Source: Bloomberg

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

PBV = 2.27 + 3.63 ROE -2.68 Standard Deviation R2 = 79.48%

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 1.71.

Predicted PBVDeuteche Bank = 2.27 + 3.63 (.0132) - 2..68 (.3579) = 1.71

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 28%.

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

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%)

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 "subjective" 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.

41 We 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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