CFA Institute

The Discount Model: A Primer Author(s): James L. Farrell, Jr. Source: Financial Analysts Journal, Vol. 41, No. 6 (Nov. - Dec., 1985), pp. 16-19+22-25 Published by: CFA Institute Stable URL: http://www.jstor.org/stable/4478881 Accessed: 30/03/2010 11:40

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http://www.jstor.org by James L. Farrell,Jr. The Dividend Discount Model: A Primer

Thedividend discount model provides a meansof developingan explicitexpected return for the stockmarket. By comparingthis returnwith the expectedreturn on bonds,as derived froma to maturitycalculation, the can calculate a returnspread between these two classes of securitiesthat can be used to assess the relativeattractiveness of each. Investorscan also use thesereturn data, along with riskdata, to determinean optimalblend of assets-, bonds, money marketinstruments or real estate-within an asset allocationframework. Elaborationson the simple dividenddiscount model providean importanttool for comparingrelative values across a sample of individualstocks. Returns derivedfrom complexmodels may be combinedwith riskdata to constructa "marketline" benchmark. Securitiesthat plot along the line may be consideredfairly priced; those that plot belowthe line would be consideredrelatively unattractive; and securitiesthat plot abovethe line presumablyoffer more return than wouldbe expected,given theirriskiness. The dividenddiscount model may also be modifiedto providean estimateof a 's duration-its sensitivityto interestrate risk. Inasmuch as themeasure of durationfor stocks is similarto themeasure of durationfor bonds,stock and bond durations may be compared to determinethe assets' relativesensitivity to interestrate changes. Similarly,the model providesa frameworkfor comparingthe sensitivitiesof stocksand bondsto unexpected changesin inflationrates.

T HEDIVIDEND DISCOUNT MODEL pro- sensitivity of common stocks, and understand- vides a means for developing explicit re- ing the effect of inflation on common stocks. turn estimates for both individual stocks as well as the aggregate market-essential in- Concepts puts for appraising the relative attractivenessof The value of a bond at a given time can be individual stocks as well as for evaluating the defined as the present value of the stream of attractiveness of the within an coupon payments plus the present value of the overall asset allocation setting. In addition, the principal payment to be received at maturity, model offers a superior framework for under- both discounted at the prevailing rate of interest standing how risk factors such as interest rate for that maturity. Following analogous reason- variations and changing inflation rates affect ing, the value of a common stock can be defined stocks. This article describes the dividend dis- as the present value of the future dividend count model framework and illustrates the stream in perpetuity. This concept is consistent model's usefulness for determining stock mar- with the assumption that the corporation will ket returns, assessing the relative attractiveness indeed have a perpetual life, in accordancewith of individual stocks, evaluating the interest rate its charter. If the value of a stock is equivalent to the value for a perpetual annuity with a constant JamesFarrell, Jr. is Chairmanof MPT Associates,Inc. level of payments, this may be expressed math-

FINANCIALANALYSTS JOURNAL / NOVEMBER-DECEMBER1985 O 16 ematically as: um comprise a basic return demanded by all , the risk-freereturn is a component of D V = k(1) all securities. k The risk premium is made up of the following where elements-interest rate risk, purchasing power V = value, risk, business risk and financial risk. The risk D = per share and premium might be considered to be a function k = percentage discount rate of the stock's systematic risk (), which is If the dividends are assumed to grow at a determined by these four fundamental risk fac- certain constant rate, the formula becomes: tors. As securities differ in their exposure to these risk elements, the premium or return that D investors require to compensate for risk will V= - ' (2) k - g differ across securities. where g represents annual constant percentage Appraising the Market growth in dividends per share and D next year's The variable of most interest to investors is, dividends. generally, the stock's discount rate, k. The price This model assumes that the growth rate for of the stock is readily found, and such variables the corporationbeing analyzed is constant. It is as the currentdividend and the growth rate can thus most suitable for use in estimating the be estimated (albeit with varying degrees of value of stable, mature companies (or, in the ease). The simplified form of the dividend capi- context of a more complex model, the residual talization model can be rearranged to estimate value representing the mature phase of a cur- the discount rate k, as shown below: rently more dynamic company). Companies D with a more erraticor cyclical earnings pattern, k= - + g. (3) or rapidly growing companies, require a more complex dividend capitalization model frame- work that can accommodate differing dividend This equation says that a stock's discount rate growth patterns. is a function of two variables-the dividend Although practical applications may require yield, which is the year-ahead dividend, D, elaborate variations of the dividend capitaliza- divided by the stock price, P, and the growth tion model, the simplified form nevertheless rate of the dividend, g. Estimatingthe dividend provides a convenient means of analyzing the and the growth rate of the dividend may be determinants of stock value. To begin with, the facilitatedif we redefine these variables. Defin- value of the stock should be greater, the greater ing E as year-ahead earnings and 1 - b as a the earning power and capacity of the corpora- payout rate, we can think of dividends as a tion to pay out current dividends, D. Corre- function of a payout rate and an earnings level spondingly, the higher the growth rate of the such that: dividends, g, the greater the value of the corpo- D = (1 - b)E. ration's stock. Finally, the greaterthe risk of the corporation(the higher the discount rate, k) the By furtherdefining b as a retention rate and r as lower the value of the stock. a return on equity, or a measure of profitability, The discount rate is alternatively referred to we can think of the growth rate of the dividend as a required return. It is composed of two as a function of the retention rate and return on elements-a risk-free return and a risk premi- equity such that: um. The risk-free return is, in turn, generally g = br. considered to consist of a real return component and an inflation premium. The real return is the With these alternative definitions, the equation basic investment compensation that investors for determining the discount rate becomes: demand for forgoing current consumption or, (1 - b) E alternatively, the compensation for saving. In- k = + br. (4) vestors also require a premium to compensate p for inflation; this premium will be high when Note that the inputs for Equation (4) are the inflation rate is expected to be high and low estimates for the following variables-the level when the inflation rate is expected to be low. of earnings, E; the retention rate, b (alternative- Because the real return and the inflation premi- ly, the payout rate, 1 - b); and the basic level of

FINANCIALANALYSTS JOURNAL / NOVEMBER-DECEMBER1985 O 17 Table I ExpectedReturn on S&P 500

PayoutRatio Returnon Retentioni Growth Year Earnings(E) (1 - b) Investment(r) Dividenids(D) Rate(b) Rate(br) 1980 14.82 42% 17.8% 6.16 58% 10.3% 1981 15.36 43 17.0 6.63 57 9.7 1982 12.65 54 12.9 6.87 46 5.9 1983 14.04 55 14.0 7.09 45 6.3 1984 16.73 45 16.3 7.53 55 9.0

(1 - b)E Expected return E(R) = p + br

= 4.5% + 9.0% = 13.5% Inflation Rate = 6.5 ExpectedReal Return = 7.0 RealizedReturn 1926-1984 = 9.5 Inflation = 3.0 RealizedReal Return = 6.5

Source:Standard & Poor's SecurityPrice Index Record,Standard & Poor'sCorporation, New York,N.Y. profitability,r. The retention, or payout, rate is At year-end 1984, the on the S&P established by the management of the compa- 500 was 4.5 per cent. Combining this with a ny. It can be assessed by examining past sustainable growth of 9 per cent indicates a payouts of earnings or, more directly, from the discount rate, or expected return, for the S&P stated policy of the corporation; for example, 500 of 13.5 per cent. Of course, this is an the management may have a policy of paying average;expected returns for individual compa- out 50 per cent of earnings over a period of nies will differ because of differences in risk. time. Estimates of the level of earnings, E, and Table I also compares the current "expected" the productivityof retained earnings, r, must be return of 13.5 per cent with that earned by made by the fundamental analyst. stocks over the 59-year period 1926-84. The current absolute return is higher than the his- An Illustration torical return over the 1926-84 period. But the Suppose that we want to estimate the dis- 9.5 per cent 1926-84 return was earned over a count rate, or expected return, of the market as period when the rate of inflation averaged only a whole. The model should be applicableto the 3.0 per cent, so the real return was 6.5 per cent. total market, since the market is simply an In the recent five-year period, inflation aver- aggregation of individual stocks; if it applies to aged 6.5 per cent. Using this as a naive proxy for the individual components, it should apply to the underlying rate of inflation implies a real the total. In fact, the simplified version of the returnon stocks of 7.0 per cent (expected return dividend capitalizationmodel may be more suit- of 13.5 per cent less underlying inflation of 6.5 ably applied to the market as whole than to per cent). The current expected real return on individual stocks, because errors in measuring stocks is thus fairly close to that earned over the inputs tend to cancel out in the aggregate. That longer term. This apparent relative stability in is, overestimates tend to be offset by underes- real return might be helpful in developing a timates. forecastof future return on stocks. In particular, Table I gives some relevant valuation data for one might build a return forecast by estimating a fairly representative index of the U.S. equity the inflation rate and adding it to the real market-the Standard & Poor's 500. This table return. shows, for the five-year period 1980-84, data on The investor can also use infor- earnings, payout ratios, return on investment mation in comparisons with bonds and other and retention rate times the return on invest- non-stock classes of securities. For example, the ment. Note that the payout ratio averaged about expected return for stocks as derived from the 45 per cent while the return on investment dividend discount model may be compared averaged 15.6 per cent for the period. with the expected return for bonds as derived The 1984 retention rate and return on invest- from a yield to maturity calculation in order to ment imply a sustainable growth of 9 per cent. determine a return spread between these two

FINANCIAL ANALYSTS JOURNAL / NOVEMBER-DECEMBER1985 0 18 classes of securities. The magnitude of this Table II ExpectedReturn and Risk for Selected Stocks spread, relative to historicalspreads and current market conditions, may be used to assess the Expected Risk Company Ticker Return Sector relative attractiveness of stocks versus bonds. Above-Average Expected Return More formally, investors can use these return Augat AUG 18.0 5 data along with risk data to determine an opti- Waste Management WMX 16.8 4 mal blend of security classes-stocks, bonds, LoctiteCorporation LOC 16.7 3 Hospital Corp. America HCA 16.0 2 money marketinstruments or real estate-with- Coca Cola KO 15.7 1 in an asset allocation framework. Average Expected Return Time Inc. TL 16.2 5 Appraising Individual Stocks Black& Decker BDK 15.8 4 The simplified form of the dividend discount Marriott MHS 15.5 3 model is also appropriatefor companies that we Weyerhaeuser WY 15.2 2 Gillette GS 14.7 1 might characterize as being of a stable, more mature Below-Average Expected Return variety-companies in such industries Data General DGN 15.1 5 as electric and telephone utility, beverage, to- Caterpillar CAT 14.5 4 bacco and food processing, retailing, banks and Woolworth Z 14.4 3 life insurance, and household Penney JCP 14.3 2 products indus- Procter& Gamble PG 13.5 1 tries. For such companies, earning patterns as well as retention rates and returns on invest- Source:Kidder, Peabody. ment are fairly stable over time. This is because their investment opportunities, which are a prime consideration in setting the retention nies derived by Kidder Peabody from a three- rate, are fairly constrained and their basic profit- stage variant of the dividend discount model ability is pretty constant over time. described above. The table also gives the risk- The formula must be modified substantially, sector rating for each stock; a "1' rating indi- however, to deal with companies that have a cates lowest risk and a "5" rating indicates highly cyclical operating pattern or exceptional- highest risk. ly high rates of earnings growth. In the case of cyclical companies, the inputs to the model The Market Line must be recast. For high-growth companies, an Using this sort of risk and return data, Figure alternative, more complex form of the dividend A plots the 15 stocks (designated by their ticker discount model is needed. symbols) on a risk-return diagram. The line More complex models typically provide for a fitted to the 15 plots provides a benchmark yearly forecast for the next five years (usually known as the marketline.2 The upward slope of based on expected results over a typical eco- the line indicates that increasing risk should be nomic cycle); a transition period of five to 20 accompanied by increasing return; alternative- years' duration (used to link current expecta- ly, high risk stocks should offer higher prospec- tions for growth, profitability and dividend tive returns than low risk stocks. payout in a corporate life cycle atmosphere to The market line provides a way of evaluating the mature state); and the residual, mature, or whether stocks are providing returns that are constant corporate phase. These complex mod- more or less than proportional to their risk and els are comprehensible; they reflect the true thereby provides an explicit way of evaluating theoretical value of a common stock; they pro- the relative attractiveness of individual stocks. vide an intellectual framework for comparing For example, the five stocks that plot on the high-profit, high-growth companies with low- market line are offering returns in line with profit, low-growth firms; and they reflect the what would be expected, given their risk; they life cycle nature of firms and industries in a offer "fair values" in the context of the market competitive environment. But these models line. The five stocks that plot above the line are may contain subtle but meaningful biases creat- offeringhigher returns than would be expected, ed by ground rules that appear very reasonable; given their risk, and the five stocks that plot they may be highly sensitive to very long-term below the line are offering lower returns than forecasts;and they requirea great deal of work.' would be expected given their risks. Stocks Table II shows rates of return for 15 compa- plotting above the line would be considered 1. Footnotes appear at end of article. relativelyattractive and those plotting below the

FINANCIAL ANALYSTS JOURNAL / NOVEMBER-DECEMBER1985 C 19 FigureA ExpectedReturn * Risk Sector, Selected Stocks, 1984

18 -MXAUG 17 -LOC m 16 - HCA BOK 15 15- ~~~~KO WY MSTL -GS z CAT DGN 13 - PG 12 - X 11 10 9 8 >< 7_ 6 5 4 3 2 1 0

0 1 2 3 4 5 Risk

line would be assessed as unattractive. comes within the general category of develop- We would ideally prefer to construct a portfo- ing duration for a perpetuity. For perpetuities lio of stocks from those that plot above the such as preferred stocks, where dividend pay- market line. Portfolios constructed from such ments are fixed, the formula for calculating individually attractive stocks should offer pro- duration, d, is:3 spective returns more than proportionalto their 1 risk. If the dividend discount mechanism has d = k (5) validity in identifying relatively attractive val- k ues, then one might anticipate that using such an approachwould result in above-averagerisk- As before, k represents the requiredreturn on adjusted portfolio performanceover time. the security, and the resulting expression is simply the inverse of the required return. Be- Interest Rate Risk cause we are dealing with perpetuities, the Investors commonly calculate the duration of requiredreturn, k, can be determined by merely fixed-income, finite-lived instruments- observing the current yield of the security. For bonds-and use the magnitude of the calculat- example, a paying a $12 divi- dend at ed duration as a gauge of sensitivity to interest and selling $100 would have -a current rate changes. In particular,long duration bonds yield of 12 per cent. Assuming that this is would be expected to be highly sensitive to representative of the required return on the interest rate changes, whereas duration security, we can use Equation(5) to calculatethe bonds would be expected to have a low sensitiv- duration of the preferred stock as follows: ity to interest rate changes. Just as we can 1 1 calculate duration for bonds, we can also calcu- d =-= = 8.3 years. k 0.12 late duration for stocks. Dividend payments on stocks are presumed Calculatingthe duration of a common stock is to continue over an indefinite period-that is, similar, except for the need to consider that infinity. Developing a duration for stocks thus common stock dividends are expected to grow

FINANCIAL ANALYSTS JOURNAL / NOVEMBER-DECEMBER1985 O 22 over time. Again using g to represent the Table III Relative Duration-Stocks Versus Bonds growth rate of the dividend, we can amend the previous equation to account for the expected 12131/84 growth in dividends. The equation for calculat- Bonds Coupon $11.70 ing the duration of common stock is then: Maturity 20 years Interest Rate 11.7% 1 Duration 8 years d= . (6) - Stocks k g Dividend $7.53 Growth Rate 9.0 Note that the denominator of the expression Discount Rate 13.5 has the same form as that of the dividend Duration 22 years capitalization model (see Equation (2)). Rear- ranging the dividend capitalization model, we see that: return component and an inflation premium that compensates for the inflation anticipated duration = over an investment holding period. Inflation dividend yield rates vary over time, however, and investors do This, in turn, indicates that stocks with low not always correctly anticipate change in the dividend yields have longer durations than rate of inflation. This results in a risk factor that stocks with high dividend yields and are rela- might be termed "unanticipated inflation," tively more sensitive to discount rate changes. which can cause securities' realized returns to High-growth stocks, which are generally char- diverge from the returns expected on the basis acterized by relatively low dividend yields, of the anticipated rate of inflation. would be more subject to this risk than low- For securities such as bonds, whose cash growth stocks. We would expect high-growth flows (coupon payments) are fixed, an unantici- stocks to carry a higher discount rate than pated increase in inflation results in a decline in lower-growth stocks in order to compensate for price. The decline in price, combined with a this risk. fixed coupon, raises the expected return and Because the measure of duration for stocks is compensates for the higher rate of inflation. similarto the measure of duration for bonds, we Conversely, an unanticipated decrease in the can compare stock and bond durations to deter- rate of inflation lowers returns by increasing mine their relative sensitivities to interest rate price. changes. Using data for a 20-year government Bonds and other fixed-income securities such bond as of the end of 1984, we calculated a as preferredstocks are thus highly vulnerableto proxy bond duration using the standard bond acceleratinginflation-that is, purchasing pow- duration formula. For stocks, we used S&P 500 er risk. By the same token, they are highly year-end 1984 data in the duration formula desirable investments during periods of defla- presented above. tion or disinflation. In fact, bonds provided Table III shows the input data and calculated relatively high returns-7.0 per cent per an- durations for stocks and bonds. At year-end num-during the deflationary period from 1984, stocks were yielding 4.5 per cent and 1929-38, when the CPI declined an average 2.0 showed a duration of 22 years, while a high- per cent per annum, and again provided an grade, 20-year yielding 11.7 above-average return of 14.8 per cent per an- per cent showed a duration of eight years. num from 1981 to 1984, when inflation deceler- Because of their perpetual life and positive ated from 12.4 to 4.0 per cent. growth character, stocks have a considerably For securities such as common stocks, whose longer duration than bonds, which have fixed cash flows (dividends) are flexible, the price of maturity periods and, of course, no growth the security does not necessarily change in characteristics.Stocks should thus be considera- response to unanticipated inflation. Stock divi- bly more responsive than bonds to changes in dends may rise to offset an increase in the rate real interest rates and carry a correspondingly of inflation, precluding any need for price ad- higher premium (via the discount rate). justment. The basic Equation(2) provides a more specific illustration of the ef- Purchasing Power Risk fect. To reflect an unanticipated increase in As noted, nominal returns contain both a real inflation, the equation is augmented by an in-

FINANCIAL ANALYSTS JOURNAL / NOVEMBER-DECEMBER1985 O 23 creased dividend growth rate, 1 + I, as follows: Table IV Inflationand Stock Prices

D(1 + I) 5% Inflation P = - . (7) k(1 + I) - g(1 -+ () Zero 100% 50% Zero Infla- Adjust- Adjust- Adjust- Note that all three variables (dividends, Stock tion ment mrent meint growth and discount rate) have been augment- Dividend 1.00 1.02 1.01 1.00 ed with the inflation factor 1 + I. When infla- Growth Rate 0.05 0.0710 0.0605 0.05 Discount Rate 0.09 0.1118 0.1118 0.1118 tion increases, we would expect the discount Stock Price $25.00 $25.00 $19.69 $16.18 rate to increase by (1 + I) to reflect the higher Price Change, % - - 0 - 21 - 35 rate. If the corporate growth rate and dividend increased directly in line with the inflation in- crease, or to g(1 + I) and D(1 + I), the company Table V CPI versus S&P 500 would offset inflation entirely, and there should be no effect on price. In this case, we can factor Consumer S&P500 out the 1 + I terms as shown below: PriceIndex Year (1967 = 100) IndexPrice Dividends (1 + I)D D PercentageChange p = =. 1947-1950 7.7 33.0 75.0 (1 + l)(k - g) (k - g) 1950-1955 11.2 123.0 11.6 1955-1960 10.6 27.7 18.9 If the corporation cannot increase its rate of 1960-1965 6.5 59.1 39.5 growth in line with inflation, or if there is only a 1965-1970 23.2 - 0.3 15.4 partial adjustment, there should be a negative 1970-1974 26.7 - 26.6 14.6 1974-1980 52.9 98.1 71.1 effect on stock prices. This happens because the discount rate increases more than the growth rate and dividend level, thus resulting in the application of a net higher discount rate. In the Note that during the 1947-65 period, the rate extreme situation where the corporationis com- of increase in dividend income was on average pletely unable to increase growth in the face of considerably above the rate of increase in con- inflation, the dividend resembles a fixed coupon sumer prices. Stock prices also appreciated sig- payment. In this case, stock price, like bond nificantly, and the total return on stocks over price, bears the full brunt of an increase in the the period provided a good hedge against infla- discount rate. tion. But stocks did not provide a hedge against Table IV illustrates the dividend growth ad- inflation during the 1965-74 period. Although justment under three different scenarios-a full dividend growth continued to be positive, it dividend growth adjustment to inflation; a par- lagged the rate of increase in inflation, which tial adjustment-in this case only a 50 per cent had acceleratedto the highest level of the post- adjustment to an increase in inflation; and a war period. Stock prices also declined, provid- zero, or bond-like, adjustment. Note that when ing a net return significantlybelow the inflation inflation increases by 2 per cent, there is essen- rate. More recently, dividend growth acceler- tially no effect on stock prices if growth in- ated and stock prices appreciated; net return creases in tandem with inflation; however, exceeded inflation, and stocks again provided a stock prices depreciate by 35 per cent if there is hedge against inflation. no adjustment and by 21 per cent if there is only These data indicate that, over the long term, a partial adjustment for inflation. How stocks corporations have been able to offset inflation adjust to inflation-that is, which of the three and provide a significant real return to inves- scenarios seems to fit stocks best-is essentially tors. Over shorter intervals, however, corporate an empirical question. performancehas been less steady. On balance, Table V provides some perspective on corpo- it appears that stocks, while exposed to pur- rations' success in offsetting inflation over long- chasing power risk, are less susceptible than er and shorter intervals. It shows price and long-term bonds or preferred stocks.E dividend data from the S&P 500 and the CPI for selected dates from 1947 to 1980, giving the percentage changes in these variables at inter- Footnotes vals over the period as an aid to evaluating the 1. For a descriptionof some of these models, see J.L. responsiveness of stocks to inflationaryforces. Farrell, Guideto PortfolioManagement (New York:

FINANCIAL ANALYSTS JOURNAL / NOVEMBER-DECEMBER1985 O 24 McGraw-Hill,1983). we'll consider that the assumption of continuous 2. The marketline is the empiricalcounterpart to the compounding is appropriate.When discrete com- (SML)of Sharpe et al. and pounding is assumed, the expression is: was pioneered by WilliamFouse at Wells Fargoto 1 +k provide a measure of the tradeoffbetween risk and d= return in the market at a given time. k 3. This expression assumes continuous compound- This expression is only slightly more complex than ing, and for purposes of illustrating duration for the one in the text, but tends to obscure the perpetuities such as preferredand common stocks analyticalexposition.

FINANCIALANALYSTS JOURNAL / NOVEMBER-DECEMBER1985 O 25