statistic that relates the price paid to current earnings.

it issimple to computefor most stocks, and is widely available, making comparisons across stocks simple.

it is aproxy for a number of other characteristicsof the firm including risk and growth.

use of PE ratios is a way, for some analysts, toavoid having to be explicit about their assumptionson risk, growth and payout ratios.

they are muchmore likely to reflect market moodsand perceptions but this can be viewed as a weakness, especially when markets make systematic errors in valuing entire sectors.

Estimating PE ratios from fundamentals

A stable firm is a firm growing at a rate comparable to the nominal growth rate in the economy in which it operates.

P0 = Value of equity DPS1 = Expected dividends per share next year

r = Required rate of return on equity gn = Growth rate in dividends (forever)

Substituting in for DPS1 = EPS0 (1+gn) (Payout ratio), the value of the equity can be written as:

Illustration 1: Estimating the PE ratio for a stable firm using DPS- Deutsche Bank AG

Deutsche Bank had earnings per share of 46.38 DM in 1994, and paid out 16.50 DM as dividends that year. The growth rate in earnings and dividends, in the long term, is expected to be 6%. The beta for Deutsche Bank is 0.92 and the long term bond rate in Germany is 7.50%. (The premium used for German stocks is 4.5%.)

Current Dividend Payout Ratio = 16.50/46.38 = 35.58%

Expected Growth Rate in Earnings and Dividends = 6%

Cost of Equity =7.50 % + 0.92*4.5% = 11.64%

PE Ratio based on fundamentals = 0.3558 *1.06 / (.1164 -.06) = 6.69

Detusche Bank was selling at a PE ratio of 13.50 at the time of this analysis. (May 1993)

Illustration 2: Estimating the PE ratio for a stable firm using FCFE – Siemens AG

Siemens had earnings per share of 32.76 DM and paid dividends per share of 13 DM in 1994. The beta for the stock is 0.93. The ten-year bond rate in Germany was 7.5% and the risk premium for stocks over bonds is assumed to be 4.50%. The company had FCFE in 1994 of 20 DM per share

Expected growth rate in earnings and dividends in long term = 6%

Cost of equity = 7.50% + 0.93 (4.50%) = 11.69 %

PE Ratio based upon fundamentals = 0.6105 * 1.06 / (.1169 – .06) = 11.37

Siemens was selling at a price-earnings multiple of 16.68 in July 1993.

The price-earnings 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 fairly simply:

EPS0 = Earnings per share in year 0 (Current year) g = Growth rate in the first n years

r = Required rate of return on equity 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

Determinants of the PE ratio for a high growth firm

The left hand side of the equation is the price earnings ratio. It is determined by–

Payout ratio during the high growth period and in the stable period:The PE ratio increases as the payout ratio increases.

Riskiness (through the discount rate r):The PE ratio becomes lower as riskiness increases.

Expected growth rate in Earnings, in both the high growth and stable phases:The PE increases as the growth rate increases, in either period.

Illustration 3: Estimating the PE ratio for a high growth firm in the two-stage model

Assume that you have been asked to estimate the PE ratio for a firm which has the following characteristics:

Growth rate in first five years = 25% Payout ratio in first five years = 20%

Growth rate after five years = 8% Payout ratio after five years = 50%

Beta = 1.0 Riskfree rate = T.Bond Rate = 6%

Required rate of return = 6% + 1(5.5%)= 11.5%

The estimated PE ratio for this firm is 28.75.

Illustration 4: Estimating the PE ratio for Nike – 1994

The following is a estimation of the appropriate PE ratio for Nike in March 1995. It is assumed to have five years of high growth left, after which the firm is expected to be in steady state.

Expected Return on Equity = 18% (This is slightly lower than the ROE in 1994 of 19.5%)

Expected Payout Ratio = 20% (This is the current payout ratio)

Growth Rate in high growth period = (1 – Payout Ratio) ROE = (1-.2) (.18) = 14.4%

Length of high growth period = 5 years

The beta of Nike currently is 1.45, and the treasury bond rate is 7.5%, yielding a cost of equity of:

Cost of Equity = 7.5% + 1.45 * (5.5%) = 15.48 %

The beta of Nike in stable growth is expected to be 1.10, leading to a cost of equity of:

Cost of Equity = 7.5% + 1.10 * (5.5%) = 13.55 %

Expected Payout Ratio in stable phase = 1 – 6%/15% = 60%

The price-earnings ratio can be estimated based upon these inputs:

Nike was trading at a price-earnings ratio of 14 in March .1995.

These are Class B shares, with limited voting rights.

PE Ratios and Expected Extraordinary Growth

As the firms anticipated extraordinary growth rate in the first five years declines from 25% to 8%, the PE ratio for the firm also decreases from 28.75 to 15.

Investment Strategies that compare PE to the expected growth rate

Portfolio managers and analysts sometimescompare PE ratios to the expected growth rateto identify under and overvalued stocks.

In the simplest form of this approach, firms withPE ratios less than their expected growth rateare viewed as undervalued.

In its more general form, theratio of PE ratio to growthis used as a measure of relative value.

Problems with comparing PE ratios to expected growth

In its simple form, there isno basisfor believing that a firm is undervalued just because it has a PE ratio less than expected growth.

This relationship may beconsistent with a fairly valuedor even an overvalued firm, ifinterest rates are high, or if a firm is high risk.

Problems with the relative comparison (PE/g)

In its relative form, where firms are ranked on the basis of the ratio of PE ratio to expected growth, the rankings will provide a measure of relative value if,

Thelength of the high growth periodis the same for all firms

All firms are ofequivalent risk. If the model used is the CAPM, all firms have the same betas.

The PE ratio of the safer firm will be higher than the PE ratio of the riskier firm at every level of growth, as illustrated in figure 14.4:

Comparisons are often made betweenprice-earnings ratios in different countrieswith the intention of finding undervalued and overvalued markets.

It is clearly misleading in these cases to compare PE ratios across different marketwithout controlling for differencesin the underlying variables.

The regression of PE ratios on these variables provides the following

PE = 33.52 – 103.5 Interest Rates + 103.85 Nominal Growth in GNP – 0.143 Country Risk R2= 36.80%

Another comparison that is often made is betweenPE ratios across time.

As thefundamentals(interest rates and expected growth) change over time, the PE ratio will also change.

A more appropriate comparison is therefore not between PE ratios across time, but between the actual PE ratio and thepredicted PE ratiobased upon fundamentals existing at that time.

There is astrong positive relationship between E/P ratios and T.Bond rates, as evidenced by the correlation of 0.67 between the two variables. In addition, there is evidence that the term structure also affects the PE ratio. In the following regression, we regress E/P ratios against the level of T.Bond rates and a term structure variable (T.Bond – T.Bill rate)

E/P = 3.34% + 0.7160 T.Bond Rate – 0.9039 (T.Bond Rate-T.Bill Rate) R2= 0.795

Other things remaining equal, this regression suggests that

Every 1% increase in the T.Bond rate increases the E/P ratio by 0.716%.

Every 1% increase in the difference between T.Bond and T.Bil

l rates reduces the E/P ratio by 0.90%. (As the term structure flattens out, E/P ratios should increase – PE ratios should decrease)

PE ratios vary across industries and across firms because ofdifferences in fundamentals- higher growth generally translates into higher PE ratios.

When comparisons are made across firms,differences in risk, growth rates and payout ratioshave to be controlled for explicitly.

Using comparable firms- Pros and Cons

The most common approach to estimating the PE ratio for a firm is to choose a

for this group and to subjectively adjust this average for differences between the firm being valued and the comparable firms.

There are several problems with this approach.

The definition of a comparable firm is essentially a

The use of other firms in the industry as the control group is often not a solution because firms within the same industry can have

There is also plenty of potential for

Even when a legitimate group of comparable firms can be constructed,

differences will continue to persist

in fundamentals between the firm being valued and this group.

Using the entire crosssection: A regression approach

In contrast to the comparable firm approach, the information in the

The simplest way of summarizing this information is with a

, with the PE ratio as the dependent variable, and proxies for risk, growth and payout forming the independent variables.

These PE ratio regressions have been updated in the following section using data from

was used to extract information on price-earnings ratios, payout ratios and earnings