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debt and equity mix and the cost-of-capital factors differ from
business to business, of course. But for a large swath of busi-
nesses this scenario is in the middle of the fairway.
Chapter 14 focuses on a decision of a retailer regarding
investing in cash registers that would generate labor cost sav-
ings in the future. The analysis reveals that $160,000 annual
returns from the cash registers investment wouldn™t be
enough to justify the investment; the annual returns would
have to be $172,463. Figures 14.2 and 14.3 illustrate these
important points. Assuming that annual returns of $172,463
could be earned for five years by using the cash registers, the
present value of the investment would be exactly $500,000.
The entry cost of the investment is $500,000; this is the initial
amount of capital that would be invested in the cash registers.

When the present value exactly equals the entry cost
of an investment, the future returns are the exact
amounts needed to recover the total capital invested in the

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DISCOUNTING INVESTMENT RETURNS EXPECTED


assets and to satisfy the business™s cost-of-capital require-
ments each year during the life of the investment. The present
value of an investment is found by discounting its future
returns.

BACK TO THE FUTURE: DISCOUNTING
INVESTMENT RETURNS
The first pass in analyzing the cash registers investment by
the retailer in Chapter 14 is a scenario in which the future
annual returns would be $160,000 for five years. Relative to
the business™s cost-of-capital requirements, this stream of
future returns would be too low. The business would not
recover the full $500,000 amount of capital that would be
invested in the cash registers. Looking at it another way, if the
business invested $500,000 and realized only $160,000 labor
cost savings for five years, the annual return on equity (ROE)
for this investment would fall short of its 18.0 percent goal.
Suppose the seller of the cash registers is willing to dicker
on the price. The $500,000 asking price for the cash registers
is not carved in stone; the seller will haggle over the price. At
what price would the cash registers investment be acceptable
relative to the company™s cost-of-capital requirements? Using
the spreadsheet model explained in Chapter 14, I lowered the
purchase price so that the total capital recovered over the life
of the investment equals the purchase price. I kept the cost-of-
capital factors the same, and I kept the future annual returns
at $160,000. Finding the correct purchase price required only
a few iterations using the spreadsheet model.
Figure 15.1 presents the solution to the question. Suppose
the retailer could negotiate a purchase price of $463,868. At
this price the investment makes sense from the cost-of-capital
point of view. The total capital recovered over the five years is
exactly equal to this purchase price. By the way, note that the
annual depreciation amounts for income tax purposes are
based on this lower purchase cost.

One important advantage of using a spreadsheet model for
capital investment analysis is that any of the variables for the
investment can be changed to explore a variety of questions
and to examine a diversity of scenarios. The scenario pre-
sented in Figure 15.1 is, “What if the purchase price were
only $463,868?”
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C A P I TA L I N V E S T M E N T A N A LY S I S




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 ($12,988) ($10,999) ($8,744) ($6,187) ($3,287)
For income tax ($21,695) ($22,491) ($23,393) ($24,416) ($25,576)
For ROE ($54,273) ($45,960) ($36,536) ($25,851) ($13,736)
Equals capital
recovery $71,044 $80,550 $91,327 $103,547 $117,401
Cumulative capital
recovery at
end of year $71,044 $151,593 $242,921 $346,467 $463,868

Capital Invested at Beginning of Year
Variable solved for in this analysis
Debt $162,354 $137,488 $109,296 $77,332 $41,090
Equity $301,514 $255,336 $202,978 $143,616 $76,310
Total $463,868 $392,824 $312,275 $220,947 $117,401

Income Tax
EBIT increase $160,000 $160,000 $160,000 $160,000 $160,000
Interest expense ($12,988) ($10,999) ($8,744) ($6,187) ($3,287)
Depreciation ($92,774) ($92,774) ($92,774) ($92,774) ($92,774)
Taxable income $54,238 $56,227 $58,483 $61,040 $63,939
Income tax $21,695 $22,491 $23,393 $24,416 $25,576
FIGURE 15.1 Purchase cost of cash registers that would justify the invest-
ment relative to the business™s cost-of-capital requirements.




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DISCOUNTING INVESTMENT RETURNS EXPECTED


Solving for the present value is called discounting the
future returns. This analysis technique is also called the dis-
counted cash flow (DCF) method and usually is explained in a
mathematical context using equations applied to the future
stream of returns.


SPREADSHEETS VERSUS EQUATIONS
The DCF method is very popular. However, I favor a spread-
sheet model to determine the present value of an investment.
Spreadsheet programs are very versatile. Furthermore, a
spreadsheet does all the irksome calculations involved in
investment analysis. Different scenarios can be examined
quickly and efficiently, which I find to be an enormous advan-
tage. In business capital investment situations, managers have
to make several critical assumptions and forecasts. The man-
ager is well advised to test the sensitivity of each critical input
factor. A spreadsheet model is an excellent device for doing
this.

Even if you are not a regular spreadsheet user, the logic and
layout of the spreadsheet presented in Figure 15.1 are impor-
tant to understand. Figure 15.1 provides the relevant informa-
tion for the management decision-making phase and for
management follow-through after a decision is made. The
year-by-year data points shown in Figure 15.1 are good
benchmarks for monitoring and controlling the actual results
of the investment as it plays out each year. In short, a spread-
sheet model is a very useful analysis tool and is a good way
for organizing the relevant information about an investment.
Frankly, another reason for using a spreadsheet model is to
avoid mathematical methods for analyzing capital invest-
ments. In Chapter 14 not one equation is presented, and so
far in this chapter not one equation is presented. In my expe-
rience, managers are put off by a heavy-handed mathematical
approach loaded with arcane equations and unfamiliar sym-
bols. However, in the not-so-distant past, personal computers
were not as ubiquitous as they are today, and spreadsheet
programs were not nearly so sophisticated.
In the old days (before personal computers came along),
certain mathematical techniques were developed to do capital
investment analysis computations. These techniques have

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


become entrenched in the field of capital investment analysis.
Indeed, the techniques and terminology are household words
that are used freely in the world of business and finance”
such as present value, discounted cash flow, and internal rate
of return. Business managers should have at least a nodding
acquaintance with these terms and a general idea of how the
techniques are applied.
The remainder of this chapter presents a quick, introduc-
tory tour of the mathematical techniques for capital invest-
ment analysis. To the extent possible, I avoid going into detailed
explanations of the computational equations, which I believe
have little interest to business managers. These quantitative
techniques are just different ways of skinning the cat. I think a
spreadsheet model is a better tool of analysis, which reminds
me of a personal incident several years ago.
I was shopping for a mortgage on the new house we had
just bought. One loan officer pulled out a well-worn table of
columns and rows for different interest rates and different
loan amount modules. He took a few minutes to determine
the monthly payment amount for my mortgage loan. I had
brought a business/financial calculator to the meeting. I
double-checked his answer and found that it was incorrect.
He was somewhat offended and replied that he had been
doing these sorts of calculations for many years, and per-
haps I had made a mistake. It took me only five seconds to
check my calculation. I was right. He took several minutes
to compute the amount again and was shocked to discover
that his first amount was wrong. I thought better of suggest-
ing that he should use a calculator to do these sorts of calcu-
lations.


DISCOUNTED CASH FLOW (DCF)
To keep matters focused on bare-bones essentials, suppose
that a business has no debt (and thus no interest to pay) and
is organized as a pass-through entity for income tax purposes.
The business does not pay income tax as a separate entity. Its
only cost-of-capital factor is its annual return on equity (ROE)
goal. Assume that the business has established an annual 15
percent ROE goal. (Of course, the ROE could be set lower or
higher than 15 percent.) Assume that the business has an


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DISCOUNTING INVESTMENT RETURNS EXPECTED


investment opportunity that promises annual returns at the
end of each year as follows:


At End of Year Returns
1 $115,000.00
2 $132,250.00
3 $152,087.50


What is the value of this investment to the business today, at
the present time? This is called the present value (PV) of the
investment.
The discounted cash flow (DCF) method of analysis com-
putes the present value as follows:

Present Value Calculations
$115,000.00 · (1 + 15%)1 = $100,000
Year 1
$132,250.00 · (1 + 15%)2 = $100,000
Year 2
$152,087.50 · (1 + 15%)3 = $100,000
Year 3
= $300,000
Present value
I rigged the future return amounts for each year so that the
calculations are easier to follow. Of course, a business should
forecast the actual future returns for an investment. The future
returns represent either increases of cash inflows from mak-
ing the investment or decreases of cash outflows (as in the
cash registers investment example). Each future return is dis-
counted, or divided by a number greater than 1. Thus, the
term discounted cash flow.

The divisor in the DCF calculations equals (1 + r)n, in
which r is the cost-of-capital rate each period and n
is the number of periods until the future return is realized.
Usually r is constant from period to period over the life of the
investment, although a different cost-of-capital rate could be
used for each period.
In summary, the present value of this investment equals
$300,000. This means that if the business went ahead and put
$300,000 capital into the investment and at the end of each
year realized a future return according to the preceding


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schedule, then the business would earn exactly 15 percent
annual ROE on the investment. To check this present value, I
used my spreadsheet model. Figure 15.2 shows the printout
of the spreadsheet model, as adapted to the circumstances of
this investment. At the end of the third year the full $300,000
capital invested is recovered, which proves that the present
value of the investment equals $300,000, using the 15 percent
cost-of-capital discount rate.

The DCF method can be used when the future returns

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