be enough to actually achieve the 18.0

percent annual ROE goal of the business. The purpose of the analysis is to test whether the $160,000 annual returns would be enough to achieve the ROE goal of the business. Of course, if the ROE goal of the business had been lower than 18.0 percent, then the deduction for ROE from the annual return would be a smaller amount.

The fourth and final demand on each year’s cash

return is for capital recovery. Capital recovery is the
residual
amount remaining after deducting interest, income tax, and the ROE amount for the year. For year 1, capital recovery is $69,100 (see Figure 14.2). This is the residual amount remaining from the annual return after deducting the requirements for interest, income tax, and ROE. The amount of capital recovery is not reinvested in additional cash registers; the company has all the cash registers it needs, at least for the time being.

In the future, the business may consider replacing the cash registers or increasing the number of cash registers it uses. But as far as this particular investment is concerned the capital recovery each year simply goes back to the cash balance of the business. The capital leaves this project (the cash registers investment). The business may put the money in another investment, or may increase its cash balance, or may reduce its debt, or may pay a higher cash dividend.

As shown in Figure 14.2, in the first year the company liquidates $69,100 of its investment in the cash registers; this much of the total capital that was originally invested in the assets is recovered and is no longer tied up in this particular investment. Therefore the amount of capital invested during the second year is reduced by $69,100 ($500,000 initial capital

− $69,100 capital recovery = $430,900 capital invested at start of year 2). Debt supplies 35 percent of this capital balance and equity the other 65 percent, as shown in the column for year 2.

From year to year this investment sizes down, because each year the business recovers part of the original capital invested in the assets. Thus the annual amounts of interest and ROE

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earnings decrease year to year as the total capital invested decreases from year to year. But note that the income tax increases year to year because the annual interest expense deduction decreases.

The cumulative capital recovery at the end of each year is shown in Figure 14.2. At the end of the fifth and final year of the investment, this amount should equal the initial amount of capital invested in the assets, which is $500,000 in this example. As Figure 14.2 shows, the cumulative capital recovery falls short of $500,000, however.

Why a Second Pass at the Investment Is Needed

Given the annual returns of $160,000 the cumulative capital recovery at the end of the investment is only $451,176 (see Figure 14.2). But the business has to recover $500,000 capital from the investment, which is the initial amount of capital invested in the cash registers. Thus the annual returns of $160,000 are not enough. The $160,000 amount of annual returns does not generate enough capital recovery after taking out interest, income tax, and earnings on equity each year—unless the ROE for each year is lowered so that more would be available for capital recovery each year.

Suppose the business goes ahead with the investment and it turns out that the annual returns are only $160,000 per year.

In this situation the actual ROE rate earned on the investment would be lower than the 18.0 percent used in Figure 14.2.

The precise ROE rate, assuming that the annual returns are $160,000, can be solved with the spreadsheet model. Instead of using the preestablished 18.0 percent rate, the ROE rate is lowered until the exact rate is found that makes the total capital recovery over the five years equal to $500,000. The appen-dix at the end of this chapter (Figure 14.5) shows the solution for the exact ROE rate, which is 14.6613 percent.

At the $160,000 level of annual returns the cash registers investment is not completely attractive, assuming that the business is serious about earning the annual 18.0 percent ROE rate. Clearly, the annual returns have to be higher than $160,000. The manager should ask his or her accountant or other financial staff person to determine the amount of annual labor cost savings that would justify the investment from the cost-of-capital viewpoint.

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Determining Exact Amounts for Returns

The investment analysis model shown in Figure 14.2 for the cash registers example is the printout of my personal com-

puter spreadsheet program. One reason for using a spreadsheet for capital investment analysis to is do all the required calculations quickly and accurately. Another reason is that the factors in the analysis can be easily changed for the purpose of investigating different scenarios for the investment.

I changed the annual cash returns in order to find the exact amount required to earn an annual 18.0 percent ROE. Other input variables were held the same; only the amount of the annual labor cost savings was changed. With a change in the amount of annual returns, the output variables for each year change accordingly—in particular, the income tax for each year and the amount of capital invested each year, which in turn change the amounts of interest and earnings on equity for each year. There is a cascade effect on the output variables from changing the amount of annual returns.

Finding the precise answer requires a trial-and-error, or plug-and-chug process that is repeated until the exact amount of future annual cash returns is found that makes total capital recovery $500,000. This may seem to be time-consuming, but it’s not. Only a few trials or passes are required to zero in on the exact answer. From Figure 14.2 I already knew that $160,000 was too low. So I bumped up the annual returns fig-

TEAMFLY

ure to $175,000. This proved to be a little too high. After a few trials I converged on the exact amount. Figure 14.3 pre-

sents the answer. Annual labor cost savings of $172,463 for five years yield an annual 18.0 percent ROE and recover exactly $500,000 capital from the investment.

Now comes the hard part. The manager must decide

whether the business could, realistically, achieve $172,463

annual labor cost savings. This is the really tough part of the decision-making process. But the manager knows that if the annual labor cost savings turn out to be this amount or higher, then the investment will prove to be a good decision from the cost-of-capital point of view.

Note in Figure 14.3 that the annual depreciation tax deduction amounts differ from the annual capital recovery amounts. For instance, the first year’s depreciation tax deduction is
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Interest rate

8.0%

ROE

18.0%

Cost-of-capital factors

Income tax rate

40.0%

Debt % of capital

35.0%

Equity % of capital

65.0%

Year 1

Year 2

Year 3

Year 4

Year 5

Annual Returns

Labor cost savings $172,463

$172,463

$172,463

$172,463

$172,463

Distribution of Returns

For interest

($ 14,000) ($ 11,856) ($ 9,425) ($ 6,668) ($ 3,543) For income tax

($ 23,385) ($ 24,243) ($ 25,215) ($ 26,318) ($ 27,568) For ROE

($ 58,500) ($ 49,540) ($ 39,382) ($ 27,865) ($ 14,806) Equals capital

recovery

$ 76,578

$ 86,824

$ 98,441

$111,612

$126,546