Determinants
of Price to Book Ratios
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 Ð the dividend discount model Ð to
explore the determinants. The value of equity in a stable growth dividend
discount model can be written as:
where,
P0 = Value of equity per share today
DPS1 = Expected dividends per share next year
ke
= Cost of equity
gn = Growth rate in dividends (forever)
Substituting
in for DPS1 = (EPS1)(Payout
ratio), the value of the equity can be written as:
Defining the return on equity (ROE)
, the value of equity can be written as:
Rewriting
in terms of the PBV ratio,
If we define return on equity using
contemporaneous earnings, ROE
, the price to book ratio can be written as:
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,
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%
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 Ð payout ratio)(ROE) = (1-0.6341)(0.1366) = .05 or 5%
PBV
ratio 
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%.
Return
on Equity 
Coat
of Equity = 7% + 1.25 (3.5%) = 11.375%
Price/Book
Value Ratio 
Estimated
MV of equity
PBV
Ratio for a high growth firm
The
price-book value ratio for a high growth firm can also be related to
fundamentals. In the special case of the two-stage dividend discount model,
this relationship can be made explicit simply. The value of equity of a high
growth firm in the two-stage dividend discount model can be written as:
Value
of Equity = Present Value of expected dividends + Present value of terminal
price
When
the growth rate is assumed to be constant after the initial high growth phase,
the dividend discount model can be written as follows:
where,
g
= Growth rate in the first n years
Payout
= Payout ratio in the first n years
gn = Growth rate after n years forever
(Stable growth rate)
Payoutn = Payout ratio after n years for the
stable firm
ke
= Cost of equity (hg: high growth period; st: stable growth period)
Rewriting EPS0 in terms of the return on equity, EPS0 = (BV0)(ROE), and
bringing BV0 to the left hand side
of the equation, we get:
where ROE is the return on equity and ke is the
cost of equity.
(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 Ð 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.
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%
Beta = 1.0 Riskfree
rate = T.Bond Rate = 6%
Return on equity = 25%
Cost of equity = 6% + 1(5.5%)= 11.5%
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 Ð 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:
Nestle
traded at a price-book value ratio of 4.40 in May 2001, which would make it
over valued.
Again,
in this valuation, we have preserved consistency by setting the growth rate
equal to the product of the return on equity and the equity reinvestment rate
(1- FCFE/ Earnings).
Growth rate during high growth = ROE
(1- FCFE/Earnings)
=
1.2298 (1 - 0.6835) = 0.0727
Growth rate during stable growth = ROE
(1- FCFE/Earnings) = 0.15 (1-0.7333) = 0.04
PBV
Ratios and Return on Equity
The
ratio of price to book value is strongly influenced by the return on equity. A
lower return on equity affects the price-book value ratio directly through the
formulation specified in the prior section and indirectly by lowering the
expected growth or payout.
Expected
growth rate = Retention Ratio * Return on Equity
The
effects of lower return on equity on the price-book value ratio can be seen by
going back to Illustration 19.3 and changing the return on equity for the firm
that we valued in that example.
Illustration
19.5: Return on Equity and
Price-Book Value
In
Illustration 19.3, we estimated a price to book ratio for the firm of 7.89, based
upon a return on equity of 25%. This return on equity, in turn, allowed the
firm to generate growth rates of 20% in high growth and 8% in stable growth.
Growth rate in first five years 
Growth rate after year 5 
If the firm's return on equity drops to
12%, the price/book value will reflect the drop. The lower return on equity
will also lower expected growth in the initial high growth period:
Expected
growth rate (first five years) 
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 
New
payout ratio after year 5 = 1 - Retention ratio = 33.33%
The new price-book value ratio can then
be calculated as follows:
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 Ð 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 19.3:
Forces of Competition and Return on Equity
In Porter's framework, a firm is able to
maintain a high return on equity because there are significant barriers to
entry by new firms or because the firm has significant advantages over its
competition. The analysis of the return on equity of a firm can be made richer
and much more informative by examining the competitive environment in which it
operates. There may also be clues in this analysis to the future direction of
the return on equity.
eqmult.xls: This spreadsheet allows you to estimate
the price earnings ratio for a stable growth or high growth firm, given its
fundamentals.