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value for the equity would be:

Value of Equity = Disney net income in 2003* Average PE ratio for sector

= $1,267 million * 47.08 = $59,650 million

In this valuation, we assume that Disney has a growth rate similar to the average for the

sector. One way of bringing growth into the comparison is to compute the PEG ratio,

which is reported in the last column. Based on the average PEG ratio of 2.79 for the

sector and the analyst estimate of growth in earnings of 12% for the next 5 years, we

obtain the following value for the equity in Disney:

Value of Equity = $ 1,267 million * 2.79 * 12 = $ 41,692 million

While this may seem like an easy adjustment to resolve the problem of differences across

firms, the conclusion holds only if these firms are of equivalent risk. Implicitly, this

approach assumes a linear relationship39 between growth rates and PE.

12.11. в˜ћ: Underlying Assumptions in Comparable Valuation

Assume that you are reading an equity research report where a buy recommendation for a

company is being based upon the fact that its PE ratio is lower than the average for the

industry. Implicitly, what is the underlying assumption or assumptions being made by

this analyst?

a. The sector itself is, on average, fairly priced

b. The earnings of the firms in the group are being measured consistently

c. The firms in the group are all of equivalent risk

d. The firms in the group are all at the same stage in the growth cycle

e. The firms in the group are of equivalent risk and have similar cash flow patterns

f. All of the above

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pe.xls: There is a dataset on the web that summarizes PE ratios and PEG ratios

by industry group in the United States for the most recent quarter.

b. Adjusting for more than one variable

When firms differ on more than one variable, it becomes difficult to modify the

multiples to account for the differences across firms. We can run regressions of the

multiples against the variables and then use these regressions to find predicted values for

each firm. This approach works reasonably well when the number of comparable firms is

large and the relationship between the multiple and the variables is stable. When these

conditions do not hold, a few outliers can cause the coefficients to change dramatically

and make the predictions much less reliable.

Illustration 12.15: Price to Book Value Ratios and Return on Equity: European Banks

Table 12.9 lists price/book value ratios of European banks and reports on their

returns on equity and risk levels (measured using the standard deviation in stock prices

over the previous 5 years):

Table 12.9: European Banks: Price to Book Value Ratio вЂ“ 2003

Name PBV Ratio Return on Equity Standard Deviation

Bayerische Hypo-Und Vereinsb 0.80 -1.66% 49.06%

Commerzbank Ag 1.09 -6.72% 36.21%

Deutsche Bank Ag -Reg 1.23 1.32% 35.79%

Banca Intesa Spa 1.66 1.56% 34.14%

Bnp Paribas 1.72 12.46% 31.03%

Banco Santander Central Hisp 1.86 11.06% 28.36%

Sanpaolo Imi Spa 1.96 8.55% 26.64%

Banco Bilbao Vizcaya Argenta 1.98 11.17% 18.62%

Societe Generale 2.04 9.71% 22.55%

Royal Bank Of Scotland Group 2.09 20.22% 18.35%

Hbos Plc 2.15 22.45% 21.95%

Barclays Plc 2.23 21.16% 20.73%

Unicredito Italiano Spa 2.30 14.86% 13.79%

39 Only by assuming a linear relationship can we compare the PEG ratio of a 10% growth firm to a 20%

growth firm.

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Kredietbank Sa Luxembourgeoi 2.46 17.74% 12.38%

Erste Bank Der Oester Spark 2.53 10.28% 21.91%

Standard Chartered Plc 2.59 20.18% 19.93%

Hsbc Holdings Plc 2.94 18.50% 19.66%

Lloyds Tsb Group Plc 3.33 32.84% 18.66%

Sector Average 2.05 12.54% 24.99%

Source: Bloomberg

Since these firms differ on both risk and return on equity, we run a regression of PBV

ratios on both variables:

R2 = 79.48%

PBV = 2.27 + 3.63 ROE -2.68 Standard Deviation

(5.56) (3.32) (2.32)

Firms with higher return on equity and lower standard deviations trade at much higher

price to book ratios. The numbers in brackets are t-statistics and suggest that the

relationships between PBV ratios and both variables in the regression are statistically

significant. The R-squared indicates the percentage of the differences in PBV ratios that

is explained by the independent variables. Finally, the regression40 itself can be used to

get predicted PBV ratios for the companies in the list. Thus, the predicted PBV ratio for

Deutsche Bank, based upon its return on equity of 1.32% and its standard deviation of

35.79%, would be 1.36.

Predicted PBVDeutsche Bank = 2.27 + 3.63 (.0132) вЂ“ 2..68 (.3579) = 1.36

Since the actual PBV ratio for Deutsche Bank at the time of the analysis was 1.23, this

would suggest that the stock is undervalued by roughly 10%.

pbv.xls: There is a dataset on the web that summarizes price to book ratios and

returns on equity by industry group in the United States for the most recent quarter.

ps.xls: There is a dataset on the web that summarizes price to sales ratios and

margins by industry group in the United States for the most recent quarter.

40 Both approaches described above assume that the relationship between a multiple and the variables

driving value are linear. Since this is not always true, we might have to run non-linear versions of these

regressions.

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3. Expanding the Range of Comparable Firms

Searching for comparable firms within the sector in which a firm operates is fairly

restrictive, especially when there are relatively few firms in the sector or when a firm

operates in more than one sector. Since the definition of a comparable firm is not one that

is in the same business but one that has the same growth, risk and cash flow

characteristics as the firm being analyzed, we need not restrict our choice of comparable

firms to those in the same industry. A software firm should be comparable to an

automobile firm, if we can control for differences in the fundamentals.

The regression introduced in the previous section allows us to control for

differences on those variables that we believe cause multiples to vary across firms. Based

upon the variables listed in Table 12.7, we should be able to regress PE, PBV and PS

ratios against the variables that should affect them:

Price Earnings = f (Growth, Payout ratios, Risk)

Price to Book Value = f (Growth, Payout ratios, Risk, ROE)

Price to Sales = f (Growth, Payout ratios, Risk, Margin)

It is, however, possible that the proxies that we use for risk (beta), growth (expected

growth rate), and cash flow (payout) may be imperfect and that the relationship may not

be linear. To deal with these limitations, we can add more variables to the regression -

e.g., the size of the firm may operate as a good proxy for risk - and use transformations of

the variables to allow for non-linear relationships.

We ran these regressions41 for PE, PBV, and PS ratios across publicly listed firms

in the United States in January 2004 against analyst estimates of expected growth in

earnings per share and other financial indicators from the most recent year. The sample,

which had more than 7000 firms in it, yielded the regressions reported below. These

regressions can then be used to get predicted PE, PBV, and PS ratios for each firm,

which, in turn, can be compared to the actual multiples to find under and over valued

firms.

PE = 9.475 + 0.814 Expected growth + 0.06 Payout + 6.283 Beta (R2 = 22.1%)

PBV= 0.140 ROE + 0.599 Beta + 0.08 Expected Growth +.002 Payout (R2= 47.1%)

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PS= 0.04 Expected Growth +0.011 Payout + 0.549 Beta + 0.234 Net Margin (R2=

71.0%)

The first advantage of this approach over the вЂњsubjectiveвЂќ comparison across

firms in the same sector, described in the previous section, is that it does quantify, based

upon actual market data, the degree to which higher growth or risk should affect the

multiples. It is true that these estimates can be noisy, but noise is a reflection of the

reality that many analysts choose not to face when they make subjective judgments.

Second, by looking at all firms in the market, this approach allows us to make more

meaningful comparisons of firms that operate in industries with relatively few firms.

Third, it allows us to examine whether all firms in an industry are under- or overvalued,

by estimating their values relative to other firms in the market.

Illustration 12.16: Applying Market Regression to Estimate Multiples - Disney

We will use the results of the market regression summarized above to estimate the

appropriate value for Disney. Consider the regression for the PE ratio:

PE = 9.475 + 0.814 Expected growth + 0.06 Payout + 6.283 Beta

The corresponding values for Disney are as follows:

Expected Growth rate = 12.00% (Analyst consensus estimate for EPS growth)

Payout Ratio = 32.31%

Beta = 1.2456

The estimated price earnings ratio for Disney is:

PS = 9.475 + 0.814 (12) + 0.06 (32.31) + 6.283 (1.2456) = 29.01

Since Disney trades at an actual PE ratio of 29.87, it is slightly overvalued, relative to the

market, by about 3%.

multregr.xls: This dataset summarizes the latest regression of multiples against

fundamentals for the United States for the most recent quarter.

41We ran the regression using absolute values for the independent variables and both with intercepts and

without intercepts. .If the intercept is negative, we have reported the regression without the intercept.

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Reconciling Different Valuations

The two approaches to valuation вЂ“ discounted cash flow valuation and relative

valuation вЂ“ yield different values for Disney42. In fact, Disney is significantly overvalued

using a discounted cashflow model but is closer to being fairly valued using relative

valuation models. Even within relative valuation, we arrive at different estimates of

value, depending upon which multiple we use and what firms we based the relative

valuation on.

The differences in value between discounted cash flow valuation and relative

valuation come from different views of market efficiency, or put more precisely, market

inefficiency. In discounted cash flow valuation, we assume that markets make mistakes,

that they correct these mistakes over time, and that these mistakes can often occur across

entire sectors or even the entire market. In relative valuation, we assume that while

markets make mistakes on individual stocks, they are correct on average. In other words,

when we value Disney relative to other entertainment companies, we are assuming that

the market has priced these companies correctly, on average, even though it might have

made mistakes in the pricing of each of them individually. Thus, a stock may be over

valued on a discounted cash flow basis but under valued on a relative basis, if the firms

used in the relative valuation are all overpriced by the market. The reverse would occur,

if an entire sector or market were underpriced.

To conclude, we suggest the following broad guidelines on gauging value using

different approaches:

The discounted cash flow models are built on the implicit assumption of long

вЂў

time horizons, giving markets time to correct their errors.

When using relative valuation, it is dangerous to base valuations on multiples

вЂў

where the differences across firms cannot be explained well using financial

fundamentals вЂ“ growth, risk, and cash flow patterns. One of the advantages of

using the regression approach described in the later part of this chapter is that

the R-squared and t-statistics from the regressions yield a tangible estimate of

the strength (or weakness) of this relationship.

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12.12. в˜ћ: Valuing an Initial Public Offering

If you were an investment banker, pricing an initial public offering, would you primarily

use discounted cash flow valuation, relative valuation or a combination of the two?

a. Relative valuation, because the buyers of the IPO will look at comparables

b. Discounted cash flow valuation, because it reflects intrinsic value

c. The higher of the two values, since it is my job to get the highest price I can for my

client

d. None of the above

Explain.

Conclusion

There are two basic approaches to valuation. The first is discounted cash flow

valuation, where the value of any asset is estimated by computing the present value of the

expected cash flows on it. The actual process of estimation, in either case, generally

requires four inputs вЂ“

the length of the period for which a firm or asset can be expected to generate growth

вЂў

greater than the stable growth rate (which is constrained to be close to the growth rate

of the economy in which the firm operates),

the cash flows during the high growth period,

вЂў

the terminal value at the end of the high growth period and

вЂў

a discount rate.

вЂў

The expected growth potential will vary across firms, with some firms already growing at

a stable growth rate and others for which the expectation, at least, is that growth will last

for some period into the future. We can value the operating assets of a firm by

discounting cashflows before debt payments, but after reinvestments, at the cost of

capital. Adding the value of cash and non-operating assets give us firm value, and

subtracting out debt yields the value of equity. We can also value equity directly by

discounting cash flows after debt payments and reinvestment needs at the cost of equity.

42Kaplan and Ruback (1995) examine valuations in acquisitions and find that discounted cash flow models

better explain prices paid than relative valuation models.

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