[ ]

P0 1 PVGO

1 (12.7)

E1 k E1/k

When PVGO 0, Equation 12.7 shows that P0 E1/k. The stock is valued like a nongrow-

ing perpetuity of EPS1. The P/E ratio is just 1/k. However, as PVGO becomes an increasingly

dominant contributor to price, the P/E ratio can rise dramatically. The ratio of PVGO to E/k

has a simple interpretation. It is the ratio of the component of firm value reflecting growth op-

portunities to the component of value reflecting assets already in place (i.e., the no-growth

value of the firm, E/k). When future growth opportunities dominate the estimate of total value,

the firm will command a high price relative to current earnings. Thus, a high P/E multiple ap-

pears to indicate that a firm is endowed with ample growth opportunities.

Return again to Takeover Target, the firm we first encountered in Example 12.4. Earnings are

$5 per share, and the capitalization rate is 15%, implying that the no-growth value of the firm

EXAMPLE 12.5

is E1/k $5/0.15 $33.33. The stock price actually is $22.22, implying that the present

value of growth opportunities equals $11.11. This implies that the P/E ratio should be P/E Ratios

P0

[ ] [ ] and Growth

1 PVGO 1 $11.11

1 1 4.44

E1 k E/k Opportunities

0.15 $33.33

In fact, the stock price is $22.22 and earnings are $5 per share, so the P/E ratio is

$22.22/$5 4.44.

Let™s see if P/E multiples do vary with growth prospects. Between 1986 and 1999, Sun Mi-

crosystems™ P/E ratio averaged about 19.4 while Consolidated Edison™s average P/E was only

11.1. These numbers do not necessarily imply that Sun was overpriced compared to Con Ed.

If investors believed Sun would grow faster than Con Ed, the higher price per dollar would be

justified. That is, an investor might well pay a higher price per dollar of current earnings if he

or she expected that earnings stream to grow more rapidly. In fact Sun™s growth rate has been

consistent with its higher P/E multiple. In the decade ending 1999, its earnings per share grew

more than 14-fold, while Con Ed™s earnings grew by only 26%. Figure 12.5 (on page 436)

shows the EPS history of the two companies.

Clearly, it is differences in expected growth opportunities that justify particular differentials

in P/E ratios across firms. The P/E ratio is in large part a reflection of the market™s optimism

concerning a firm™s growth prospects. In their use of a P/E ratio, analysts must decide whether

they are more or less optimistic than the market. If they are more optimistic, they will recom-

mend buying the stock.

There is a way to make these insights more precise. Look again at the constant growth

DDM formula, P0 D1/(k g). Now recall that dividends equal the earnings that are not rein-

vested in the firm: D1 E1(1 b). Recall also that g ROE b. Hence, substituting for D1

and g, we find that

E1(1 b)

P0

k (ROE b)

Bodie’Kane’Marcus: IV. Security Analysis 12. Equity Valuation © The McGraw’Hill

Essentials of Investments, Companies, 2003

Fifth Edition

430 Part FOUR Security Analysis

Plowback Ratio (b)

TA B L E 12.3

0 0.25 0.50 0.75

Effect of ROE and

plowback on growth

A. Growth Rate, g

and the P/E ratio

ROE

10% 0% 2.5% 5.0% 7.5%

12 0 3.0 6.0 9.0

14 0 3.5 7.0 10.5

B. P/E Ratio

ROE

10% 8.33 7.89 7.14 5.56

12 8.33 8.33 8.33 8.33

14 8.33 8.82 10.00 16.67

Note: Assumption: k 12% per year.

implying that the P/E ratio for a firm growing at a long-run sustainable pace is

P0 1b

(12.8)

E1 k (ROE b)

It is easy to verify that the P/E ratio increases with ROE. This makes sense, because high ROE

projects give the firm good opportunities for growth.5 We also can verify that the P/E ratio in-

creases for higher plowback, b, as long as ROE exceeds k. This too makes sense. When a firm

has good investment opportunities, the market will reward it with a higher P/E multiple if it

exploits those opportunities more aggressively by plowing back more earnings into those

opportunities.

Remember, however, that growth is not desirable for its own sake. Examine Table 12.3,

where we use Equation 12.8 to compute both growth rates and P/E ratios for different combi-

nations of ROE and b. While growth always increases with the plowback ratio (move across

the rows in Panel A of Table 12.3), the P/E ratio does not (move across the rows in Panel B).

In the top row of Table 12.3B, the P/E falls as the plowback rate increases. In the middle row,

it is unaffected by plowback. In the third row, it increases.

This pattern has a simple interpretation. When the expected ROE is less than the required

return, k, investors prefer that the firm pay out earnings as dividends rather than reinvest earn-

ings in the firm at an inadequate rate of return. That is, for ROE lower than k, the value of the

firm falls as plowback increases. Conversely, when ROE exceeds k, the firm offers superior

investment opportunities, so the value of the firm is enhanced as those opportunities are more

fully exploited by increasing the plowback ratio.

Finally, where ROE just equals k, the firm offers “break-even” investment opportunities

with a fair rate of return. In this case, investors are indifferent between reinvestment of earn-

ings in the firm or elsewhere at the market capitalization rate, because the rate of return in ei-

ther case is 12%. Therefore, the stock price is unaffected by the plowback ratio.

One way to summarize these relationships is to say the higher the plowback ratio, the

higher the growth rate, but a higher plowback ratio does not necessarily mean a higher P/E

ratio. A higher plowback ratio increases P/E only if investments undertaken by the firm of-

fer an expected rate of return higher than the market capitalization rate. Otherwise, higher

5

Note that Equation 12.8 is a simple rearrangement of the DDM formula, with ROE b g. Because that formula

requires that g k, Equation 12.8 is valid only when ROE b k.

Bodie’Kane’Marcus: IV. Security Analysis 12. Equity Valuation © The McGraw’Hill

Essentials of Investments, Companies, 2003

Fifth Edition

431

12 Equity Valuation

plowback hurts investors because it means more money is sunk into prospects with inade-

quate rates of return.

Notwithstanding these fine points, P/E ratios commonly are taken as proxies for the ex-

pected growth in dividends or earnings. In fact, a common Wall Street rule of thumb is that the

growth rate ought to be roughly equal to the P/E ratio. In other words, the ratio of P/E to g, of-

ten called the PEG ratio, should be about 1.0. Peter Lynch, the famous portfolio manager, puts

it this way in his book One Up on Wall Street:

The P/E ratio of any company that™s fairly priced will equal its growth rate. I™m talking here about

growth rate of earnings. . . . If the P/E ratio of Coca-Cola is 15, you™d expect the company to be

growing at about 15% per year, etc. But if the P/E ratio is less than the growth rate, you may have

found yourself a bargain [page 198].

Let™s try his rule of thumb.

Assume:

rf 8% (about the value when Peter Lynch was writing) EXAMPLE 12.6

rM rf 8% (about the historical average market risk premium) P/E Ratio versus

b 0.4 (a typical value for the plowback ratio in the U.S.) Growth Rate

Therefore, rM rf Market risk premium 8% 8% 16%, and k 16% for an average

( 1) company. If we also accept as reasonable that ROE 16% (the same value as the

expected return on the stock) we conclude that

g b

ROE 16% 0.4 6.4%

and

1 0.4

P/E 6.26

0.16 0.064

Thus the P/E ratio and g are about equal using these assumptions, consistent with the rule of

thumb. However, note that this rule of thumb, like almost all others, will not work in all cir-

cumstances. For example, the value of rf today is more like 5%, so a comparable forecast of

rM today would be:

rf Market risk premium 5% 8% 13%

1, and ROE still is about the same as k, then

If we continue to focus on a firm with

g 13% 0.4 5.2%

while

1 0.4

P/E 7.69

0.13 0.052

The P/E ratio and g now diverge and the PEG ratio is now 1.5. Nevertheless, it still is the case

that high P/E stocks are almost invariably expected to show rapid earnings growth, even if the

expected growth rate does not precisely equal the P/E ratio.

Whatever its shortcomings, the PEG ratio is widely followed. Figure 12.3 is the PEG ratio for

the S&P over the last 15 years. It typically has fluctuated within the range between 1.0 and 1.4.

<

5. ABC stock has an expected ROE of 12% per year, expected earnings per share of Concept

$2, and expected dividends of $1.50 per share. Its market capitalization rate is

CHECK

10% per year.

a. What are its expected growth rate, its price, and its P/E ratio?

b. If the plowback rate were 0.4, what would be the firm™s expected dividend per

share, growth rate, price, P/E, and PEG ratio?

Bodie’Kane’Marcus: IV. Security Analysis 12. Equity Valuation © The McGraw’Hill

Essentials of Investments, Companies, 2003

Fifth Edition

432 Part FOUR Security Analysis

1.6

1.5

1.4

1.3

PEG ratio

1.2

1.1

1

0.9

0.8

0.7

0.6

Jan 85

Jan 86

Jan 87

Jan 88

Jan 89

Jan 90

Jan 91

Jan 92

Jan 93

Jan 94

Jan 95

Jan 96

Jan 97

Jan 98

Jan 99

Jan 00

Jan 01

F I G U R E 12.3

Historical PEG ratio for the S&P 500

Source: Thomson Financial Services, Global Comments, December 2001.

The importance of growth opportunities is nowhere more evident than in the Internet boom

of the late 1990s. Many companies that had yet to turn a profit were valued by the market at

billions of dollars. The value of these companies was exclusively growth opportunities. The

box on page 433, written at the height of the boom, compares some of these “new-economy”

firms to their “old-economy” cousins engaged in similar activities and points out that whether

these tech firms were overvalued depended on one™s assessment of future growth.

Of course, when company valuation is determined primarily by growth opportunities, those

values can be very sensitive to reassessments of such prospects. For example, on September

27, 2000, Priceline.com announced that its third-quarter revenue would fall short of expecta-

tions by about 8% and that instead of breaking even for the quarter, it would have a loss of one

cent per share. Its stock price fell 42% in one day. By the end of 2000, the stock price was

about $2 per share, down from nearly $100 earlier that year. Priceline had plenty of company

as the Internet bubble burst in 2000: The stock prices of most other Internet firms fell dramat-

ically as the market became more skeptical of their business prospects, that is, as it revised the

estimates of growth opportunities downward.