ñòð. 35 |

cent, then the deduction for ROE from the annual return

would be a smaller amount.

The fourth and final demand on each yearâ€™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 remain-

ing 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 regis-

ters it uses. But as far as this particular investment is con-

cerned 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

âˆ’ $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

202

DETERMINING INVESTMENT RETURNS NEEDED

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 exam-

ple. 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 yearâ€”

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 capi-

tal 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.

203

C A P I TA L I N V E S T M E N T A N A LY S I S

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 spread-

sheet 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 accordinglyâ€”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

Y

from changing the amount of annual returns.

FL

Finding the precise answer requires a trial-and-error, or

plug-and-chug process that is repeated until the exact amount

AM

of future annual cash returns is found that makes total capital

recovery $500,000. This may seem to be time-consuming, but

itâ€™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

TE

$160,000 was too low. So I bumped up the annual returns fig-

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 yearâ€™s depreciation tax deduction is

204

DETERMINING INVESTMENT RETURNS NEEDED

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

Cumulative capital

recovery at

end of year $ 76,578 $163,401 $261,842 $373,454 $500,000

Capital Invested at Beginning of Year

Debt $175,000 $148,198 $117,810 $ 83,355 $ 44,291

Equity $325,000 $275,225 $218,789 $154,803 $ 82,255

Total $500,000 $423,422 $336,599 $238,158 $126,546

Income Tax

EBIT increase $172,463 $172,463 $172,463 $172,463 $172,463

Interest expense ($ 14,000) ($ 11,856) ($ 9,425) ($ 6,668) ($ 3,543)

Depreciation ($100,000) ($100,000) ($100,000) ($100,000) ($100,000)

Taxable income $ 58,463 $ 60,607 $ 63,038 $ 65,794 $ 68,919

Income tax $ 23,385 $ 24,243 $ 25,215 $ 26,318 $ 27,568

FIGURE 14.3 Exact amount of future returns required for investment.

$100,000 (using the straight-line method) but the capital

recovery for the first year is $76,578. Both the total deprecia-

tion over the five years and the total capital recovery over the

five years are $500,000. But the two amounts differ from year

to year. This disparity is typical of capital investments and

205

C A P I TA L I N V E S T M E N T A N A LY S I S

does not present a problem when using a spreadsheet model

for analysis. (The difference between these two factors is

much more of a nuisance in using the mathematical analysis

techniques discussed in the Chapter 15.)

FLEXIBILITY OF A SPREADSHEET MODEL

As mentioned before, any factor in the analysis can be

changed to test how sensitive the annual returns would be to

the change. For instance, instead of the straight-line method

the accelerated depreciation method could be used in calculat-

ing income tax. Instead of uniform labor cost savings across

the years, returns could be set lower in the early years and

higher in the later yearsâ€”or vice versa. The debt-to-equity

ratio can be shifted. Of course, the interest rate and ROE tar-

get rate can be changed. Once a change is entered, the effects

of the change are instantly available on screen.

To illustrate an alternative scenario for the cash registers

example, assume the following cost of capital situation for the

retailer instead of the preceding example:

Capital Structure and Cost of Capital Factors

â€¢ No debt; 100 percent equity source of capital

â€¢ Annual interest rate on debtâ€”not applicable

â€¢ 40 percent income tax rate

â€¢ 18.0 percent annual ROE objective

In this alternative scenario, the business uses no debt capital;

all its capital comes from equity sources (capital invested by

its shareowners and retained earnings). The ROE target rate

is the same as before (18 percent annual ROE). Figure 14.4

shows the annual returns that would be needed in this situa-

tion. The required annual returns would jump to $199,815

compared with $172,463 in the earlier example, an increase

of more than $27,000 per year! This is a rather significant

increase. The capital structure of the business makes a differ-

ence on the future returns needed from an investment.

LEASING VERSUS BUYING LONG-TERM ASSETS

Business managers have opportunities for leasing instead of

buying long-term operating assets. Most long-term operating

206

DETERMINING INVESTMENT RETURNS NEEDED

Interest rate 0.0%

ROE 18.0% Cost-of-capital factors

Income tax rate 40.0%

Debt % of capital 0.0%

Equity % of capital 100.0%

Year 1 Year 2 Year 3 Year 4 Year 5

Annual Returns

Labor cost savings $199,815 $199,815 $199,815 $199,815 $199,815

Distribution of Returns

For interest $ 0$ 0$ 0$ 0$ 0

For income tax ($ 39,926) ($ 39,926) ($ 39,926) ($ 39,926) ($ 39,926)

For ROE ($ 90,000) ($ 77,420) ($ 62,576) ($ 45,059) ($ 24,390)

Equals capital

recovery $ 69,889 $ 82,469 $ 97,313 $114,830 $135,499

Cumulative capital

recovery at

end of year $ 69,889 $152,358 $249,671 $364,501 $500,000

Capital Invested at Beginning of Year

Debt $ 0 $ 0 $ 0 $ 0 $ 0

Equity $500,000 $430,111 $347,642 $250,329 $135,499

Total $500,000 $430,111 $347,642 $250,329 $135,499

Income Tax

EBIT increase $199,815 $199,815 $199,815 $199,815 $199,815

Interest expense $ 0$ 0$ 0$ 0$ 0

Depreciation ($100,000) ($100,000) ($100,000) ($100,000 ($100,000)

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