Price Earnings Ratio (PE) (2024)

Determinantsof the PE ratio

InChapter 17, the fundamentals that determine multiples were extracted using adiscounted cash flow model Ð an equity model like the dividend discount modelfor equity multiples and a firm value model for firm multiples. The priceearnings ratio, being an equity multiple, can be analyzed using an equityvaluation model. In this section, the fundamentals that determine the priceearnings ratio for a high growth firm are analyzed.

ADiscounted Cashflow Model perspective on PE ratios

InChapter 17, we derived the PE ratio for a stable growth firm from the stablegrowth dividend discount model.

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Ifthe PE ratio is stated in terms of expected earnings in the next time period,this can be simplified.

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The PE ratio is an increasing function ofthe payout ratio and the growth rate and a decreasing function of the riskinessof the firm. In fact, we can state the payout ratio as a function of theexpected growth rate and return on equity.

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Substituting back into the equation above,

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Theprice-earnings ratio for a high growth firm can also be related tofundamentals. In the special case of the two-stage dividend discount model,this relationship can be made explicit fairly simply. When a firm is expectedto be in high growth for the next n years and stable growth thereafter, thedividend discount model can be written as follows:

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where,

EPS0 = Earnings per share in year 0 (Currentyear)

g= Growth rate in the first n years

k_e,hg= Cost of equity in high growth period

k_e,st= Cost of equity in stable growth period

Payout= Payout ratio in the first n years

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

PayoutRation = Payout ratio after n yearsfor the stable firm

Divide both sides of the equation by EPS0.

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Here again, we can substitute in thefundamental equation for payout ratios.

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where ROE_hgis the return on equity in the high growth period and ROE_st is thereturn on equity in stable growth:Theleft hand side of the equation is the price earnings ratio. It is determinedby:

(a) Payout ratio (and return onequity) during the high growth period and in the stable period: The PE ratio increases as the payoutratio increases, for any given growth rate. An alternative way of stating thesame proposition is that the PE ratio increases as the return on equity increasesand decreases as the return on equity decreases.

(b) Riskiness (through the discountrate k_e): ThePE 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 eitherperiod.

This formula is general enough to beapplied 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 firmsthat pay significantly less in dividends than they can afford to.

Illustration18.1: Estimating the PE ratio for a high growth firm in the two-stage model

Assume that you have been asked toestimate the PE ratio for a firm that has the following characteristics.

Growth rate in first five years = 25% Payoutratio in first five years = 20%

Growth rate after five years = 8% Payoutratio after five years = 50%

Beta = 1.0 Riskfreerate = T.Bond Rate = 6%

Required rate of return<![if !supportFootnotes]>[1]<![endif]> = 6% + 1(5.5%)= 11.5%

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The estimated PE ratio for this firm is28.75. Note that the returns on equity implicit in these inputs can also becomputed.

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Illustration18.2: Estimating a Fundamental PE ratio for Procter and Gamble

Thefollowing is an estimation of the appropriate PE ratio for Procter and Gamblein May 2001. The assumptions on the growth period, growth rate and cost ofequity are identical to those used in the discounted cash flow valuation ofP&G in Chapter 13. The assumptions are summarized in Table 18.2.

Table18.2: Summary Inputs for P& G

Thecurrent payout ratio of 45.67% is used for the entire high growth period. Afteryear 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).

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Theprice-earnings ratio can be estimated based upon these inputs.

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Basedupon its fundamentals, you would expect P&G to be trading at 22.33 timesearnings. Multiplied by the current earnings per share, you get a value pershare of $66.99, which is identical to the value obtained in Chapter 13, usingthe dividend discount model.

PERatios and Expected Extraordinary Growth

ThePE ratio of a high growth firm is a function of the expected extraordinarygrowth rate - the higher the expected growth, the higher the PE ratio for afirm. In Illustration 18.1, for instance, the PE ratio that was estimated to be28.75, with a growth rate of 25%, will change as that expected growth ratechanges. Figure 18.2 graphs the PE ratio as a function of the extraordinarygrowth rate during the high growth period.

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Asthe firm's expected growth rate in the first five years declines from 25% to5%, the PE ratio for the firm also decreases from 28.75 to just above 10.

Theeffect of changes in the expected growth rate varies depending upon the levelof interest rates. In Figure 18.3, the PE ratios are estimated for differentexpected growth rates at four levels of riskless rates Ð 4%, 6%, 8% and 10%.

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ThePE ratio is much more sensitive to changes in expected growth rates wheninterest rates are low than when they are high. The reason is simple. Growthproduces cash flows in the future and the present value of these cash flows ismuch smaller at high interest rates. Consequently the effect of changes in thegrowth rate on the present value tend to be smaller.

Thereis a possible link between this finding and how markets react to earningssurprises from technology firms. When a firm reports earnings that aresignificantly higher than expected (a positive surprise) or lower than expected(a negative surprise), investorsÕ perceptions of the expected growth rate forthis firm can change concurrently, leading to a price effect. You would expectto see much greater price reactions for a given earnings surprise, positive ornegative, in a low-interest rate environment than you would in a high-interestrate environment.

PEratios and Risk

ThePE ratio is a function of the perceived risk of a firm and the effect shows upin the cost of equity. A firm with a higher cost of equity will trade at alower multiple of earnings than a similar firm with a lower cost of equity.

Again, the effect of higher risk on PEratios can be seen using the firm in Illustration 18.1. Recall that the firm,which has an expected growth rate of 25% for the next 5 years and 8%thereafter, has an estimated PE ratio of 28.75, if its beta is assumed to be 1.

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If you assume that the beta is 1.5, thecost of equity increases to 14.25%, leading to a PE ratio of 14.87:

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The higher cost of equity reduces thevalue created by expected growth.

In Figure 18.4, you can see the impact ofchanging the beta on the price earnings ratio for four high growth scenarios Ð8%, 15%, 20% and 25% for the next 5 years.

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As the beta increases, the PE ratiodecreases in all four scenarios. However, the difference between the PE ratiosacross the four growth classes is lower when the beta is very high andincreases as the beta decreases. This would suggest that at very high risklevels, a firmÕs PE ratio is likely to increase more as the risk decreases thanas growth increases. For many technology firms that are viewed as both veryrisky and having good growth potential, reducing risk may increase value muchmore than increasing expected growth.

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