In contrast, the electric utilities are more representative of mature firms. For this industry,

return on assets is lower, 8.0%; dividend payout is higher, 53.3%; and average growth is

lower, 6.5%.

To value companies with temporarily high growth, analysts use a multistage version of the

two-stage DDM

dividend discount model. Dividends in the early high-growth period are forecast and their com-

Dividend discount bined present value is calculated. Then, once the firm is projected to settle down to a steady

model in which growth phase, the constant growth DDM is applied to value the remaining stream of dividends.

dividend growth is

We can illustrate this with a real-life example using a two-stage DDM. Figure 12.2 is a

assumed to level

Value Line Investment Survey report on the defense contractor, Raytheon. Some of Raytheon™s

off only at some

relevant information in late 2001 is highlighted.

future date.

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

Essentials of Investments, Companies, 2003

Fifth Edition

425

12 Equity Valuation

B

A

C

D

E

F I G U R E 12.2

Value Line Investment Survey report on Raytheon

Source: From Value Line Investment Survey, 9/28/01. Reprinted by permission of Value Line Investment Survey.

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

Essentials of Investments, Companies, 2003

Fifth Edition

426 Part FOUR Security Analysis

Raytheon™s beta appears at the circled A, its recent stock price at the B, the per-share divi-

dend payments at the C, the ROE (referred to as “return on shareholder equity”) at the D, and

the dividend payout ratio (referred to as “all dividends to net profits”) at the E. The rows end-

ing at C, D, and E are historical time series. The boldfaced italicized entries under 2002 are es-

timates for that year. Similarly, the entries in the far right column (labeled 04“06) are forecasts

for some time between 2004 and 2006, which we will take to be 2005.

Value Line projects rapid growth in the near term, with dividends rising from $.80 in 2002

to $1.25 in 2005. This rapid growth rate cannot be sustained indefinitely. We can obtain divi-

dend inputs for this initial period by using the explicit forecasts for 2002 and 2005 and linear

interpolation for the years between:

2002 $ .80

2003 $ .95

2004 $1.10

2005 $1.25

Now let us assume the dividend growth rate levels off in 2005. What is a good guess for

that steady-state growth rate? Value Line forecasts a dividend payout ratio of 0.29 and an ROE

of 10.0%, implying long-term growth will be

g ROE b 10.0% (1 0.29) 7.1%

Our estimate of Raytheon™s intrinsic value using an investment horizon of 2005 is therefore

obtained from Equation 12.2, which we restate here

D2002 D2003 D2004 D2005 P2005

V2001

(1 k)2 (1 k)3 k)4

(1 k) (1

.80 .95 1.10 1.25 P2005

(1 k)2 (1 k)3 k)4

1 k (1

Here, P2005 represents the forecast price at which we can sell our shares of Raytheon at the end

of 2005, when dividends enter their constant growth phase. That price, according to the con-

stant growth DDM, should be

D2006 D2005(1 g) 1.25 1.071

P2005

kg kg k .071

The only variable remaining to be determined to calculate intrinsic value is the market capi-

talization rate, k.

One way to obtain k is from the CAPM. Observe from the Value Line data that Raytheon™s

beta is .85. The risk-free rate on longer term bonds in 2001 was about 5%. Suppose that the

market risk premium were forecast at 8.0%. This would imply that the forecast for the market

return was

Risk-free rate Market risk premium 5.0% 8.0% 13.0%

Therefore, we can solve for the market capitalization rate for Raytheon as

k rf [E(rM) rf]

5% .85 (13.0 5.0) 11.8%

Our forecast for the stock price in 2005 is thus

$1.25 1.071

P2005 $28.48

.118 .071

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

Essentials of Investments, Companies, 2003

Fifth Edition

427

12 Equity Valuation

and today™s estimate of intrinsic value is

.80 .95 1.10 1.25 28.48

V2001 $21.29

(1.118)2 (1.118)3 (1.118)4

1.118

We know from the Value Line report that Raytheon™s actual price was $32.50 (at the circled

B). Our intrinsic value analysis indicates Raytheon was overpriced. Should we sell our hold-

ings of Raytheon or even sell Raytheon short?

Perhaps. But before betting the farm, stop to consider how firm our estimate is. We™ve had

to guess at dividends in the near future, the ultimate growth rate of those dividends, and the

appropriate discount rate. Moreover, we™ve assumed Raytheon will follow a relatively simple

two-stage growth process. In practice, the growth of dividends can follow more complicated

patterns. Even small errors in these approximations could upset a conclusion.

For example, suppose the market risk premium is lower than our estimate, 6% rather than

8%. While lower than the historical average, this value is consistent with some recent re-

search.4 This seemingly modest change will reduce the market capitalization rate to 10.1%. At

this lower rate, the intrinsic value of the stock based on the two-stage growth model rises to

$33.55, just about equal to the stock price at the time. Therefore, our conclusion regarding

mispricing is reversed.

This exercise shows that finding bargains is not as easy as it seems. While the DDM is easy

to apply, establishing its inputs is more of a challenge. This should not be surprising. In even

a moderately efficient market, finding profit opportunities has to be more involved than sitting

down with Value Line for a half-hour.

The exercise also highlights the importance of assessing the sensitivity of your analysis to

changes in underlying assumptions when you attempt to value stocks. Your estimates of stock

values are no better than your assumptions. Sensitivity analysis will highlight the inputs that

need to be most carefully examined. For example, we just found that very small changes in the

estimated risk premium of the stock result in big changes in intrinsic value. Similarly, small

changes in the assumed growth rate change intrinsic value substantially. On the other hand,

reasonable changes in the dividends forecast between 2002 and 2005 have a small impact on

intrinsic value.

<

4. Confirm that the intrinsic value of Raytheon using E(rM) rf 6.0% is $33.55. Concept

(Hint: First calculate the discount rate and stock price in 2005. Then calculate the

CHECK

present value of all interim dividends plus the present value of the 2005 sales

price.)

Multistage Growth Models

The two-stage growth model that we just considered for Raytheon is a good start toward real-

ism, but clearly we could do even better if our valuation model allowed for more flexible pat-

terns of growth. Multistage growth models allow dividends per share to grow at several

different rates as the firm matures. Many analysts use three-stage growth models. They may

assume an initial period of high dividend growth (or instead make year-by-year forecasts of

dividends for the short term), a final period of sustainable growth, and a transition period in

4

Recent research suggests that in the last 50 years the average excess return of the market index portfolio was con-

siderably better than market participants at the time were anticipating. Such a pattern could indicate that the economy

performed better than initially expected during this period or that the discount rate declined. For evidence on this is-

sue, see Ravi Jagannathan, Ellen R. McGrattan, and Anna Scherbina, “The Declining U.S. Equity Premium,” Federal

Reserve Bank of Minneapolis Quarterly Review 4 (Fall 2000) pp. 3“19, and Eugene F. Fama and Kenneth R. French,

“The Equity Premium,” Journal of Finance 57 (April 2002), pp. 637“660.

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

Essentials of Investments, Companies, 2003

Fifth Edition

E XC E L Applications www.mhhe.com/bkm

> Three-Stage Growth Model: Raytheon Example

A B

The spreadsheet in this box presents a three- 1 Three Stage Growth Model

stage dividend discount model. Rather than 2

3

forecasting year-by-year dividends in the first 4 Initial Earnings 4.00

stage, in this version of the model the analyst 5 Initial Dividend 2.00

6 Stage 1 Growth 0.35

forecasts an initial high dividend growth rate. In 7 Duration of Growth 1 10

the last stage, dividends are forecast to grow in- 8 Stage 2 Growth 0.15

9 Duration of Growth 2 10

definitely at a constant rate. In the transition 10 Estimated Constant Growth 0.08

years, the analyst forecasts a dividend growth 11 Beta Coefficient 1.25

12 T-Bill Rate 0.05

rate in between the initial high rate and the 13 Market Risk Premium 0.08

more moderate sustainable rate. This spread- 14

15 Required Return 0.15

sheet is available at www.mhhe.com.bkm. 16 Ratio of (1+g1)/(1+k) 1.17391304

17 Ratio of (1+g2)/(1+k) 1

18 Closed End Ratio 1 26.80

19 Closed End Ratio 2 10.00

20

21 PValue of the Stage 1 Dividends 53.60

22 PValue of the Stage 2 Dividends 99.40

23 PValue of the Constant Growth Dividends 153.36

24 Value of the Stock 306.36

25

26 Analysis of Growth Opportunities

27 Value of NoGrowth Firm 26.67

28 Present Value of Growth Opportunities 279.69

29

30 Price to Earnings Ratios

31 Price /Current Earnings 76.59

32 Price / Next Years Expected Earnings 56.73

between, during which dividend growth rates taper off from the initial rapid rate to the ulti-

mate sustainable rate. These models are conceptually no harder to work with than a two-stage

model, but they require many more calculations and can be tedious to do by hand. It is easy,

however, to build an Excel spreadsheet for such a model. We refer you to the nearby Excel ap-

plication for an example of such a spreadsheet.

12.4 PRICE“EARNINGS RATIOS

The Price“Earnings Ratio and Growth Opportunities

Much of the real-world discussion of stock market valuation concentrates on the firm™s

price“earnings multiple, the ratio of price per share to earnings per share, commonly called

price“earnings

the P/E ratio. In fact, one common approach to valuing a firm is to use an earnings multiplier.

multiple

The value of the stock is obtained by multiplying projected earnings per share by a forecast of

The ratio of a stock™s

the P/E ratio. This procedure seems simple, but its apparent simplicity is deceptive. First, fore-

price to its earnings

casting earnings is challenging. As we saw in the previous chapter, earnings will depend on in-

per share.

ternational, macroeconomic, and industry as well as firm-specific factors, many of which are

highly unpredictable. Second, forecasting the P/E multiple is even more difficult. P/E ratios

vary across industries and over time. Nevertheless, our discussion of stock valuation provides

some insight into the factors that ought to determine a firm™s P/E ratio.

428

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

Essentials of Investments, Companies, 2003

Fifth Edition

429

12 Equity Valuation

Recall our discussion of growth opportunities, in which we compared two firms, Growth

Prospects and Cash Cow, each of which had earnings per share of $5. Growth Prospects rein-

vested 60% of its earnings in prospects with an ROE of 15%, while Cash Cow paid out all of

its earnings as dividends. Cash Cow had a price of $40, giving it a P/E multiple of 40/5 8.0,

while Growth Prospects sold for $57.14, giving it a multiple of 57.14/5 11.4. This observa-

tion suggests the P/E ratio might serve as a useful indicator of expectations of growth oppor-

tunities. We can see this explicitly by rearranging Equation 12.6 to