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from an investment are known or can be predicted
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 problems”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 owner™s manual). Another way is to use the
financial functions included in a spreadsheet program.
(Excel® 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 doesn™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 ’ $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 · (1 + 15%)1 = $102,608.70
Year 1
$139,240.00 · (1 + 15%)2 = $105,285.44
Year 2
$164,303.20 · (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 it™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 IRRs”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 don™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 doesn™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
investments”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 retailer™s sources of capital and
its cost of capital factors are as follows:

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

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DISCOUNTING INVESTMENT RETURNS EXPECTED



• 40 percent income tax rate (combined federal and state)
• 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% — [(8.0%)(1 ’ 40% tax rate)] = 1.68%
[65% — 18.0%] = 11.70%
Equity
= 13.38%
After-tax cost-of-capital rate


ROE is an after-tax rate; net income earned on the
owners™ 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 ’ 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 company™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 company™s after-tax cost-of-capital
rate is 13.38 percent. Instead of applying this discount rate

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