# Aswath Damodaran SESSION 18 BOOK VALUE MULTIPLES 1

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Aswath Damodaran SESSION 18: BOOK VALUE MULTIPLES ‹#› 1

Accounting Value. . 2 Aswath Damodaran 2

III. Price to Book Ratio Going back to a simple dividend discount model, Defining the return on equity (ROE) = EPS 0 / Book Value of Equity, the value of equity can be written as: If the return on equity is based upon expected earnings in the next time period, this can be simplified to, 3 Aswath Damodaran 3

Price Book Value Ratio: Stable Growth Firm Another Presentation This formulation can be simplified even further by relating growth to the return on equity: g = (1 - Payout ratio) * ROE Substituting back into the P/BV equation, The price-book value ratio of a stable firm is determined by the differential between the return on equity and the required rate of return on its projects. Building on this equation, a company that is expected to generate a ROE higher (lower than, equal to) its cost of equity should trade at a price to book ratio higher (less than, equal to) one. 4 Aswath Damodaran 4

Now changing to an Enterprise value multiple EV/ Book Capital To see the determinants of the value/book ratio, consider the simple free cash flow to the firm model: Dividing both sides by the book value, we get: If we replace, FCFF = EBIT(1 -t) - (g/ROC) EBIT(1 -t), we get: 5 Aswath Damodaran 5

An Example: An Eyeballing Exercise with P/BV Ratios for European Banks in 2010 Name BAYERISCHE HYPO-UND VEREINSB COMMERZBANK AG DEUTSCHE BANK AG -REG BANCA INTESA SPA BNP PARIBAS BANCO SANTANDER CENTRAL HISP SANPAOLO IMI SPA BANCO BILBAO VIZCAYA ARGENTA SOCIETE GENERALE ROYAL BANK OF SCOTLAND GROUP HBOS PLC BARCLAYS PLC UNICREDITO ITALIANO SPA KREDIETBANK SA LUXEMBOURGEOI ERSTE BANK DER OESTER SPARK STANDARD CHARTERED PLC HSBC HOLDINGS PLC LLOYDS TSB GROUP PLC Average Median 6 Aswath Damodaran PBV Ratio 0. 80 1. 09 1. 23 1. 66 1. 72 1. 86 1. 98 2. 04 2. 09 2. 15 2. 23 2. 30 2. 46 2. 53 2. 59 2. 94 3. 33 2. 05 2. 07 Return on Equity -1. 66% -6. 72% 1. 32% 1. 56% 12. 46% 11. 06% 8. 55% 11. 17% 9. 71% 20. 22% 22. 45% 21. 16% 14. 86% 17. 74% 10. 28% 20. 18% 18. 50% 32. 84% 12. 54% 11. 82% Standard Deviation 49. 06% 36. 21% 35. 79% 34. 14% 31. 03% 28. 36% 26. 64% 18. 62% 22. 55% 18. 35% 21. 95% 20. 73% 13. 79% 12. 38% 21. 91% 19. 93% 19. 66% 18. 66% 24. 99% 21. 93% 6

The median test… We are looking for stocks that trade at low price to book ratios, while generating high returns on equity, with low risk. But what is a low price to book ratio? Or a high return on equity? Or a low risk One simple measure of what is par for the sector are the median values for each of the variables. A simplistic decision rule on under and over valued stocks would therefore be: � Undervalued stocks: Trade at price to book ratios below the median for the sector, (2. 07), generate returns on equity higher than the sector median (11. 82%) and have standard deviations lower than the median (21. 93%). � Overvalued stocks: Trade at price to book ratios above the median for the sector and generate returns on equity lower than the sector median. 7 Aswath Damodaran 7

How about this mechanism? We are looking for stocks that trade at low price to book ratios, while generating high returns on equity. But what is a low price to book ratio? Or a high return on equity? Taking the sample of 18 banks, we ran a regression of PBV against ROE and standard deviation in stock prices (as a proxy for risk). PBV = 2. 27 + (5. 56) 3. 63 ROE (3. 32) - 2. 68 Std dev (2. 33) R squared of regression = 79% 8 Aswath Damodaran 8

And these predictions? 9 Aswath Damodaran 9

A follow up on US Banks 10 Aswath Damodaran 10

Example 2: The Largest Market Cap Companies - PBV versus ROE 11 Aswath Damodaran 11

Missing growth? 12 Aswath Damodaran 12

PBV, ROE and Risk: Large Cap US firms Most overval ued Cheapest Most underval ued 13 Aswath Damodaran 13

Bringing it all together… Largest US stocks in January 2010 14 Aswath Damodaran 14

Market Regressions - Global Region Regression – January 2016 R 2 US PBV= -1. 68 + 14. 59 g. EPS – 0. 99 Beta + 3. 79 Payout + 19. 58 ROE 50. 2% Europe PBV = 2. 66 + 6. 30 g. EPS – 1. 40 Beta + 9. 39 ROE + 1. 80 Payout 40. 6% Japan PBV= 2. 01 + 2. 15 g. EPS – 1. 18 Beta + 0. 97 Payout + 8. 28 ROE 29. 1% Emerging Markets PBV= -0. 43 + 2. 71 g. EPS - 0. 74 Beta + 2. 48 Payout + 18. 91 ROE 34. 1% Australia, NZ, Canada PBV= -1. 20 + 8. 97 g. EPS - 0. 69 Beta + 1. 01 Payout + 21. 90 ROE 55. 4% Global PBV= 0. 22 + 5. 41 g. EPS - 0. 95 Beta + 2. 68 Payout +16. 09 ROE 43. 1% g. EPS=Expected Growth: Expected growth in EPS/ Net Income: Next 5 years Beta: Regression or Bottom up Beta Payout ratio: Dividends/ Net income from most recent year. Set to zero, if net income < 0 15 ROE: Net Income/ Book value of equity in most recent year. 15