12.3The Ratio Comparison Approach

Apopular way that investment bankers and analysts value firms, projects, or assets is

to compare them with other traded firms, projects, or assets. One of the best examples

of this occurs in the field of real estate. The standard discounted cash flow method

often is used to value real estate, but it is not the principal method. For example, most

commercial real estate is valued relative to comparable real estate that recently sold. A

building should sell for $20 million if it has twice the annual cash flow (rent revenues

less maintenance costs) as a building across the street that recently sold for $10 million.

The implicit assumption is that the cash flows of the two buildings will grow at the

same rate, so that two times the cash flows of the comparable building tracks the future

cash flows of the subject building.

While the current annual cash flows of the building being valued may be twice that

of the comparable building, this method is reasonable only if all future cash flows of

the subject building are going to be twice as large as those of the comparable build-

ing. When this is not a reasonable assumption, other variables besides current cash

flows might better summarize all future cash flows and thus serve as better proxies for

generating the tracking investment.

For example, investment bankers consider a multiple of the forecasted annual earn-

ings of comparison firms when valuing the initial public offering (IPO) of a company’s

common stock.¹⁰Earnings are often smoothed proxies for long-run cash flows and may

⁹The risk-free return is not mentioned in Example 12.7 because it does not affect any of the

conclusions. The production method with the largest risk-neutral expected profit is also the method with

the largest present value.

¹⁰To

price a firm that is going public, the firm’s investment bankers generally will try to project the

earnings of the firm and then come up with an earnings multiple by analyzing the price/earnings ratios of

comparison firms. This provides an initial estimate of the firm’s value which is likely to be adjusted for

any specific risks of the IPO and unusual market conditions.

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444Part IIIValuing Real Assets

work better as proxies than the current cash flow in determining the tracking portfolio.

In some cases, these comparisons are based on book values or replacement values. For

example, it is common to describe the prices of real estate investment trusts (REITs),

which are real estate portfolios that list and trade like shares of stock on an exchange,

as a percentage of the book values of their assets. Other variables besides cash flow,

earnings, and book value also are used in valuation. For example, a multiple of the

number of subscribers is typically used to estimate the prices of nontraded cable tele-

vision companies. Stock analysts value money management firms as a fraction of the

amount of assets they have under management. Newspapers and magazines are valued

relative to their advertising revenue and circulation.

These approaches to valuation assume that a new investment should sell for at

approximately the same ratio of price to some salient economic variable as an exist-

ing investment with an observable ratio, which is why this approach is called the ratio

comparison approach.This section illustrates the ratio comparison approach by using

the ratio of price to earnings, P/NI,where NIstands for net income (that is, earnings)

on the accounting income statement.¹¹However, the examples above show that it is

possible to use alternative numbers for earnings—sales revenue, book value, sub-

scribers, monthly rents, advertising lines, or cash flow—as the denominator for this

comparison.

The Price/Earnings Ratio Method

With the price/earnings ratio method, one obtains the present value of a project’s

future cash flows as follows:

Result	12.5	(The Price/Earnings Ratio Method.)The present value of the future cash flows of a proj-
		ect can be found by (1) obtaining the appropriate price/earnings ratio for the project from
		a comparison investment for which this ratio is known and (2) multiplying the price/earn-
		ings ratio from the comparison investment by the first year’s net income of the project. In
		a similar vein, a company should adopt a project when the ratio of its initial cost to earn-
		ings is lower than the price to earnings ratio of the comparison investment. (Alternative
		ratio comparison methods simply substitute a different economic variable for earnings.)

Subtracting the cost of initiating the project from this present value (PV) yields the net

present value (NPV). Acompany should adopt a project whenever the project’s NPV

is positive, which occurs when the project produces the future cash flow stream more

cheaply than the comparable investment. Expressed another way, if the cost-to-earnings

ratio of the project is less than the price/earnings ratio of a comparison investment, the

project is a bargain, since it generates a dollar of earnings at a lower cost than the com-

parable investment.

Keep in mind that the market price of an investment incorporates both the appro-

priate discount rate as well as the appropriate earnings growth rate. As a result, the

price/earnings ratio method may avoid some of the difficulties in estimating either dis-

count rates or growth rates. The price/earnings ratio method assumes, however, that the

comparison investment on which the price/earnings multiple is based has the same dis-

count rate and earnings growth as the project being valued. This is a a safe assump-

tion in some settings, but it may be inappropriate in others.

¹¹This is sometimes referred to as the P/E ratio, but we often use the variable Ein the text to

represent the market value of equity, so we employ P/NI.

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When Comparison Investments Are Hidden in Multibusiness Firms

Finding an investment with an observable value that is comparable to, for example, a

specialty steel plant, is more difficult than finding something comparable to an office

building. Therefore, it may be necessary to examine combinations of the traded secu-

rities of a number of firms to identify an appropriate comparison investment. This

approach is similar to the identification of beta risk when the betas of comparison firms

are generated by multiple lines of business. (See Chapter 11, Example 11.3.) When

using price/earnings ratios to value projects, it may be necessary to use the following

result:

Result 12.6

The price/earnings ratio of a portfolio of stocks 1 and 2 is a weighted average of theprice/earnings ratios of stocks 1 and 2, where the weights are the fraction of earnings gen-erated, respectively, by stocks 1 and 2. Algebraically

PPP

12

ww

NI¹NI²NI

12

where

P/NI price/earnings ratio of the portfolio

P/NI price/earnings ratio of stock i(i 1 or 2)

ii

w fraction of portfolio earnings from stock i.¹²

i

To apply this result to the specialty steel plant, consider a situation where the only

potential comparison firm producing specialty steel also is in the oil business. How

does an analyst filter out the impact of the oil business on the price/earnings ratio of

the comparison firm?

Result 12.6 implies that the comparison firm in combination with a firm produc-

ing similar oil-related products might be a pure specialty steel portfolio, which can be

used to determine the appropriate price/earnings ratio for valuing the specialty steel

division. Example 12.8 illustrates how to do this when the line of business is the pro-

duction of passenger buses (rather than specialty steel).

Example 12.8:Price/Earnings Ratio Comparisons with Multiple Lines

ofBusiness

Ford is considering the opportunity to enter the U.S.passenger bus market.Assume that

General Motors (GM) currently produces similar buses from which it realizes 10 percent of

its earnings.The rest of GM’s cash flows come from automobile lines that are essentially

the same as Ford’s.

If GM’s price/earnings ratio is 9.7, and if the price/earnings ratio of its automobile divi-

sion is (as seems reasonable) assumed to be the same as the price/earnings ratioof Ford,

which is 10, what is the implied price/earnings ratio for the bus division?

Answer:Ninety percent of GM’s earnings have a price/earnings ratio of 10, 10 percent

of the earnings have a price/earnings ratio of x,and the total GM value is 9.7 times the com-

pany’s total earnings.Viewing GM as a portfolio of a pure automobile business and a pure

bus business, and applying Result 12.6, implies that xmust solve

¹²This

result is derived by noting that

NIPNIP

P PP 1 1 NI 2 2 NI, implying

1²NINININI

12

PNIPNIPPP

1 1 2 2 w 1w 2

NININININI¹ NI²NI

1212

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446Part IIIValuing Real Assets

	.9(10) .1x 9.7
Thus, x 7.

If the cost of the bus plant in Example 12.8 is less than seven times the initial earn-

ings of the plant, and if it is realistic to assume that those earnings will grow at the

same rate and have the same risk as the General Motors bus plant, then Ford should

accept the project.

The Effect of Earnings Growth and Accounting Methodology on Price/Earnings Ratios

The price/earnings ratio method is useful in many circumstances, yet it has drawbacks.

As mentioned earlier, the earnings of the project and the comparison portfolio must

have similar growth rates. For example, if the earnings of the comparison portfolio are

growing at a faster rate than those of the project, the price/earnings ratio method is

invalid because the value of the comparison portfolio will be enhanced by the faster

growth rate. Even if the project costs little to initiate and seems to have a favorable

cost-to-earnings ratio compared to the price/earnings ratios available from similar

investments, the project could destroy value if the low cost does not make up for the

project’s low earnings growth rate.

Analysts who use the price/earnings ratio method also must be especially careful

that the earnings calculations reflect the true economic earnings of the firm. For exam-

ple, accounting changes, such as one-time write-downs, can dramatically affect the

reported earnings of firms without affecting their cash flows or their market values.

Companies can also artificially inflate reported earnings by paying a portion of

employee wages as stock options, which are not an immediate expense of the company.

Reported earnings are also influenced by R&D, advertising, and other expenditures that

are immediately expensed rather than depreciated. Analysts who naively use reported

earnings to calculate the appropriate value of a project will substantially misvalue the

project. For this reason, some analysts who employ the price/earnings ratio method use

EVAor similar measures of adjusted earnings in lieu of earnings per se.

In general, the valuation expert must be aware of how accounting earnings differ

from true economic earnings; specifically, how accrual accounting, working capital

changes, and depreciation affect reported earnings. To address these concerns, some

analysts use the price-to-cash-flow ratio in lieu of the price/earnings ratio. However, it

is also easy to distort the comparison with the price-to-cash-flow ratio. For example, a

comparison firm may find itself cash rich simply because a major customer decides to

obtain an income tax deduction by paying its bill at the end of the year instead of at

the beginning of the new year. Customers who speed up the payment of their bills by

a few days have a negligible effect on the comparison firm’s present value, but they

may substantially increase the reported cash flow in the relevant fiscal year and reduce

the cash flow in the year after.

The Effect of Leverage on Price/Earnings Ratios

To use the price/earnings ratio method to make capital allocation decisions, it also is

important to understand how leverage affects a firm’s net income per share (EPS) and,

consequently, its price/earnings ratio. As this chapter will demonstrate shortly, an

increase in leverage, holding the firm’s operations and total value constant, will increase

or decrease the firm’s net income per share and price/earnings ratio, depending on the

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Chapter 12

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447

relative sizes of the price/earnings ratio and the reciprocal of the yield on debt

borrowing.

When Leverage Increases the Price/Earnings Ratio.Example 12.9 illustrates a

hypothetical case where leverage increases the P/NIratio.

Example 12.9:ACase Where Leverage Increases the Price/Earnings Ratio

The information below applies to Micro Technologies at the beginning of its fiscal year:

Assets (book value)	$500,000,000
Liabilities (book value)	$100,000,000
Equity (book and market value)	$400,000,000
Number of shares outstanding	40,000,000

$400,000,000

Equity per share (book and market value)$10

40,000,000

Expected net income

$20,000,000

	$20,000,000
Expected EPS	$.50
	40,000,000

P	$10
	20
NI	$.50

ROE	NI$20,000,000 5.0%
	P$400,000,000

Assume that Micro Technologies issues $100 million in debt at the beginning of the fiscal

year at a rate of 6 percent, and that equity is decreased by the same amount through a

repurchase of 10 million shares at $10 each (that is, assuming market value equals book

value).Assuming no taxes and thus no response in stock price per share to the increase in

leverage, how does the debt issue affect Micro’s balance sheet account and expected finan-

cial performance for the year?

Answer:As a result of the debt issuance, resulting in a $100 million increase in liabili-

ties and a $100 million decrease in equity, Micro’s balance sheet accounts and expected

financial performance for the year will be as follows:

Assets (book value)	$500,000,000
Liabilities (book value)	$200,000,000
Equity (book and market value)	$300,000,000
Number of shares outstanding	30,000,000

$300,000,000

Equity per share (book and market value)$10

30,000,000

Expected net income	$14,000,000
	$20,000,000 ($100,000,000)(.06)

	$14,000,000
Expected EPS	$.47
	30,000,000

P	$10
	21.28
NI	$.47

ROE	NI$14,000,000 4.7%
	P$300,000,000

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Example 12.9 illustrates that the increased debt reduces Micro Technologies’EPS.

Since there was no share price response to the debt increase, the reduction in EPSled

to an increase in the firm’s price/earnings ratio. We provide a more realistic example

of the effect of leverage on the price/earnings ratios below.

The Effect of a Leveraged Acquisition on Maytag’s Price/Earnings Ratios

The Maytag Corporation dramatically increased its leverage in the late 1980s. From year-

end 1987 to year-end 1989, the company’s long-term debt as a percentage of total capital

(long-term debt plus book equity) rose from 23.3 percent to 46.8 percent. Exhibit 12.10 pro-

vides some relevant financial information for the Maytag Corporation over these years.

Maytag’s increased debt level, owing primarily to the debt financing of its acquisition of

Chicago Pacific Corporation in January 1989, resulted in a significant increase in interest

expense during 1989 (from $19.7 million in 1988 to $83.4 million in 1989). Following this

increase in leverage, the firm’s EPSdecreased substantially.

The increase in Maytag’s price/earnings ratio may have been due to increased interest

expense caused by the leverage taken on to acquire Chicago Pacific. Example 12.10 illus-

trates how to filter out the drop in Maytag’s earnings per share that is due to the increase

in its leverage.

Example 12.10:The Impact of Leverage on Maytag’s Earnings perShare

Assume that Maytag chooses to maintain its 1987 ratio of long-term debt to capital, 23.3per-

cent.Calculate what Maytag’s 1989 EPSwould have been without any change in the company’s

leverage.

Answer:Holding all other decisions of the firm constant, Maytag’s financial data for 1989

would have been as follows:

Maytag Corporation

Financial Statement

	With No
Actual	Leverage
1989 Data	Change

Long-term debt (LTD) ($ millions)

$1,877

$1,437

Long-term debtbook equity
(LTDBE) ($ millions)	$1,875	$1,875

LTD
Leverage ratio	46.8%	23.3%
LTDBE

Earnings ($ millions)	$1,131	$1166*
Number of shares outstanding	105,560,000	126,047,576†
Earnings per share	$1.24‡	11.32
		$

Notes to Financial Data

*Earnings would have been $35 million higher due to the decreased interest cost.Assuming

an after-tax interest cost of 8 percent on the additional debt in the actual data, earnings

in the hypothetical situation would be (in millions):$131($877$437).08 $166.

^†Assuming the issuance of $437 million in equity at the average 1989 share price of

$21.34 (on 20,487,576 shares), to substitute for the debt issuance.

^‡Value

Line’s EPSof $1.27 is based on earnings divided by the average number of shares

outstanding throughout the 1989 fiscal year.The EPSof $1.24 is based on Value Line’s

aggregate earnings over end-of-year shares outstanding.The $0.08 increase in EPS

owing to leverage should be approximately the same with either method of computing EPS.

Example 12.10 illustrates that Maytag’s EPSwas reduced from $1.32 to $1.24 because

it had increased its leverage ratio. Hence, only a small part, $0.08, of the large decrease in

actual EPSfrom 1988 to 1989 is due to leverage.

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EXHIBIT12.10Selected Financial Information forthe Maytag Corporation

	Interest	Interest
	Expense	Coverage			Value
EPS	($ millions)	Ratio*	ROE (%)	Price/Earnings	($ billions)

1986	$1.51	$12.0	18.5	25.1%	14.7	$1.9
1987	1.91	10.8	25.3	33.4	13.5	2.0
1988	1.77	19.7	11.9	29.6	13.0	1.8
1989	1.27	83.4	3.5	16.1	16.8	2.3

*See the preface to Part IVof the text for more detail about interest coverage ratios.

Source: Value Line Investment Survey, Dec. 21, 1990.

ACase Where Leverage Decreases the Price/Earnings Ratio.If a firm’s stock price

is high because earnings are expected to grow at an exceptionally fast rate, then an increase

in leverage could decrease the price/earnings ratio, as Example 12.11 demonstrates.

Example 12.11:Leverage Can Decrease the Price/Earnings Ratio

The Gamma Feron Biotech Company, currently an all-equity firm, has 1 million shares of

stock trading at $25 a share and a price/earnings ratio (using next year’s expected earnings

in the denominator) of 12.5.The company plans to reinvest 50 percent of its earnings in the

company and to pay the remaining 50 percent as dividends.

First, calculate next year’s expected earnings.Then compute the growth rate of earnings,

assuming that the $25 share price is consistent with the Gordon growth model (a dividend

discount model discussed in Chapters 9 and 11), at a cost of capital of 10 percent per year.

Finally, assume that there are no taxes, and compute the effect on earnings and the

price/earnings ratio of a leveraged recapitalization (see Chapter 2), in which 50 percent of

the company’s shares are retired in a purchase financed with risk-free debt earning interest

at 6 percent per year.Assume that the price per share does not change as a consequence

of the leveraged recapitalization.

Answer:Next year’s expected unlevered earnings(income from the firm’s operations,

assuming that the firm is all equity financed, also EBI), are $2 per share, which implies a

dividend of $1 per share at a 50 percent reinvestment rate.The dividend discount model

says that the price per share div(rg), or $25 $1/(.1g),implying g 6 percent

1E

per year.As a result of the leveraged recapitalization, the price remains at $25 per share,

but the earnings per share drop to

Unlevered earningsDebt interest

EPS

Number of shares outstanding

$2 million.06($12.5 million)

$2.50 per share, which generates

.5 million

Price$25

10

Earnings$2.50

In Example 12.11, the debt issue decreased Gamma Feron’s price/earnings ratio from

12.5 to 10. If debt is default free, so that debt interest is always paid, more leverage will

decrease the price/earnings ratio whenever the ratio of unlevered earnings to price exceeds

the yield ron the risk-free debt. (If there had been corporate taxes in Example 12.11, the

D

comparison would have to be made with the after-tax cost of debt, r(1 tax rate).)

D

In this case, the 8 percent ratio of unlevered earnings to price, ($2/$25), exceeds the

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6percent yield on Gamma Feron’s debt. Thus, every dollar of equity retired in the

leveraged recapitalization leaves remaining shareholders with extra earnings of $0.08.

However, each retired dollar of equity is exchanged for a dollar of debt that soaks up

only $0.06. The remaining equity shares have $0.02 more earnings remaining per dol-

lar of debt exchanged for equity, implying, with a constant price per share, that the

price/earnings ratio decreases.

What Determines WhetherLeverage Increases orDecreases the Price/Earnings

Ratio?The general principle is formally stated as follows:

Result	12.7	Assume the market value of the firm’s assets is unaffected by its leverage ratio. Also assume
		that all debt is risk free. Then, if the ratio of price to earnings of an all-equity firm is larger
		than 1/r,where ris the interest rate on the firm’s (assumed) risk-free perpetual debt, then
		DD
		an increase in leverage increases the price/earnings ratio. If the price/earnings ratio of an
		all-equity firm is less than 1/r,then the increase in leverage lowers the price/earnings ratio
		D
		of the firm.

To prove this result, simply write out the price/earnings ratio, assuming risk-free

perpetual debt, where

A	the market value of the assets
X	unlevered earnings
A/X	the price/earnings ratio of an all-equity firm

The ratio of the market value of equity to the firm’s total net income (assuming zero

taxes) is

Price	AD
		(12.1)
Earnings	XrD
	D

A/X

1 XrD

1/r^D

D

rXrD

DD

Note that the expression in brackets in the equation above is either larger or smaller

than 1, depending on the relative size of A/Xand 1/r.An increase in D,which moves

D

the expression in brackets closer to 1, decreases the price/earnings ratio when

A/X1/rand increases it otherwise.

D

Adjusting for Leverage Differences

If one uses a comparison firm’s price/earnings ratio to value a particular project, it is

important to value the project with the unleveraged price/earnings ratio, which is the

ratio that would exist if the comparison investment were all equity financed, rather than

the leveraged price/earnings ratio that one observes. One values the project as the prod-

uct of the unlevered earnings of the project and the unleveraged price/earnings ratio of

the comparison; that is

A

PV (X)

^projectX^project

comparison

To “unlever” a price/earnings ratio, use equation (12.1) in reverse. First, substitute

the measured price/earnings ratio on the left-hand side and then solve for the A/X,the

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451

unleveraged price/earnings ratio that makes equation (12.1) hold.¹³

With corporate

taxes, multiply the denominator expression in brackets, XrD,by 1 corporate

D

tax ratebefore solving for A/X.