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if the ROE goal of the business had been lower than 18.0 per-
cent, 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 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
’ $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


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 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 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.


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 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-
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


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


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.)

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 years”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
• No debt; 100 percent equity source of capital
• Annual interest rate on debt”not applicable
• 40 percent income tax rate
• 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.

Business managers have opportunities for leasing instead of
buying long-term operating assets. Most long-term operating


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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