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CHAPTER 19
BOOK VALUE MULTIPLES
The relationship between price and book value has always attracted the attention of investors. Stocks selling for well below the book value of equity have generally been considered good candidates for undervalued portfolios, while those selling for more than book value have been targets for overvalued portfolios. This chapter begins by examining the price/book value ratio in more detail, the determinants of this ratio and how best to evaluate or estimate the ratio. In the second part of the chapter, we will turn our attention to variants of the price to book ratio. In particular, we focus on the value to book ratio and Tobin’s Q – a ratio of market value of assets to their replacement cost.
Price to Book Equity The market value of the equity in a firm reflects the market’s expectation of the firm’s earning power and cashflows. The book value of equity is the difference between the book value of assets and the book value of liabilities, a number that is largely determined by accounting conventions. In the United States, the book value of assets is the original price paid for the assets reduced by any allowable depreciation on the assets. Consequently, the book value of an asset decreases as it ages. The book value of liabilities similarly reflects the "at-issue" values of the liabilities. Since the book value of an asset reflects its original cost, it might deviate significantly from market value if the earning power of the asset has increased or declined significantly since its acquisition.
Why analysts use book value and the down side… There are several reasons why investors find the price-book value ratio useful in investment analysis. The first is that the book value provides a relatively stable, intuitive measure of value that can be compared to the market price. For investors who instinctively mistrust discounted cashflow estimates of value, the book value is a much simpler benchmark for comparison. The second is that, given reasonably consistent accounting standards across firms, price-book value ratios can be compared across similar firms for signs of under or over valuation. Finally, even firms with negative earnings, which cannot be valued using price-earnings ratios, can be evaluated using price-book
value ratios; there are far fewer firms with negative book value than there are firms with negative earnings. There are several disadvantages associated with measuring and using price-book value ratios. First, book values, like earnings, are affected by accounting decisions on depreciation and other variables. When accounting standards vary widely across firms, the price-book value ratios may not be comparable. A similar statement can be made about comparing price-book value ratios across countries with different accounting standards. Second, book value may not carry much meaning for service and technology firms which do not have significant tangible assets. Third, the book value of equity can become negative if a firm has a sustained string of negative earnings reports, leading to a negative price-book value ratio.
Definition The price to book ratio is computed by dividing the market price per share by the current book value of equity per share.
Price to Book Ratio = PBV = (^) Book value of equity per sharePrice per share
While the multiple is fundamentally consistent – the numerator and denominator are both equity values – there is a potential for inconsistency if you are not careful about how you compute book value of equity per share. In particular,
- If there are multiple classes of shares outstanding, the price per share can be different for different classes of shares and it is not clear how the book equity should be apportioned among shares.
- You should not include the portion of the equity that is attributable to preferred stock in computing the book value of equity, since the price per share refers only to common equity. Some of the problems can be alleviated by computing the price to book ratio using the total market value of equity and book value of equity, rather than per share values.
Price to Book Ratio = PBV = Market Value of EquityBook value of equity
The safest way to measure this ratio when there are multiple classes of equity is to use the composite market value of all classes of common stock in the numerator and the
you have a firm that has a market value of equity of $100 million and a book value of equity of $50 million; its price to book ratio is 2.00. If the firm borrows $25 million and buys back stock, its book equity will decline to $25 million and its market equity will drop to $75 million. The resulting price to book ratio is three. With acquisitions, the effect on price to book ratios can vary dramatically depending upon how the acquisition is accounted for. If the acquiring firm uses purchase accounting, the book equity of the firm will increase by the market value of the acquired firm. If, on the other hand, it uses pooling, the book equity will increase by the book value of the acquired firm. Given that the book value is less than the market value for most firms, the price to book ratio will be much higher for firms that use pooling on acquisitions than purchase accounting. To compare price to book ratios across firms, when some firms in the sample buy back stocks and some do not or when there are wide differences in both the magnitude and the accounting for acquisitions, can be problematic. One way to adjust for the differences is to take out the goodwill from acquisitions and to add back the market value of buybacks to the book equity to come up with an adjusted book value of equity. The price to book ratios can then be computed based upon this adjusted book value of equity.
Description To get a sense of what comprises a high, low or average price to book value ratio, we computed the ratio for every firm listed in the United States and Figure 19. summarizes the distribution of price to book ratios in July 2000.
Note that this distribution is heavily skewed, as is evidenced by the fact that the average price to book value ratio of firms is 3.25 while the median price to book ratio is much lower at 1.85. Another point worth making about price to book ratios is that there are firms with negative book values of equity – the result of continuously losing money – where price to book ratios cannot be computed. In this sample of 5903 firms, there were 728 firms where this occurred. In contrast, though, 2045 firms had negative earnings and PE ratios could not be computed for them.
pbvdata.xls : There is a dataset on the web that summarizes price to book ratios and fundamentals by industry group in the United States for the most recent year
Analysis The price-book value ratio can be related to the same fundamentals that determine value in discounted cashflow models. Since this is an equity multiple, we will use an equity discounted cash flow model – the dividend discount model – to explore the
Figure 19.1: Price to Book Value Ratios
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0-0.5 0.5- 1 1-1.5 1.5-2 2- 2.5 2.5 - 3 3 - 3.5 3.5 - 4 4 - 4.5 4.5 - 5 5- 10 > Price to Book Ratio
Number of firms
The PBV ratio is an increasing function of the return on equity, the payout ratio and the growth rate and a decreasing function of the riskiness of the firm. 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,
n
n 0
0 r- g PBV ROE-g BV
P = =
The price-book value ratio of a stable firm is determined by the differential between the return on equity and its cost of equity. If the return on equity exceeds the cost of equity, the price will exceed the book value of equity; if the return on equity is lower than the cost of equity, the price will be lower than the book value of equity. The advantage of this formulation is that it can be used to estimate price-book value ratios for private firms that do not pay out dividends.
Illustration 19.1: Estimating the PBV ratio for a stable firm - Volvo Volvo had earnings per share of 11.04 Swedish Kroner (SEK) in 2000 and paid out a dividend of 7 SEK per share, which represented 63.41% of its earnings. The growth rate in earnings and dividends, in the long term, is expected to be 5%. The return on equity at Volvo is expected to be 13.66%. The beta for Volvo is 0.80 and the riskfree rate in Swedish Kroner is 6.1%. Current Dividend Payout Ratio = 63.41% Expected Growth Rate in Earnings and Dividends = 5% Return on Equity = 13.66% Cost of Equity = 6.1% + 0.80*4% = 9.30% PBV Ratio based on fundamentals ( )( )
( )( )
- 01
k -g = ROE PayoutRatio e n
Since the expected growth rate in this case is consistent with that estimated by fundamentals, the price to book ratio could also have been estimated from the return differences. Fundamental growth rate = (1 – payout ratio)(ROE) = (1-0.6341)(0.1366) = .05 or 5%
PBV ratio
- 01
Costofequity-Growthrate
ROE-growthrate
Volvo was selling at a P/BV ratio of 1.10 on the day of this analysis (May 2001), making it significantly under valued. The alternative interpretation is that the market is anticipating a much lower return on equity in the future and pricing Volvo based upon this expectation.
Illustration 19.2: Estimating the price-book value ratio for a 'privatization' candidate - Jenapharm (Germany) One of the by-products of German reunification was the Treuhandanstalt, the German privatization agency set up to sell hundreds of East German firms to other German companies, individual investors and the public. One of the handful of firms that seemed to be a viable candidate for privatization was Jenapharm, the most respected pharmaceutical manufacturer in East Germany. Jenapharm, which was expected to have revenues of 230 million DM in 1991, also was expected to report net income of 9 million DM in that year. The firm had a book value of assets of 110 million DM and a book value of equity of 58 million DM at the end of 1990. The firm was expected to maintain sales in its niche product, a contraceptive pill, and grow at 5% a year in the long term, primarily by expanding into the generic drug market. The average beta of pharmaceutical firms traded on the Frankfurt Stock exchange was 1.05, though many of these firms had much more diversified product portfolios and less volatile cashflows. Allowing for the higher leverage and risk in Jenapharm, a beta of 1.25 was used for Jenapharm. The ten-year bond rate in Germany at the time of this valuation in early 1991 was 7% and the risk premium for stocks over bonds is assumed to be 3.5%.
P 0
BV 0 =^ (^ ROEhg)
( Payout Ratio) (1+g ) 1 −^ (1+g^ )
n
ke,hg -g + ROE(^ st)^
( Payout Ratio n) (1+g )n^ (1+g n)
( ke,st -g^ n) (1+k e,hg)n
where ROE is the return on equity and ke is the cost of equity. The left hand side of the equation is the price book value ratio. It is determined by: (a) Return on equity : The price-book value ratio is an increasing function of the return on equity. (b) Payout ratio during the high growth period and in the stable period : The PBV ratio increases as the payout ratio increases, for any given growth rate. (c) Riskiness (through the discount rate r): The PBV ratio becomes lower as riskiness increases; the increased risk increases the cost of equity. (d) Growth rate in Earnings, in both the high growth and stable phases: The PBV increases as the growth rate increases, in either period, holding the payout ratio constant. This formula is general enough to be applied to any firm, even one that is not paying dividends right now. Note, in addition, that the fundamentals that determine the price to book ratio for a high growth firm are the same as the ones for a stable growth firm – the payout ratio, the return on equity, the expected growth rate and the cost of equity. In Chapter 14, we noted that firms may not always pay out what they can afford to and recommended that the free cashflows to equity be substituted in for the dividends in those cases. You can, in fact, modify the equation above to state the price to book ratio in terms of free cashflows to equity.
P 0
BV 0 = ROE(^ hg)*
FCFE
Earnings
hg
(^ 1+g ) 1 −^ (1+g^ )
n
(^ 1+r )n
r -g +^ (ROE^ st)
FCFE
Earnings
n
( 1+g )n( 1+g n)
(^ r -g n) (1+r )n
The only substitution that we have made is the replacement of the payout ratio by the FCFE as a percent of earnings.
Illustration 19.3: Estimating the PBV ratio for a high growth firm in the two-stage model Assume that you have been asked to estimate the PBV ratio for a firm that is expected to be in high growth for the next five years. The firm has the following characteristics: EPS Growth rate in first five years = 20% Payout ratio in first five years = 20% EPS Growth rate after five years = 8% Payout ratio after five years = 68% Beta = 1.0 Riskfree rate = T.Bond Rate = 6% Return on equity = 25% Cost of equity = 6% + 1(5.5%)= 11.5%
PBV = 0.
( 0.2) (1.20 ) 1 −^ 1.
5 1.115^5
0.115 − 0.20 +^ 0.^
( 0.115^ −^ 0.08) (1.115 5 ) =^ 7.
The estimated PBV ratio for this firm is 7.89.
Illustration 19.4: Estimating the Price/Book Value Ratio for a high growth firm using FCFE - Nestle In Chapter 14, we valued Nestle using a two-stage FCFE model. We summarize the inputs we used for that valuation in the Table 19.1. Table 19.1: Nestle – Summary of Inputs High Growth Stable Growth Length 10 years Forever after year 10 ROE 22.98% 15% FCFE/Earnings 68.35% 73.33% Growth rate 7.27% 4% Cost of Equity 8.47% 8.47% The price-book value ratio, based upon these inputs, is calculated below:
Expected growth rate (first five years)
( )( ) ( )( )
- 6 %
Retentionratio ROE
=
After year 5, either the retention ratio has to increase or the expected growth rate has to be lower than 8%. If the retention ratio is adjusted,
New retention ratio after year 5 =ExpectedROE^ growth=12%8% =66.67% New payout ratio after year 5 = 1 - Retention ratio = 33.33% The new price-book value ratio can then be calculated as follows:
PBV = ( 0.12)
( 0.2) (1.096 ) 1 −^ (1.096^ )
5 ( 1.115 )^5
0.115 − 0.096 +^ (^ 0.12)^
( 0.3333) (1.096 )^5 (1.08 ) ( 0.115^ −^ 0.08) (1.115 )^5 =^ 1.
The drop in the ROE has a two-layered impact. First, it lowers the growth rate in earnings and/or the expected payout ratio, thus having an indirect effect on the P/BV ratio. Second, it reduces the P/BV ratio directly. The price-book value ratio is also influenced by the cost of equity, with higher costs of equity leading to lower price-book value ratios. The influence of the return on equity and the cost of equity can be consolidated in one measure by taking the difference between the two – a measure of excess equity return. The larger the return on equity relative to the cost of equity, the greater is the price-book value ratio. In the illustration above for instance, the firm, which had a cost of equity of 11.5%, went from having a return on equity that was 13.5% greater than the required rate of return to a return on equity that barely broke even (0.5% greater than the required rate of return). Consequently, its price-book value ratio declined from 7.89 to 1.25. The following graph shows the price-book value ratio as a function of the difference between the return on equity and required rate of return.
Note that when the return on equity is equal to the cost of equity, the price is equal to the book value.
The Determinants of Return on Equity
The difference between return on equity and the required rate of return is a measure of a firm's capacity to earn excess returns in the business in which it operates. Corporate strategists have examined the determinants of the size and expected duration of these excess profits (and high ROE) using a variety of frameworks. One of the better known is the "five forces of competition" framework developed by Porter. In his approach, competition arises not only from established producers producing the same product but also from suppliers of substitutes and from potential new entrants into the market. Figure 19.3 summarizes the five forces of competition:
Figure 19.2: Price-Book Value as a Function of Return
Differential
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13.50% 11.50% 9.50% 7.50% 5.50% 3.50% 1.50% -0.50% -2.50% ROE - Cost of Equity
P/BV Ratio
There are several potential applications for the principles developed in the last section and we will consider three in this section. We will first look at what causes price to book ratios for entire markets to change over time and when a low (high) price to book ratio for a market can be viewed as a sign of under (over) valuation. We will next compare the price to book ratios of firms within a sector and extend this to look at firms across the market and what you need to control for in making these comparison. Finally, we will look at the factors that cause the price to book ratio of an individual firm to change over time and how this can be used as a tool for analyzing restructurings.
PBV ratios for a Market
The price to book value ratio for an entire market is determined by the same variables that determine the price to book value ratio for an individual firm. Other things remaining equal, therefore, you would expect the price to book ratio for a market to go up as the equity return spread (ROE – Cost of equity) earned by firms in the market increases. Conversely, you would expect the price to book ratio for the market to decrease as the equity return spread earned by firms decreases. In Chapter 18, we noted the increase in the price earnings ratio for the S&P 500 from 1960 to 2000. Over that period, the price to book value ratio for the market has also increased. In Figure 19.4, we report on the price to book ratio for the S&P 500 on one axis and the return on equity for S&P 500 firms on the other.
The increase in the price to book ratio over the last two decades can be at least partially explained by the increase in return on equity over the same period.
Comparisons across firms in a Sector
Price-book value ratios vary across firms for a number of reasons - different expected growth, different payout ratios, different risk levels and most importantly, different returns on equity. Comparisons of price-book value ratios across firms that do not take into account these differences are likely to be flawed. The most common approach to estimating PBV ratios for a firm is choose a group of comparable firms, to calculate the average PBV ratio for this group and to base the PBV ratio estimate for a firm on this average. The adjustments made to reflect differences in fundamentals between the firm being valued and the comparable group are usually subjectively. There are several problems with this approach. First, the definition of a 'comparable' firm is essentially a subjective one. The use of other firms in the industry as the control group is often not a complete solution because firms within the same industry can have very different business mixes, risk and growth profiles. There is also plenty of
Figure 19.4: Price to Book Ratios and ROE - S&P 500
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1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000Year
Price to Book Ratio
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ROE
(^) PBV ROE
If we assume that firms within a sector have similar costs of equity, we could replace the equity return spread with the raw return on equity.
Regression Approach
If the price to book ratio is largely a function of the return on equity, we could regress the former against the latter. PBV = a + b ROE If the relationship is strong, we could use this regression to obtain predicted price to book ratios for all of the firms in the sector, separating out those firms that are under from those that are over valued. This regression can be enriched in two ways. The first is to allow for non-linear relationships between price to book and return on equity - this can be done by either transforming the variables (natural logs, exponentials, etc.) or by running non-linear regressions. The second is to expand the regression to include other independent variables such as risk and growth.
Return on Equity - Cost of Equity
High Price to Book High Equity return spread
Low Price to Book Low Equity return spread
Low Price to Book High Equity return spread
Undervalued
High Price to Book Low Equity return spread
Overvalued
Illustration 19.6: Comparing Price to Book Value Ratios: Integrated Oil companies In Table 19.2, we report on the price to book ratios for integrated oil companies listed in the United States in September 2000. Table 19.2: Price to Book Ratios and Returns on Equity
Company Name
Ticker Symbol PBV ROE
Std Deviation Crown Cent. Petr.'A' CNPA 0.29 -14.60% 59.36% Giant Industries GI 0.54 7.47% 38.87% Harken Energy Corp. HEC 0.64 -5.83% 56.51% Getty Petroleum Mktg. GPM 0.95 6.26% 58.34% Pennzoil-Quaker State PZL 0.95 3.99% 51.06% Ashland Inc. ASH 1.13 10.27% 21.77% Shell Transport SC 1.45 13.41% 31.61% USX-Marathon Group MRO 1.59 13.42% 45.31% Lakehead Pipe Line LHP 1.72 13.28% 19.56% Amerada Hess AHC 1.77 16.69% 26.89% Tosco Corp. TOS 1.95 15.44% 34.51% Occidental Petroleum OXY 2.15 16.68% 39.47% Royal Dutch Petr. RD 2.33 13.41% 29.81% Murphy Oil Corp. MUR 2.40 14.49% 27.80% Texaco Inc. TX 2.44 13.77% 27.78% Phillips Petroleum P 2.64 17.92% 29.51% Chevron Corp. CHV 3.03 15.69% 26.44% Repsol-YPF ADR REP 3.24 13.43% 26.82% Unocal Corp. UCL 3.53 10.67% 34.90% Kerr-McGee Corp. KMG 3.59 28.88% 42.47% Exxon Mobil Corp. XOM 4.22 11.20% 19.22% BP Amoco ADR BPA 4.66 14.34% 27.00% Clayton Williams CWEI 5.57 31.02% 26.31%
