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recovery at

end of year

$ 79,951

$168,864

$267,744

$377,709

$500,000

Capital Invested at Beginning of Year

Debt

$175,000

$147,017

$115,898

$ 81,290

$ 42,802

Equity

$325,000

$273,032

$215,238

$150,966

$ 79,489

Total

$500,000

$420,049

$331,136

$232,256

$122,291

Income Tax

EBIT increase

$160,000

$160,000

$160,000

$160,000

$160,000

Interest expense ($ 14,000) ($ 11,761) ($ 9,272) ($ 6,503) ($ 3,424) Depreciation

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

$ 46,000

$ 48,239

$ 50,728

$ 53,497

$ 56,576

Income tax

$ 18,400

$ 19,295

$ 20,291

$ 21,399

$ 22,630

FIGURE 14.5
Exact ROE rate for cash registers capital investment with
$160,000 annual returns.

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C H A P T E R 15

1

Discounting

Investment Returns

Expected

TThis chapter and Chapter 14 are like a set of bookends. Chapter 14 explains the analysis of long-term investments in operating assets by businesses. This chapter continues the topic, with one key difference.

The time line of analysis in the previous chapter goes like this:

Present

Future

Starting with a given amount of capital invested today, the analysis looks forward in time to determine the amounts of future returns that would be needed in order to satisfy the cost-of-capital requirements of the business.

The time line of analysis in this chapter goes like this: Present

Future

Starting with the amounts of future returns from an investment (which are treated as fixed) the analysis travels back-ward in time to determine an amount called the
present value
of the investment. The present value is the most that a business should be willing to invest today to receive the future returns from the investment, based on its cost-of-capital requirements. The present value is compared with the entry cost of an investment.

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TIME VALUE OF MONEY AND COST

OF CAPITAL

The pivotal idea in this and the previous chapter is the
time
value of money.
This term refers not only to money but also more broadly to capital and economic wealth in general. Capi-

tal should generate income, gain, or profit over the time it is used. The ratio of earnings on the capital invested over a period of time, one year being the standard time period of ref-

erence, is the measure for the time value of money. Karl Marx said that capital is “dead labor” and argued that capital should be publicly owned for the good of everyone. I won’t pursue this economic philosophy any further. Quite clearly, in our economic system capital does have a time value—or a time cost depending on whose shoes you’re standing in.

The business example in Chapter 14 has the following capi-

tal structure and cost-of-capital factors:

Capital Structure and Cost-of-Capital Factors

• 35 percent debt and 65 percent equity mix of capital sources

• 8.0 percent annual interest rate on debt

• 40 percent income tax rate (combined federal and state)

• 18.0 percent annual ROE objective

The same business example is continued this chapter. The debt and equity mix and the cost-of-capital factors differ from TEAMFLY

business to business, of course. But for a large swath of businesses 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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assets and to satisfy the business’s cost-of-capital requirements 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 presented in Figure 15.1 is, “What if the purchase price were only $463,868?”

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C A P I T A L I N V E S T M E N T A N A L Y 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 investment relative to the business’s cost-of-capital requirements.

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Solving for the present value is called
discounting
the future returns. This analysis technique is also called the
discounted 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 spreadsheet 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 advantage. In business capital investment situations, managers have to make several critical assumptions and forecasts. The manager 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 important to understand. Figure 15.1 provides the relevant information 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 spreadsheet 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 investments. In Chapter 14 not one equation is presented, and so far in this chapter not one equation is presented. In my experience, 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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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 investment 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 perhaps 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 suggesting that he should use a calculator to do these sorts of calculations.

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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