Holt (Influence of Growth Duration on Share Prices)

8/13/2019 Holt (Influence of Growth Duration on Share Prices)

1/12

T HE I NF L UE NCE OF GROW T H DURAT I ONON SHARE PRICES*

CHARLES C . HoLTf

INTRODUCTION

T H E SPECTACULAR INVES TME NT performance of growth stock s inrecent years has focused attention on the problem of evaluating thesecurities of fast-growing companies. Unfortunately, methods forplacing valuations on such securities are not yet adequately de-veloped, and investors make their buy-and-sell decisions as best theycan.

T ha t a company's high rate of grow th may come to an end is animportant, but little-emphasized, investment consideration in theevaluation of growth stocks . To call attention to this poin t, we presen tin this paper an exploratory analysis of the relationship betweenprice-earnings ratio, rate of growth, and the duration of growth. Inomitting risk from the present analysis, we are explicitly neglectingthe fact that investments in growth stocks are often riskier than innon-growth stocks. Consistent with this, the capitalization rates forboth kinds of securities are assumed to be the same, and hence anydifferences in their price-earnings ratios are attributable to differ-ences in their growth of earnings.

The obvious investment success of growth stocks has led investorsto seek out iJiese securities for purchase, with the result that theirprices have been driven up so th at growth stocks now generally carryhigh price-earnings ratios. But just how high it is wise for investorsto drive price-earnings ratios is not clear. If a growth stock is eval-uated by discounting future growing dividends back to the present,the paradoxical result is obtained that an infinite price-earnings ratiois justified for a stock whose dividends per share are expected togrow at a per cent per annum) rate that is higher than the discountrate. This clearly untenable result comes from the implicit assump-

tion of an indefinite continuation of exponential growth and may beConversations with M H; MOler and F Modigliani supplied much of the stimula


2/12

466 The Journal of Finance

avoided by limiting the assumed growth period.^ Another method^has received considerable attention in investors' literature and seemsto have had considerable infiuence. The growth in earnings per shareof a company is extrapolated, say five years into the future, at thegrowth rate indicated from the recent past. The current price of thestock is divided by this forecast of earnings five years hence, to ob-tain a price-earnings ratio. In this way, more normal, i.e., lower price-earnings ratios are obtained for growth stocks and some useful indi-cation is given on whether the existing price of the security is justifiedor not. However, this method is rather crude in ignoring any divi-dends that might be received during the five-year period or growth

that might occur after this arbitrarily selected period.D U R AT I O N OF GROWTH

If investments in the common stocks of growth companies were ex-pected to continue growing indefinitely at a constant exponential rate,then the investor's problem would be largely one of selecting thecompanies with the highest forecasted growth rates.* But before any-one chose to follow such an investment policy, he would be well ad-

vised to question seriously the assumption of indefinitely continuedgrowth. Studies of the past growth in the applications of inventionsand in the sales of companies and industries show growth curves inwhich very high rates of growth are achieved initially, but ultimatelythe growth rates tend to slow down or stop as maturity is reached.This logistic type of growth curve is rather complicated, and the fore-casting of its leveling-off is quite difficult from both the statistical andthe forecasting points of view. Although we shall not attempt thisdegree of refinement, it does seem desirable to assume that the

1. 0. K. Burrell, A Mathematical Approach to Growth Stock Valuation, FinancialAnalysts Journal, XVI (May-June, 1960), 69-76; John C. Clendenin and Maurice VanCleave, Growth and Common Stock Values, Journal of Finance IX (1954), 365-76.

2. Julian G. Buckley, A Method of Evaluating Growth Stocks, Financial AnalystsJournal,X.\ I (March-April, 1960), 19 21 .

3. The more subtle point that the dividend returns from a growth stock are fartherin the future tlian those from non-growth stocks and hence that forecasts of the divi-dends are riskier has not been adequately treated as yet, nor will it be considered here.See David Durand, Gro-ivth Stocks and the Petersburg Paradox, Jotirnal of Finance,XII (September, 1957), 348-63; and Henry Allen Latane, Individual Risk Preference

in Portfolio Selection, Journal of Finance IV (March, 1960), 45-52.4. For a moi c refined analysis ol growth see M. H. Miller and F. Modigliani, Divi-

dend Policy Growth and the Valuation of Shares Journal of Business XXXIV


3/12

Injluence oj Growth D uration on Share Prices 467

growth opportunities of a gro wth company are likely at some pointin time to slow down to the rate that is normally achieved by com-panies generally. Presumably, this more modest growth rate can be

maintained indefinitely. As the period of high growth passes, theprice-earnings ratio of a company will drop back to the normal levelcharacteristic of non-growth stock s. Th is perhaps distant, bu t al-most inevitable, decline in price-earnings ratio constitutes one of theimportant risks of investing in a growth stock, especially since thetermination of rapid growth is so difficult to forecast.

T o simplify m atters , we shall make the assumption th at th e growthin earnings per share (adjusted for stock dividends and splits) of a

company w ill continue a t a high co nstant exponential rate u ntil somepoint in time when the rate drops abruptly to the average rate fornon-growth companies. Under this assumption, the duration ojgrowth for a company becomes a simple concept, i.e., the time dura-tion of the high growth rate. Clearly, companies with long durationsof growth should be valued more highly than those with short dura-tions of growth, other things being equal. Also companies with highgrowth ra tes of earnings should be valued higher than companies withlow growth rates, other things being equal.

Both the duration and the rate of growth need to be taken intoaccount in valuing a growth stock. One way to do this is to considerthe following question. How long, at a minimum, will the presenthigh rate of earnings growth of a company have to continue in orderto attain the same level of earnings that can be achieved by an alter-native investment in non-growth stocks of comparable risk? Assumethat beyond Ithis time the high growth rate drops to the normal rate,the low dividend pay-o ut rises, and the high price-earnings ra tio falls

so that the two investments become virtually equivalent. In sayingthis, we have, of course, roughed over the uncertainty problem bj^assuming comparable risk for both investments. This time is theminimum required growth duration for the growth stock to justify itshigh price-earnings ratio. Of course, in both cases we need to takeinto Eiccount the dividend jdelds.

If we can formulate an analysis for determining the duration ofgrowth estimate that is implicit in the market price of a growth stock,

this may be useful to investors in making judgm ents as to whe ther th ehigh price-earnings ratio of the growth stock is justified or not. Web i h k ' i f d i f h f ll If


4/12

468 The Journal oj Finance

the present, when / = 0) and let ^E be the per cent per annumgrowth rate of earnings per share, then an estimate of future earningsper share as long as this growth rate continues is given by the follow-

ing expression:E ' (O= ' (O) (1 - | -A ) ' . ( 1 )

It is convenient for analysis to assume the reinvestment of divi-dend income to obtain additional growth so that it can be com-bined simply with the above expression.' This is done by pretendingthat the dividends are used to buy more (perhaps fractional) sharesof the same stock. This assumption is purely for analytical purposes,to put all securities on a common no dividend payment basis.

Thus if D is the constant per cent per annum dividend yield (i.e.,ratio of dividends to market price), the number of shares N{t) at theend of year t is

+ D ) , ( 2 )

assuming that one share was bought originally when ^ = 0. The totalearnings E{t) at the end of year t on the original and purchasedshares combined are

E{t =E {t N{t = ' (0 ) [ (1 -FAE) (1 + > ) ] ' . (3)

ince D and AE are "small" and for the one original share E {0) =E ( 0 ) , we obtain

4)

This growth measurement of investment return is equally appli-cable to growth and non-growth stocks. We apply it to both and intro-duce the subscript g to indicate a growth stock and the subscript a to

indicate an alternative non-growth stock of comparable risk.After the duration oj growth, which we designate as T, we haveassumed that the growth stock has the same general characteristicsas the non-growth stock. Hence in the year r their market values willbe in direct proportion to their earnings of that year.'' Since uncer-tainty has been left out of our analysis and since no dividends arewithdrawn, we would expect that the market would tend to value theshares of the two stocks for current purchase in direct proportion totheir value in year r and hence in direct proportion to the forecastedearnings in the year r. If this proportionality condition were not

5 Th i li l i f l di i i b di id d i d i l i


5/12

Influence oj Growth Duration on Share Prices 469

satisfied, investors would tend to buy the relatively underpricedstock., in order to be in a better position in the year T, thereby drivingup the low price. T hu s the m arket will tend to satisfy this relation be-

tween the current share prices of the growth and the non-growthstocks, Pa{0) and P


6/12


shown by the heavy sloping line through the origin of Figure 1. Tintersection of these two lines determines a p oint labeled A Droppingvertically we can read from the horizontal scale th at the m arket esm ate of duration of growth is evidently 6 yea rs. T ha t is to say tmarket is valuing the growth stock as if its present high rate ofgrowth would continue for 6 years and then decline sharply to t

Relative Growth Rate

6.0

5 .0

4 . 0

.2 3 .0

P : 2 -0

1.40 1.30 1.20

i

A

/

/

/

/

/

t

1.1

1.1

1.0


7/12

Injluence oj Growth D uration on Share Prices 471

normal level. The graph has made it easy to find that T == 6. Thi svalue, of course, satisfies equation (6) for this exa.mple:

3 + 0.01Y15 ^V l - f -0 .05- f 0 .05

Another way to interpret the six-year growth duration is in termsof total growth potential. A 30 per cent growth rate is, say, 25 percent above the normal growth rate, taking the non-growth stock asthe sta nda rd. If this rate continues for 6 yea rs, we would have a tota lgrowth poten tial of (1.25)* = 3.82 or 382 per cen t. Th is amounts toforecasting that the ratio of earnings per share of tlie growth stock tothe non-growth stock will ultim ately improve b y almost a factor of 4.

A N ILLUSTRATION USING MARKET DATA

The use of this analysis may be illustrated by selecting the Dow-Jones index as a representative alternative non-growth investment,and selecting the following growth common stocks: Ampex, Interna-tional Business Machines, Litton, Polaroid, and Texas Instruments.The dividend yields and price-earnings ratios for May, 1960, wereused.

For the Dow-Jones index, the price earnings ratio Pa Ea was 18,Da was 3 per cent per y ear, and AEa was 5 per cent per year. Th eseforecasts were extrapolations of the previous 5 ye ar s history . W ehave obtained AEg for each of the growth companies by plotting onsemilog paper the earnings per share, adjusted for stock splits andstock dividends, for 1956 through 1959 and estimated the slope.

Before plotting points for each growth com pany. Figure 1 wasmodified by changing its scales to incorporate the Dow-Jones index

as the standard non-growth alternative^ (see Fig. 2). Plotting theseda ta on Figure 2 indicates the growth du ration periods shown in thesecond column of Table 1. In interpreting these results, one istempted, at first blush, to say that Litton is the better buy because itwill justify its high price-earnings ratio relative to a Dow-Jones in-vestment in a shorter period of time than the other companies. How-ever, valid conclusions require a comparison for each company be-tween the m arket estim ate of dura tion of growth and the investor sown estimate. The investor can compare his judgments with thoseof the market and act accordingly where he feels the market is inerror Clearty if growth duration actually proves to be longer than


8/12

7 The Journal oj Finance

purchase. A stock with growth duration shorter than the markestima te will prove to have been a poor investment. As always, the ivestor must bet that his forecast is better than that of the market.

he can forecast growth durations successfully, growth stocks maoffer important investment opportunities.

This analysis may be used in another way. An estimate of th

Growth Rate {^E, -f

25

100

90

80

70

60

5 0

4 0

30

20

i

/

^

/

/ /

^~

///

//

111J

/

/

/

//

50/

//

T I

1

//

/

/

40

j1 ?_

_//

/

/

/

/

IBM

/

/

- ^

.

30/

/

/

/

/

/

/

/

/

. . -

20

15

10


9/12

Influence of Growth Duration on Share Prices 7

growth duration for a company may be made by the investor and thecorresponding line draw n vertically on Figure 1 or F igure 2 until itintersects the sloping grow th-rate line and then move left horizontally

to read the price-earnings ratio. This is the price-earnings ratio thatwould be warranted by this duration of growth. This could be com-pared with the price-earnings ratio existing in the market and pur-chase-sell decisions made accordingly.

ADJ US TM ENT F OR TAXES

An extension of the analysis might well take into account the factthat long;-term capital gains are taxed at an advantageously low rate,

so that income through price appreciation is more desirable thanTABLE 1

Company

Ampex. . .

International Business Machines...LittonPolaroidTexas Instruments

Market Esti-mate of

Durationof Growth

Years)

4 .1

7.53 46 35 .3

Adjustedfor Taxes

Years)

4.2

7.53 46 8 7

dividend income. An exact adjustment for taxes would greatly com-plicate the analysis, but, by ignoring the fact that capital gains taxesare postponable, we may make an approximate adjustment. By mak-ing the simplifying assumption tha t capital gains are taxed in the year

in which they occur, we can modify formula 7) to refiect grow thafter taxes.The growth from dividend reinvestment is reduced by taxes to

1 KD D, where KD is the m arginal tax rate applicable to dividendincome. Similarly, the growth of earnings is reduced to 1 Kc ^E,where Ko is the marginal tax rate applicable to capital gains income.A person whose marginal income tax rate was 30 per cent would betaxed a t half th at r ate on capital gains, i.e., KB = 0.3 and Kc = 0.15.The maximum Ko is, of course, 0.25.

Recalling that the price-earnings ratio of the growth stock falls asthe term ination of the high growth ra te ap proaches we need to recog


10/12


by applying the capital gains tax to the decline in price-earningsratio. If we rewrite the left pa rentheses of formula 7) ,

PJE, Pa/Ea+{Pa/Eo-PJEa)

we can interpret the right parentheses in formula 8) as the capital loss component for the growth stock as the result of the reductionin price-earnings ratio to that of the non-growth stock. We ap ply thecapital gains tax to this loss adjustment by multiplying the lossterm by 1 Kc):

PjEa+ {PJE,-PJE,) ji-Kc) , y/Pg/Eo

Incorporating the above adjustments in formula 7) , we obtain

1 0 )

n + i-Kc)AE+ l-KD)D,l+ 1 - Kc AEa+ {1 -

The inclusion of the tax adjustm ent does not complicate thegraphs, but it does complicate somewhat the computation step beforentering the graphs. The effect of the adjustment will be to reflectthe preference of the high-income person for companies that do notpay out their growth in the form oi dividends. Applying this adjust-men t to the com panies tha t we have alread y considered and assuminan investor whose tax rates are KD = O.S and Kc = 0.2S, we obtainthe overtake periods shown in the third column of Table 1. In thiscase, the overtake periods were not greatly affected by the adjust-ment for taxes.

CONCLUSION

Four limitations of this analysis need to be noted. Firstan d mostimportantthe uncertainty of forecasting earnings in the distantfuture is a much more important consideration for growth stocksthan for non-growth stocks. Hence, ignoring the risk inherent inprobabilistic forecast errors is an im po rtan t om ission which will tend

to make growth stocks appear more attractive than they really are.Second, the analysis rests on forecasts of constant earnings-per-share


11/12

Influence of Growth D uration on Share Prices 47 S

which may reflect increasing risk rather than growth. Third, therelative tax advantage of capital gains income, which is the principalreturn from growth stocks, is somewhat understated by neglectingthe deferred collection of the capital gains tax, so that growth stocksappear less attractive than they really areespecially for high-income investors. Fourth, we hardly expect the growth of earningsto terminate sharply but, rather, would expect the growth rate todecline gradually as the special advantages enjoyed by the growtlicompany are whittled away by increasing competition, expiration ofpate nts, appearance of substitute produ cts, etc. Th us the high growthrate would tend to last longer than the above analysis would indicate,but the rate of growth would be reduced.

T he need for a really adequate th eory of investment und er ce rtain-ty is emphasized by the gross approximations that were used in thisexploratory analysis. Granting these limitations, the analysis doesoffer a systematic framework for evaluating growth stocks that in-cludes many of the relevant variables with a minimum of complexityand computation. Hopefully, the analysis is simple enoughevenusing the adjustm ent for taxes to be useful to investors.*

8. An independent, but equivalent, analysis by iRobert Ferguson has recently yielded

a nom ograph which reduces the com putations to a simple mechanical procedure ( ANomograph for Valuing Growth Stocks, Financial Analysts Journal XVII [May-June, 1961], 29-34). Unfortunately, the underlying assumptions of his analysis arenot fully explicit.


12/12

Holt (Influence of Growth Duration on Share Prices)

Documents

Transcript of Holt (Influence of Growth Duration on Share Prices)