Chapter 9 - Ch16

By Philip Wood,2014-05-07 20:50
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Chapter 9 - Ch16


     CHAPTER 9


     Earnings multiples remain the most commonly used measures of relative value. In this chapter, you begin with a detailed examination of the price earnings ratio and then move on to consider a variant that is often used for technology firms the price earnings

    to growth ratio (PEG). You also look at value multiples, and in particular, the value to EBITDA multiple and other variants of earnings multiples in the second part of the

    chapter. You will use the four-step process described in chapter 8 to look at each of these multiples.

    Price Earnings Ratio (PE)

    The price-earnings multiple (PE) is the most widely used and misused of all

    multiples. Its simplicity makes it an attractive choice in applications ranging from pricing initial public offerings to making judgments on relative value, but its relationship to a firm's financial fundamentals is often ignored, leading to significant errors in applications. This chapter provides some insight into the determinants of price-earnings ratios and how best to use them in valuation.

    Definitions of PE ratio

     The price earnings ratio the ratio of the market price per share to the earnings per


    PE = Market Price per share / Earnings per share

    The PE ratio is consistently defined, with the numerator being the value of equity per

    share and the denominator measuring earnings per share, which is a measure of equity

    earnings. The biggest problem with PE ratios is the variations on earnings per share used in computing the multiple. In chapter 8, you saw that PE ratios could be computed using

    current earnings per share, trailing earnings per share, forward earnings per share, fully diluted earnings per share and primary earnings per share. With technology firms, the PE


    ratio can be very different depending upon which measure of earnings per share is used.

    This can be explained by two factors:

    ? The high growth in earnings per share at these firms: Forward earnings per share can

    be substantially higher than trailing earnings per share, which, in turn, can be

    significantly different from current earnings per share.

    ? Management Options: Since technology firms tend to have far more employee options

    outstanding, relative to the number of shares, the differences between diluted and

    primary earnings per share tend to be large.

    When the PE ratios of technology firms are compared, it is difficult to ensure that the earnings per share are uniformly estimated across the firms for the following reasons:

    ? Technology firms often grow by acquiring other firms, and they do not account for

    with acquisitions the same way. Some do only stock-based acquisitions and use only

    pooling, others use a mixture of pooling and purchase accounting, still others use

    purchase accounting and write of all or a portion of the goodwill as in-process R&D.

    These different approaches lead to different measures of earnings per share and

    different PE ratios.

    ? Using diluted earnings per share in estimating PE ratios might bring the shares that

    are covered by management options into the multiple, but they treat options that are

    deep in-the-money or only slightly in-the-money as equivalent. ? The expensing of R&D gives firms a way of shifting earnings from period to period,

    and penalizes those firms that are spending more on research and development. Technology firms that account for acquisitions with pooling and do not invest in R&D

    can have much lower PE ratios than technology firms that use purchase accounting in

    acquisitions and invest substantial amounts in R&D.

    Cross Sectional Distribution of PE ratios


     A critical step in using PE ratios is to understand how the cross sectional multiple

    is distributed across firms in the sector and the market. In this section, the distribution of

    PE ratios across the entire market is examined first, followed by an examination of PE

    ratios in the technology sector.

    Market Distribution

     Figure 9.1 presents the distribution of PE ratios for U.S. stocks in July 2000. The

    current PE, trailing PE and forward PE ratios are all summarized in this figure.

    Figure 9.1: Current, Trailing and Forward PE RatiosU.S. Stocks - July 2000





    600Current PETrailing PE500Forward PE400




    0< 4 4 - 8 8 - 12 12 - 1616 - 20 20 - 2525 - 30 30 -4040 -5050 -75 75 ->100100


Table 9.1 presents summary statistics on all three measures of the price earnings ratio,

    thstarting with the mean and the standard deviation, and including the median, and 10 and

    th90 percentile values. In computing these values, the PE ratio is set at 200 if it is greater

    than 200, to prevent outliers from having too large of an influence on the summary


1 The mean and the standard deviation are the summary statistics that are most likely to be affected by these



    Table 9.1: Summary Statistics PE Ratios for U.S. Stocks

     Current PE Trailing PE Forward PE

    Mean 31.30 28.49 27.21

    Standard Deviation 44.13 40.86 41.21

    Median 14.47 13.68 11.52

    Mode 12.00 7.00 7.50

    th10 percentile 5.63 5.86 5.45

    th90 percentile 77.87 63.87 64.98

    Skewness 17.12 25.96 19.59 Looking at all three measures of the PE ratio, the average is consistently higher than the

    median, reflecting the fact that PE ratios can be very high numbers but cannot be less than

    zero. This asymmetry in the distributions is captured in the skewness values. The current

    PE ratios are also higher than the trailing PE ratios, which, in turn, are higher than the

    forward PE ratios.

    Technology Stocks

     Technology stocks generally have higher price earnings ratios than other firms in

    the market. This is evident when you look at figure 9.2, which provides the distribution of

    PE ratios for technology stocks in the United States in July 2000.


    Figure 9.2: Current, Trailing and Forward PE RatiosTechnology Stocks - United States- July 2000





    600Current PETrailing: All500Forward PE400




    0< 4 4 - 8 8 - 12 12 - 1616 - 20 20 - 2525 - 30 30 -4040 -5050 -75 75 ->100100


Table 9.2 presents summary statistics on PE ratios for technology stocks, with the PE

    ratios capped at 200.

    Table 9.2: Summary Statistics PE Ratios for U.S. Technology Stocks

     Current PE Trailing PE Forward PE

    Mean 72.05 66.41 60.61

    Standard Deviation 67.14 62.56 62.06

    Median 43.24 40.45 32.56

    Mode 83.00 109.00 7.50

    th10 percentile 10.68 11.08 10.71

    th90 percentile 200.00 200.00 200.00

    Skewness 7.99 11.49 19.59 As in Table 9.1, the current PE ratio is lower than the trailing PE, which is lower than the

    forward PE. Illustrating the impact of outliers in the distribution, not capping the PE

    ratios at 200 would have yielded an average current PE ratio of 199, an average trailing


    PE of 190.84 and an average forward PE of 120.52. The PE ratios for technology stocks

    are also consistently higher than the PE ratios for the rest of the market.

    The contrast between the PE ratios of technology stocks and other stocks is clear

    when you look at the percent of stocks that fall into each PE ratio class for the two groups

    in figure 9.3.

A much higher proportion of technology stocks have PE ratios greater than 100 than non-

    technology stocks. In general, the distribution of PE ratios is skewed upwards for

    technology stocks.

    There is one final point that should be made about the PE ratio and that relates to

    the number of firms that had negative earnings and no meaningful PE ratios. A far greater

    proportion of technology stocks fell into this category than stocks in other sectors. Table

    9.3 summarizes the statistics on the number of stocks in each group that had negative

    earnings, and the biases introduced into the statistics as a result.

    Table 9.3: Negative Earnings Companies

     Technology Stocks Non-technology Stocks


    Number of firms in sample 1103 4800 Number of firms with 677 1456 negative earnings

    % of firms with negative 61.38% 30.33% earnings

    Average Trailing PE 190.84 35.01 Market Capitalization/ 263.45 39.06 Earnings

    If you average the PE ratio only across firms where the PE ratio can be estimated, you

    obtain an estimate of 190.84 for technology firms and 35.01 for non-technology firms. If

    you divide the market capitalization of all firms in the group by the collective net income

    of these firms (including those with negative earnings), the estimate of the PE ratio shifts

    upwards. The shift is much larger for technology stocks.

    pedata.xls: There is a dataset on the web that summarizes price earnings ratios

    and fundamentals by industry group in the United States for the most recent year

    Determinants of the PE ratio

     In chapter 8, the fundamentals that determine multiples were extracted using a

    discounted cash flow model an equity model like the dividend discount model for

    equity multiples and a firm value model for firm multiples. The price earnings ratio,

    being an equity multiple, can be analyzed using a equity valuation model. In this section,

    the fundamentals that determine the price earnings ratio for a high growth firm are


    A Discounted Cashflow Model perspective on PE ratios

     In chapter 8, you derived the PE ratio for a stable growth firm from the stable

    growth dividend discount model:


    P)Payout Ratio*(1?g0n?PE= EPSr-g0nIf the PE ratio is stated in terms of expected earnings in the next time period, this can be

    simplified to,

    PPayout Ratio0?Forward PE= EPS1k-genThe PE ratio is an increasing function of the payout ratio and the growth rate, and a

    decreasing function of the riskiness of the firm.

     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. When a firm is expected to be in high growth for the next n

    years and stable growth thereafter, the dividend discount model can be written as follows:

    n????(1+g)????EPS*Payout Ratio*(1+g)*1?0nn(1+k)????EPS*Payout Ratio*(1+g)*(1+g)e,hg0nnP=+ 0n-g(k-g)(1+k)ke,hge,stne,hg


     EPS = Earnings per share in year 0 (Current year) 0

     g = Growth rate in the first n years

     k = Cost of equity in high growth period e,hg

     k = Cost of equity in stable growth period e,st

     Payout = Payout ratio in the first n years

     g = Growth rate after n years forever (Stable growth rate) n

     Payout = Payout ratio after n years for the stable firm n

    Bringing EPS to the left hand side of the equation, 0


    n????(1+g)????Payout Ratio*(1+g)*1?nn(1+k)????PPayout Ratio*(1+g)*(1+g)e,hg0nn=+ nEPS-g(k-g)(1+k)k0e,hge,stne,hgThe left hand side of the equation is the price earnings ratio. It is determined by--

    (a) Payout ratio during the high growth period and in the stable period: The PE ratio

    increases as the payout ratio increases.

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

    (c) Expected growth rate in Earnings, in both the high growth and stable phases: The PE

    increases as the growth rate increases, in either period.

    This formula is general enough to be applied to any firm, even one that is not paying

    dividends right now. In fact, the ratio of FCFE to earnings can be substituted for the

    payout ratio for firms that pay significantly less in dividends than they can afford to.

    Illustration 9.1: 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 that 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%

    2Required rate of return = 6% + 1(5.5%)= 11.5%

    5????(1.25)????0.2 * (1.25) * 1?55????(1.115)0.5 * (1.25)*(1.08) + PE = = 28.755(.115 - .25)(.115-.08) (1.115)

    The estimated PE ratio for this firm is 28.75.

2 For purposes of simplicity, the beta and cost of equity are estimated to be the same in both the high growth

    and stable growth periods. They could have been different.


    Illustration 9.2: Estimating a Fundamental PE ratio for Motorola

     The following is an estimation of the appropriate PE ratio for Motorola in July

    2000. The assumptions on the growth period, growth rate and cost of equity are identical

    to those used in the discounted cash flow valuation of Motorola in chapter 7. The

    assumptions are summarized below:

     High Growth Period Stable Growth Length 5 years Forever after year 5 Cost of Equity 10.85% 10.00% Expected Growth Rate 13.63% 5% Payout Ratio 36.00% 66.67% The current payout ratio of 36% is used for the entire high growth period. After year 5,

    the payout ratio is estimated based upon the expected growth rate of 5% and a return on

    equity of 15% (based upon industry averages):

    Stable period payout ratio = 1- Growth rate/ Return on equity = 1- 5%/15% = 66.67%

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

    5??(1.1363)????0.36 * (1.1363) * 1?55????(1.1085)*(1.05)0.6667 * (1.1363)PE = = 17.79+ 5(.10-.05) (1.1085)(.1085 - .1363)

    Based upon its fundamentals, you would expect Motorola to be trading at 17.79 times


    PE Ratios and Expected Extraordinary Growth

     The PE ratio of a high growth firm is a function of the expected extraordinary

    growth rate - the higher the expected growth, the higher the PE ratio for a firm. In

    illustration 9.1, for instance, the PE ratio that was estimated to be 28.75, with a growth

    rate of 25%, will change as that expected growth rate changes. Figure 9.4 graphs the PE

    ratio as a function of the extraordinary growth rate during the high growth period.

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