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fairly accurately. The purpose is to determine the present

value (PV) of an investment, which is the maximum amount

that a business should invest today in exchange for the future

Interest rate 0.0%

ROE 15.0% Cost-of-capital factors

Income tax rate 0.0%

Debt % of capital 0.0%

Equity % of capital 100.0%

Year 1 Year 2 Year 3

Annual Returns

Labor cost savings $115,000.00 $132,250.00 $152,087.50

Distribution of Returns

For interest $ 0.00 $ 0.00 $ 0.00

For income tax $ 0.00 $ 0.00 $ 0.00

For ROE ($ 45,000.00) ($ 34,500.00) ($ 19,837.50)

Equals capital recovery $ 70,000.00 $ 97,750.00 $132,250.00

Cumulative capital recovery

at end of year $ 70,000.00 $167,750.00 $300,000.00

Capital Invested at Beginning of Year

Debt $ 0.00 $ 0.00 $ 0.00

Equity $300,000.00 $230,000.00 $132,250.00

Total $300,000.00 $230,000.00 $132,250.00

FIGURE 15.2 Check on the present value calculated by the DCF method.

220

DISCOUNTING INVESTMENT RETURNS EXPECTED

returns. The DCF technique is correct, of course. But it has

one problem. Well, actually two problemsâ€”one not so serious

and one more serious.

The not-so-serious problem concerns how to do the com-

putations required by the DCF method. One way is to use a

handheld business/financial calculator. These are very power-

ful, relatively cheap, and fairly straightforward to use (assum-

ing you read the ownerâ€™s manual). Another way is to use the

financial functions included in a spreadsheet program.

(ExcelÂ® includes a complete set of financial functions.)

The second problem in using the DCF method is more sub-

stantive and has nothing to do with the computations for

present value. The problem concerns the lack of information

in using the DCF technique. The unfolding of the investment

over the years is not clear from the present value (PV) calcula-

tion. Rather than opening up the investment for closer inspec-

tion, the PV computation closes it down and telescopes the

information into just one number. The method doesnâ€™t reveal

important information about the investment over its life.

Figure 15.2 presents a more complete look at the invest-

ment. It shows that the cash return at the end of year one is

split between $45,000 earnings on equity and $70,000 capital

recovery. The capital recovery aspect of an investment is very

important to understand. The capital recovery portion of the

cash return at the end of the first year reduces the amount of

capital invested during the second year. Only $230,000 is

invested during the second year ($300,000 initial amount

invested âˆ’ $70,000 capital recovered at end of year one =

$230,000 capital invested at start of year 2). Business invest-

ments are self-liquidating over the life of the investment; there

is capital recovery each period, as in this example.

Managers should anticipate what to do with the $70,000 capi-

tal recovery at the end of the first year. (For that matter, man-

agers should also plan what to do with the $45,000 net

income.) Will the capital be reinvested? Will the business be

able to reinvest the $70,000 and earn 15 percent ROE? To

plan ahead for the capital recovery from the investment, man-

agers need information as presented in Figure 15.2, which

tracks the earnings and capital recovery year by year. The

DCF technique does not generate this information.

221

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

NET PRESENT VALUE AND INTERNAL RATE

OF RETURN (IRR)

Suppose the business has an investment opportunity that

would cost $300,000 to enter today. (Recall that in this exam-

ple the business has no debt and is a pass-through tax entity

that does not pay income tax.) The manager forecasts the

future returns from the investment would be as follows:

At End of Year Returns

1 $118,000.00

2 $139,240.00

3 $164,303.20

The present value and the net present value for this stream of

future returns is calculated as follows:

Present Value Calculations

$118,000.00 Ã· (1 + 15%)1 = $102,608.70

Year 1

$139,240.00 Ã· (1 + 15%)2 = $105,285.44

Year 2

$164,303.20 Ã· (1 + 15%)3 = $108,032.02

Year 3

= $315,926.16

Present value

Entry cost of investment ($300,000.00)

= $15,926.16

Net present value

The present value is $15,926.16 more of the amount of capital

that would have to be invested. The difference between the

calculated present value (PV) and the entry cost of an invest-

ment is called its net present value (NPV). Net present value is

negative when the PV is less than the entry cost of the invest-

ment. The NPV has informational value, but itâ€™s not an ideal

measure for comparing alternative investment opportunities.

For this purpose, the internal rate of return (IRR) for each

investment is determined and the internal rates of return for

all the investments are compared.

The IRR is the precise discount rate that makes PV

exactly equal to the entry cost of the investment. In

the example, the investment has a $300,000 entry cost. The

222

DISCOUNTING INVESTMENT RETURNS EXPECTED

IRR for the stream of future returns from the investment is

18.0 percent, which is higher than the 15.0 percent cost-of-

capital discount rate used to compute the PV. The IRR rate is

calculated by using a business/financial calculator or by enter-

ing the relevant data in a spreadsheet program using the IRR

financial function.

Figure 15.3 demonstrates that the IRR for the investment is

18.0 percent. This return-on-capital rate is used to calculate

the earnings on capital invested each year that is deducted

from the return for that year. The remainder is the capital

recovery for the year. The total capital recovered by the end of

the third year equals the $300,000 entry cost of the invest-

ment (see Figure 15.3). Thus the internal rate of return (IRR)

is 18.0 percent.

Interest rate 0.0% Internal rate of return (IRR)

ROE 18.0%

Income tax rate 0.0%

Debt % of capital 0.0%

Equity % of capital 100.0%

Year 1 Year 2 Year 3

Annual Returns

Labor cost savings $118,000.00 $139,240.00 $164,303.20

Distribution of Returns

For interest $ 0.00 $ 0.00 $ 0.00

For income tax $ 0.00 $ 0.00 $ 0.00

For ROE ($ 54,000.00) ($ 42,480.00) ($ 25,063.20)

Equals capital recovery $ 64,000.00 $ 96,760.00 $139,240.00

Cumulative capital recovery

at end of year $ 64,000.00 $160,760.00 $300,000.00

Capital Invested at Beginning of Year

Debt $ 0.00 $ 0.00 $ 0.00

Equity $300,000.00 $236,000.00 $139,240.00

Total $300,000.00 $236,000.00 $139,240.00

FIGURE 15.3 Illustration that internal rate of return (IRR) is 18.0 percent.

223

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

A business should favor investments with higher IRRs in

preference to investments with lower IRRsâ€”all other things

being the same. A business should not accept an investment

that has an IRR less than its hurdle rate, that is, its cost-of-

capital rate. Another way of saying this is that a business

should not proceed with an investment that has a negative net

present value. Well, this is the theory.

Capital investment decisions are complex and often involve

many nonquantitative, or qualitative, factors that are difficult

to capture fully in the analysis. A company may go ahead with

an investment that has a low IRR because of political pres-

sures or to accomplish social objectives that lie outside the

profit motive. The company might make a capital investment

even if the numbers donâ€™t justify the decision in order to fore-

stall competitors from entering its market. Long-run capital

investment decisions are at bottom really survival decisions.

Y

A company may have to make huge capital investments to

FL

upgrade, automate, or expand; if it doesnâ€™t, it may languish

and eventually die.

AM

AFTER-TAX COST-OF-CAPITAL RATE

So far I have skirted around one issue in discussing dis-

TE

counted cash flow techniques for analyzing business capital

investmentsâ€”income tax. DCF analysis techniques were

developed long before personal computer spreadsheet pro-

grams became available. The DCF method had to come up

with a way for dealing with the income tax factor, and it did,

of course. The trick is to use an after-tax cost-of-capital rate

and to separate the stream of returns from an investment and

the depreciation deductions for income tax.

An example is needed to demonstrate how to use the after-

tax cost of capital rate. The cash registers investment exam-

ined in the previous chapter is a perfect example for this

purpose. To remind you, the retailerâ€™s sources of capital and

its cost of capital factors are as follows:

Capital Structure and Cost-of-Capital Factors

â€¢ 35 percent debt and 65 percent equity mix of capital sources

â€¢ 8.0 percent annual interest rate on debt

224

DISCOUNTING INVESTMENT RETURNS EXPECTED

â€¢ 40 percent income tax rate (combined federal and state)

â€¢ 18.0 percent annual ROE objective

The after-tax cost of capital rate for this business is calcu-

lated as follows:

After-Tax Cost-of-Capital Rate

Debt 35% Ã— [(8.0%)(1 âˆ’ 40% tax rate)] = 1.68%

[65% Ã— 18.0%] = 11.70%

Equity

= 13.38%

After-tax cost-of-capital rate

ROE is an after-tax rate; net income earned on the

ownersâ€™ equity of a business is after income tax. To

put the interest rate on an after-tax basis, the interest rate is

multiplied by (1 âˆ’ tax rate) because interest is deductible to

determine taxable income. The debt weight (35 percent in this

example) is multiplied by the after-tax interest rate, and the

equity weight (65 percent in this example) is multiplied by the

after-tax ROE rate. The after-tax cost of capital, therefore, is

13.38 percent for the business.

Recall that the entry cost of investing in the cash registers

is $500,000. Assume that the future annual returns from this

investment are $172,463 for five years. Figure 14.3 in the

previous chapter shows that for this stream of future returns

the companyâ€™s cost of capital requirements are satisfied exactly.

Therefore, the present value of the investment must be exactly

$500,000, which is the entry cost of the investment. Using the

after-tax cost-of-capital rate to discount the returns from the

investment proves this point.

As just calculated, the companyâ€™s after-tax cost-of-capital

rate is 13.38 percent. Instead of applying this discount rate

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