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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 wouldnâ€™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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assets and to satisfy the businessâ€™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 businessâ€™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 companyâ€™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, â€œWhat if the purchase price were

only $463,868?â€

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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 ($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 businessâ€™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 financeâ€”

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 Ã· (1 + 15%)1 = $100,000

Year 1

$132,250.00 Ã· (1 + 15%)2 = $100,000

Year 2

$152,087.50 Ã· (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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C A P I TA L I N V E S T M E N T A N A LY S I S

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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