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D I S C O U N T I N G I N V E S T M E N T R E T U R N S E X P E C T E D

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 computes the present value as follows:

Present Value Calculations

Year 1

$115,000.00 ÷ (1 + 15%)1 = $100,000

Year 2

$132,250.00 ÷ (1 + 15%)2 = $100,000

Year 3

$152,087.50 ÷ (1 + 15%)3 = $100,000

Present value

= $300,000

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 making the investment or decreases of cash outflows (as in the cash registers investment example). Each future return is discounted, 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 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.

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D I S C O U N T I N G I N V E S T M E N T R E T U R N S E X P E C T E D

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 computations required by the DCF method. One way is to use a handheld business/financial calculator. These are very powerful, relatively cheap, and fairly straightforward to use (assuming 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 substantive 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) calculation. Rather than opening up the investment for closer inspection, 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 investment. 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 investments 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 capital recovery at the end of the first year. (For that matter, managers 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, managers 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.

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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

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 example 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

Year 1

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

Year 2

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

Year 3

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

Present value

= $315,926.16

Entry cost of investment

($300,000.00)

Net present value

= $15,926.16

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 investment is called its
net present value
(NPV). Net present value is negative when the PV is less than the entry cost of the investment. 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
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D I S C O U N T I N G I N V E S T M E N T R E T U R N S E X P E C T E D

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 entering 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 investment (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.

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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

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.

A company may have to make huge capital investments to upgrade, automate, or expand; if it doesn’t, it may languish and eventually die.

AFTER-TAX COST-OF-CAPITAL RATE

So far I have skirted around one issue in discussing discounted cash flow techniques for analyzing business capital TEAMFLY

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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Team-Fly®

D I S C O U N T I N G I N V E S T M E N T R E T U R N S E X P E C T E D

• 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 calculated as follows:

After-Tax Cost-of-Capital Rate

Debt

35% × [(8.0%)(1 − 40% tax rate)] = 1.68%

Equity

[65% × 18.0%] = 11.70%

After-tax cost-of-capital rate

= 13.38%

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.