An Alternative to the Pure Discount Model

William Carlson, Palumbo/Donahue School of Business, Duquesne University Conway Lackman, Palumbo/Donahue School of Business, Duquesne University

ABSTRACT

The pure dividend model cannot be used to analyze with a zero or nominal dividend payout. Given the recent global financial crisis, this deficiency could exacerbate future global crises. The multiplier model redeveloped here is a general model capable of analyzing such stocks. Two stage models can give the same results as multistage models with fewer assumptions. Graham and Dodd (1962) estimated a multiplier of about 15 for the average S and P . Our update of their results gives a multiplier estimate of 16.4. They used data from 1871 to 1960 for their estimate. We added 1961-94 and 2005-1H06 in our update excluding 1995-2004 which was distorted by the dot.com bubble. Two useful by-product results emerged. It is estimated that the historic value of (kM–gM) is .0354. The terminal market growth rate gM was estimated to be .0711. Combining these two estimates gives an estimate of .1065 for kM which is a key number in the equation. Keywords: , dividend models

INTRODUCTION

The simple (DDM) P = Do (1+g) / (k–g) cannot be used for high growth companies when the growth rate g exceeds the discount rate k. Accordingly, two and three stage models have been created to solve the problem. In turn there are two versions of the multistage model. One, presented in Reilly and Norton can be called the pure dividend discount model. This model has a problem caused by the assumption that the payout ratio does not change (if zero in Stage 1 it is zero in latter stages as well). Hence it cannot be used to analyze companies that do not pay a dividend such as Google, or even companies with a small dividend such as XTO Energy (payout ratio 6%). The other model, contained in Graham and Dodd (1962) can be called the Molodovsky earnings multiplier model. This model can analyze such companies as Google with no difficulty. Molodovsky’s model is described qualitatively in Graham and Dodd. We present it algebraically and show that the key characteristic is flexibility in the payout ratio. The difference between the two models is just two subscripts but the performance difference is enormous. Also there are differences regarding some key parameters. In the Walgreen analysis the high growth stage is expected to last 9 years whereas Graham and Dodd (1962) recommend that the maximum length of the high growth stage be no more than 4 years. A second difference involves the (k–g) term in the terminal stage of the models. Reilly and Norton (2007) assume the difference to be .01 whereas our historical study indicates a value of about .035 for the average stock This difference has a major impact on the relative performance of the two models. There are some problems with the payout ratio market multiplier model. Historical values for key parameters work well for the period 1926-94 even through the Great Depression and WWII. Then came the market “bubble” of 1995-2000 which sent the market P/E multiplier to unprecedented heights. At the same time the formal payout ratio dropped to unprecedented lows due in part to increased informal payouts in the form of stock buybacks. Another complication involves the reliability of earnings reports. The problems were so severe that S and P developed a new measure of earnings called “core” earnings. Using the combined dividend buyback payout ratio suggested by Silverblatt (2006A) parameters seem to have reverted back to more normal values in 2005-1H06. These values allow the analysis of Google, Walgreen, and XTO to show the differences between the pure dividend and multiplier models.

METHOD

Why the Dividend Model Cannot Analyze Zero Dividend Stocks. In Reilly and Norton (2007) in their Exhibit 1 (p.322-3) shows the Bourke Company example. . The Bourke’s dividend of $2.00 appears in every term of the equation which they have written out term by term. Now suppose that the dividend Do is zero as it is for Google. In this case all the terms are zero and the total value is zero.

Exhibit 1: Bourke Company Year Dividend Growth Rate Current Dividend Do

1-3 25% $7.00/share 4-6 20% 7-9 15% 10+ 9%

2 3 V1 = 2.00 (1.25) + 2.00 (1.25) + 2.00 (1.25) 1.14 (1.14)2 (1.14)3

+ 2.00 (1.25)3 (1.20) + 2.00 (1.25)3 (1.20)2 (1.14)4 (1.14)5

+ 2.00 (1.25)3 (1.20)3 + 2.00 (1.25)3 (1.20)3 (1.15) (1.14)6 (1.14)7

+ 2.00 (1.25)3 (1.20)3 (1.15)2 + 2.00 (1.25)3 (1.20)3 (1.15)3 (1.14)8 (1.14)9

2.00 (1.25)3 (1.20)3 (1.15)3 (1.09) + (0.14 – 0.09) = 94.21 (15) (1.14)9 Comment: This equation is crucial. It is direct evidence that if the dividend is zero (as it is for Google) instead of $2.00, the value is zero.

The Bourke case is illustrative. On p. 490-1, Exhibit 2, an actual company, Walgreen, is analyzed. Reilly and Norton (2007) did not write out the equation so we added it at the bottom as equation 1. They also did some rounding off. Taking the results to four places rather than two the value is $27.24 rather than $24.05. The initial dividend Do of $.17 appears in all terms. If the company had paid no the equation would have calculated a value of zero.

Exhibit 2: Walgreen Summary Year Dividend Growth Rate Current Dividend Do -7 13% $.17 8 12% 9 11% 10 10% 11 9% 12+ 8%

Stage 1 vs. Stage 2 Overshoot Years Stage 1 Stage 2 Overshoot 1-6 .13 .13 0 7 .13 .12 .01 8 .13 .11 .02 9 .08 .10 .02 10 .08 .09 .01 11-14 .08 .08 0 ______

P = .17 1.13 + .17 1.132 + .17 1.133 + . . . . + .17 1.137 1.09 1.092 1.093 1.097

+ .17 1.137 1.12 + .17 1.137 1.12 (1.11) + .17 1.137 1.12 (1.11) 1.10 1.098 1.099 1.0910

+ .17 1.137 1.12 (1.11) 1.10 (1.09) + .17 1.137 1.12 (1.11) 1.10 (1.09) 1.08 1.0911 1.0912

+ .17 1.137 1.12 (1.11) 1.10 (1.09) 1.08 1.08 = 27.24 (16) 1.0912 .09-.08

Reilly and Norton (2007) imply that a two stage model could have been used to analyze Walgreen but they chose to use three stage ramp models... We prefer an equivalent two stage model. A problem with their three stage model is that one has to pick two times, how the first stage lasts and how long the second ramp down stage lasts. In the two stage model the job is cut in half since only the time for the first stage is needed. Their Exhibit 3 shows how the three stage model can be reformulated into an equivalent two stage model that gets the same answer. As can be seen in the exhibit the overshoot of the first stage is cancelled by the undershoot of the terminal stage at T = 9 years. The beginning setup is Equation 1. Factoring we get Equation 2. The terms in the brackets are geometric series. Closed form formulas Equation 3. This shows another advantage of the two stage approach, calculations can be made much more quickly than the term by term method needed for the three stage approach. We get the same answer within a penny.

Exhibit 3: TWO STAGE EQUIVALENT DDM FUNCTION (1) P = .17 1.13 + .17 1.132 + .17 1.133 + . . . . + .17 1.139 1.09 1.092 1.093 1.099

+ .17 1.139 1.08 + .17 1.139 1.082 + . . . . + .17 1.139 1.0800 1.099 1.09 1.099 1.092 1.099 1.0900

(2) P = .17 1.13 + 1.13 2 + . . . . 1.13 9 1.09 1.09 1.09

+ .17 1.139 1.08 + 1.08 2 + . . . . + 1.08 00 1.099 1.09 1.09 1.09

(3) P = .17 1.13 1 - 1.13 9 + .17 1.13 9 1.08 = 27.23 .09-.13 1.09 1.09 .09-.08

T T (4) P = Do 1 + g 1 - 1 + g + Do 1 + gT 1 + g k – g 1 + k k – gT 1 + k

T T (5) P = POR 1 + g 1 - 1 + g + POR 1 + gT 1 + g Eo k – g 1 + k k – gT 1 + k

The 4th equation is the dividend model in symbolic form. The only variable that changes value is g, the growth nd rate. In Stage 1 it has the high growth value g. Then it declines to gT in the terminal or 2 stage. Reilly and Norton do

not discuss how to find the of g in any detail. Since gT holds in perpetuity it should not be larger than the long run growth of the economy or the market. If the company grows at say 8% in perpetuity and the economy only 6%, eventually the company would own the whole economy which cannot happen. This is discussed in detail below. The 5th equation is the 4th divided through by Eo to convert it into a P/E model. Do/Eo is the payout ratio POR. In this form the dividend model can be compared directly to the payout ratio multiplier model developed below. The two stage simplification does not solve the zero payout problem. The .17 dividend Do is in all the terms and if Do is zero the function gives a zero valuation as above.

RESULTS

The problem with the pure dividend models is the implicit assumption that the payout ratio does not change. If the initial dividend is zero it (and the payout ratio) stays at zero, even when the growth rate changes. Hence Equations 4 and 5 would give Google a value of zero. Ten years ago Microsoft was in Google’s today, no dividends and no intention to start. Despite Microsoft’s attempts at denial (when a “growth” company starts paying a dividend it is considered by many that the company is no longer the growth company it was in the past) Microsoft finally caved in under pressure to pay a dividend. Someday the same pressures will affect Google. What we need is a model that allows the payout ratio to change. The Payout Multiplier Model – The Role of the One Stage Model. The one stage, or constant growth, or Gordon model: P = D1 / (k–g) [forward version] or P = Do (1+g) / (k–g) [TTM version] is standard in virtually all finance texts. Because the growth of the average stock or the market average gM is less than kM , the market discount rate the model does not go to infinity as it does when g > k. Hence we can use the one stage model to estimate the P/E of the market. The TTM one stage model is converted into a P/E model by dividing both sides by Eo, the of the most recent 12 months: P/Eo = Do/Eo (1+g) / (k–g). But Do/Eo equals POR, the payout ratio. Hence P/Eo = POR (1+g) / (k–g). If we use market values for the variables:

PORM being the payout ratio of the market average or of the average stock, kM being the discount factor for the market, and gM being the growth rate of the average stock, the equation becomes: (P/Eo)M = PORM (1+gM) / (kM–gM). This function is important because it is part of the Molodovsky payout ratio earnings multiplier alternative model. We now can construct the two stage P/E model with a flexible payout ratio which is described in Graham and Dodd (1962) on p. 528-9. The Payout Ratio Model. In the dividend model (Equation 5 derived from Exhibit 3), the only variable that changes value from stage 1 to stage 2 (in Year 9) is the growth rate from g (.13) to the terminal stage growth rate gT (.08). The discount factor k does not change nor does the implicit payout ratio. In the payout ratio model it is assumed that the high growth characteristics of the company hold only through the first stage. In the second stage it is assumed that the company has matured and become an average company with the characteristics of the market average. In the first stage the growth rate is g, the discount factor k and the payout ratio POR. In the second stage the growth rate declines to the market growth rate gM, the payout ratio increases to the market payout ratio PORM, and the discount factor changes from k to kM. Graham and Dodd (1962) on p. 450-1, 514 recommend that the high growth Stage 1 projection be limited to four years. Hence in this model T = 4. They develop the payout ratio model in Exhibit 4. The first line is the traditional setup with one modification. In year 5, the first year of stage two, it is assumed that the discount rate changes from the company value to that of the average company. Line 1a is most important. In Stage One the dividend payout ratio is POR which for a high growth company such as Google currently may be zero. In Stage Two the company is assumed to have the payout ratio of the market average PORM. It is this assumption that gives the model the ability to value such companies as Google. If POR is stuck at zero then the model cannot give Google a value. In line 2 the terms in line 1a are substituted into line 1. Line 3 factors out the POR’s which now are different in the two stages. Line 4 calculates the growth of EPS which is at the rate of g in the first stage and slows to gM in the second stage, analogous to the assumption in the pure dividend model. Given more substitution and factoring, the bracketed series in line 5 are geometric series with the closed form formulas of line 5a. Line 6 shows the function in closed form.

Exhibit 4: (1) P = D1 + D2 + D3 + D4 + D5 + D6 + … 2 3 4 4 4 4 1 + k (1 + k) (1 + k) (1 + k) (1 + k) (1 + km) (1 + k) (1+km)

(1a) D1 = POR E1 D2 = POR E2 . . . D4 = POR E4 D5 = PORmE5 D6 = PORm E6

(2) P = POR E1 + POR E2 + POR E3 + POR E4 + PORmE5 + PORmE6 + … 2 3 4 4 4 2 (1 + k) (1 + k) (1 + k) (1 + k) (1 + k) (1 + km) (1 + k) (1 + km)

(3) P = PORE1 + E2 + E4 + PORm E5 + E6 + … 2 4 4 4 + k (1 + k) (1 + k) (1 + k) (1 + km) (1 + k) (1+km)

2 4 4 4 2 (3a) E1=Eo(1+g) E2=Eo (1+g) . . E4=Eo (1+g) E5=Eo (1+g) (1+gm) E6=Eo (1+g) (1+gm)

2 4 4 4 2 (4) P = POR Eo (1+g)+Eo(1+g) +.Eo(1+g) +PORm Eo(1+g) (1+gm) +Eo(1+g) (1+gm) +. 2 4 4 4 2 1+k (1+k) (1+k) (1+k) (1+km) (1+k) (1+km)

2 4 4 2 oo (5) P = POR 1+g + 1 +g +.. 1+g + PORm 1+g 1+gm + 1+gm +…1+gm Eo 1+k 1+k 1+k 1+k 1+km 1+km 1+km

4 (5a) 1 + g 1 - 1 + g 1 + gm k - g l + k km - gm

4 4 (6) P = POR 1+g l - 1+g + PORm 1+gm 1+g Eo k-g 1+k km-gm 1+k

(6a) PORm 1+gm = P = P of the market = market multiplier MM km-gm Eo m E

(7) P = POR 1+g l - 1+g 4 + MM 1+g 4 Eo k-g 1+k 1+k

A Direct Comparison of the Models Equation 5 derived from Exhibit 3 shows the P/E version of the pure dividend discount model. Equation 6 derived from Exhibit 4 shows the change in payout ratio model. T T P/Eo = POR (1+g / k–g) [1 – (1+g / 1+k) ] +POR (1+gT / k–gT) (1+g / 1+k) . (1) T P/Eo =POR(1+g / k–g) [1 – (1+g / 1+k) ] +PORM (1+gM / kM–gM) (1+g / 1+k) (2) The stage 1 portions are identical. The crucial difference is the payout ratio in the second stage. In the dividend model POR is frozen at the first stage level and if the first stage level POR is zero so is the second stage. In the payout model PORM becomes that of the market. This allows the second stage to take on positive values. Both models assume that the high growth rate g declines to a terminal value. Reillyand Norton’s terminal value permanent growth rate to infinity gT is .08 for Walgreen. We believe that .08 is higher than the permanent growth rate gM of the economy which historically has been about 6% and in economic terms is a fallacy of composition overestimate. The growth rate of the economy is studied below. The last difference is that the discount rate stays at k in the dividend model and changes to kM in the payout model. The Market Multiplier Version. The theoretical value of the market was found to be:

(P/Eo)M = PORM (1+gM) / (kM–gM) = MM (3) This set of terms is in equation 6 of Exhibit 4. Substituting gives Equation 7 of Exhibit 4. Matching the Equation 7 to Molodovsky’s Procedure in Graham and Dodd. If we multiply Equation 7 of Exhibit 4 by Eo and substitute Do for POR Eo we get: P = Do (1+g / k–g) [1 – (1+g / 1+k) T] + MM Eo (1+g) T / (1+k) T (4) This algebraic equation describes the Molodovsky (editor of Financial Analyst’s Journal 1964-69 and pioneering securities researcher) step by step procedure in Graham and Dodd (3, p. 528-9). Molodovsky used T = 10 years in his

example. In Step A he assumed tenth year earnings of $2 per share [Eo (1+g) T]. This is multiplied by a market multiplier MM of 13.5 giving a future value of $27. The discount factor assumed is 7½ % giving a present value factor of 1/1.07510 = .4852. $27 x .4852 = $13.10. In Step B Molodovsky approximates the present value of dividends and gets $6.30, using the first stage term with g = .072 yields an answer of $6.08. Step C adds the answers of A and B. Molodovsky gets $19.30 as the value of a share, our equation gets $19.18. Developing the Payout or Multiplier Model to Analyze Google. We can use either Equation 6 or Equation 7 from Exhibit 5 to analyze Google. Since the current POR is zero Stage One in both equations is zero and the equations are simply: T P/Eo = PORM (1+gM) / (kM–gM) [1+g /1+k] (5) P/Eo = MM [1+g /1+k] T (6) The easiest equation to use is Equation 6. All that is needed is an appropriate market multiplier, perhaps modified by sector characteristics (homebuilders tend to have P/E’s about half the market or even less). In Chapter 37 on The Capitalization Rate for Earnings and Dividends, Graham and Dodd (1962) have two suggestions for finding the multiplier of the market. The first is examining the historical record. The second is their “central value” approach which bears a resemblance to the so-called “Fed” model of . The following table shows Graham and Dodd’s historical P/E data for the Cowles-S and P Index from their Table 37-1 to 1960 along with our summarized updates in Table 1. Graham and Dodd found a P/E of 13.6 for the period 1871-1960. Continuing their table we find that the average P/E from 1960-1994 was 14.76. A problem is caused by the period 1994-1999 which took the P/E to unprecedented heights. Alan Greenspan said the market suffered from “” in December 1996 and many consider that this period was a “bubble”. Also it is almost certain that the earnings for this period are overstated and P/E’s understated. Liesman and Weil (2001) note that the “idea that prior profits have been overstated helps economists explain what to them was one of the mysteries of the late 1990s. Generally, corporate profits have grown in line with the economy. For the past five years, however, S and P 500 profits have expanded about twice as fast as the economy’s total output.” They note that write- offs for the six month period ending March 31, 2001 were the highest by far for any such period. The implication is that the huge write-offs meant that past profits had been overstated. The accounting problems and controversies were so severe that Standard and Poor’s felt compelled to develop a new concept called “core” earnings. in a release of May 14, 2002.

Table 1: P/E RATIOS-HISTORICAL Years P/E Years P/E 1871-80 11.2 1960-72 17.85 to 1890 16.0 to 1982 9.26 1900 16.1 1994 16.25 1910 13.2 1920 9.7 1960-94 14.76 1930 11.0 1940 16.3 1995-99 24.96 1950 9.7 to 2004 25.19 1960 13.2 2005 17.85 1871-1960 13.6 Jun 2006 17.05

Earnings controversies continue. There are GAAP earnings, operating earnings, core earnings, company “pro forma” earnings (see Google, SanDisk, QLogic, etc. press releases), and other analyst (First Call, etc.) earnings. And now we have the stock option backdating scandal. We consider the high P/E 1994-2004 period to be an abnormal period, an outlier that should be disregarded. It appears from 2005 data and the first half of 2006 that we have returned to a more normal P/E, the most recent being 17.05. If we ignore the abnormal 1994-2004 period the long run P/E over 124 years (2004-1871 + 2005) is about 15 which is exactly what Graham and Dodd found in their 1962 book p. 511.

Graham and Dodd’s (1962) second method of finding a market multiplier is their central value method. Originally it was (S and P data):

P = EPS / 2 iAaaMoody’s, where the interest rate is the 3 year moving average rate on Moody’s Aaa bonds. It was th modified to P = EPS / 1.33333 iAaa in their 4 Edition. Dividing by EPS and inverting we get E/P = 1.333 iAAA. E/P is the . The implication is that if the earnings yield is greater than 1 1/3 the Aaa rate the market is undervalued. If E/P is less than 1.333 times the Aaa rate the market is overvalued. And if E/P is equal to 1.333 iAaa the market is fairly valued. As of June 2006 the 3 year Aaa average was 5.5075% implying a fair value E/P of 7.3433% and a P/E of 13.62. This model is quite similar to the “” popularized by Alan Greenspan in 1997 which compares the earnings yield (E/P) of the S and P to the yield on the 10 year Treasury bond. As above, if the earnings yield is greater than the yield on the 10 year the stock market is undervalued, etc. With the 10 year Treasury at 4.60% the fair value forward P/E is 21.74 (Note: The 12 month earnings for the S and P in September 1929 were $1.63, the index 31.30 for a P/E of 19.20). We believe the P/E from the Fed formula is too high.

Another approach is to estimate the parameters of the one stage model: P/Eo = PORM (1+gM) / (kM–gM). Table 2 has S and P yearly data from 1926 (we intend to redo this work with quarterly data, another project is to use “real” or inflation adjusted data). A condensed summary is shown in Table 2.

Table 2: PARAMETER ESTIMATES * Year P/Eo DivYield PORM End EPS gM Implied (kM–gM) 1925 1.22e 1926-29 14.855 4.228% 61.715% 1.61 7.180% 4.453% 1930-39 16.523 5.675 90.106 .90 –5.650 5.153 1940-49 10.933 5.719 59.366 2.32 9.932 5.969 1950-60 12.847 4.610 55.025 3.27 3.169 4.419 1961-72 17.847 3.121 55.337 6.42 5.783 3.280 1973-82 9.262 4.344 43.045 12.64 7.009 4.973 1983-94 16.247 3.430 53.757 30.60 7.646 3.562 1995-99 24.962 1.662 39.504 48.17 9.499 1.733 2000-04 25.190 1.518 38.126 58.55 3.980 1.574 **2.24 2005 17.850 1.780 31.774 69.93 19.436 2.126 **3.63 Jun 2006 17.050 1.845 31.467 74.49 13.467 2.094 **3.68 * equals PORM (1+gM) / (P/Eo). ** with buyback adjustment from Graham and Dodd’s Exhibit 5.

The “Bubble” and Other Problems It is evident from Table 2 that the 1995-2004 behavior was quite different from the preceding seven decades (and even back to 1871 from the Graham and Doddd and Cowles Commission P/E data). One cause is the bubble which raised P/E’s to historic heights. But this does not account for the decrease in the payout ratio. There are perhaps four reasons why the payout ratio has decreased. The first reason was tax efficiency. When the tax rate on dividend income exceeded the rate on capital gains it was cheaper for the company to distribute funds by buying back stock rather than paying dividends A fairly well known case (Nyberg, 2001) is that in 2001 when the CEO of Ultramar Diamond Shamrock announced a stock buyback financed by a dividend cut the stock rose 4% immediately. The second reason stock buybacks are a good substitute for formal dividends is that buybacks are flexible. An increase cash dividend is considered to be a commitment to maintain it in the future and cuts, if not done for the Ultramar reason, may lead to the stock being punished. Stock buybacks do not necessarily promise a long term commitment and can be discontinued. Stock buybacks for these reasons should count as dividends. There is a third reason for stock buybacks. Executive stock option grants have increased for many companies substantially. Frequently companies buy back stock to reduce the dilution caused by the stock option programs. These repurchases are not dividends but an indirect recognition of executive pay. Standard and Poor’s, Howard Silverblatt, has been concerned about the and payout problems as exposited in his pioneering articles (Silverblatt, 2006A-C). The articles contain S and P buyback data identified in

Table 3 along with our adjusted payout ratios for 1999-2005 (we are hoping to get more buyback data from S and P back to at least 1993). The “new” idea of S and P is to consider that buybacks are dividends in disguise. In Silverblatt (2006A) article dividends and buybacks are added together and the combined dividend and buyback yield calculated. Similarly we combine dividends and buybacks to get the combined dividend and buyback payout ratio in Table 3. There are two problems, one minor and one major. The minor problem is the set of accounting problems particularly write offs that plague the “As Reported Earnings” (GAAP) numbers especially hard in 2001-2. Accordingly we use adjusted operating earnings as a replacement for the GAAP numbers (378.64 replacing 253.50 for 2002 and 313.87 replacing 222.74 for 2001) as calculated in the footnote. Without this adjustment the 2001-2 results are junk outliers. The major problem is that the combined dividend buyback payout ratio (POR Div+BB) is far too high with values higher than all 1926-94 periods except the Great Depression. Counting all buybacks is “overkill”. But some buybacks should not be counted. Stock bought back to counter the dilution from stock option grants should not be counted as dividends since that is essentially an indirect payment to management for services rendered. Silverblatt (2006B) mentions that some shares are accumulated for mergers and acquisitions, and these repurchases should not be counted as dividends either. This article states that “the issuance of shares to cover employee stock options is still a major component of buybacks”. It would be nice to have the percentages of buybacks due to stock option activity, mergers, and dividend substitutes available but unfortunately such data is not available currently. Accordingly we make a simple assumption, that the major component of buybacks due to options as well as potential merger activity is 60% of buybacks leaving 40% as a dividend proxy. The column POR Div+.4BB is the payout ratio measured as dividends plus 40% of buybacks divided by the As Reported Earnings (which is the series that goes back to 1926 and before).

Summarizing the Historical Data for the PORM (1+gM) / (kM–gM) Approach

Using the adjusted data and even counting the .0224 value for 2000-4 the (kM–gM) has a post 1960 value of about .0354 (the 1926-60 average is about .0508). The post 1960 payout ratio including the adjusted 2000-05 value 45.5 of .51219 is about .50840. The compounded growth rate of EPS from 3.27 (1+gM) = 74.49 is . 0711. Substituting into the function gives a market multiplier for the average stock of 17.67. S and P Data (website and articles). Copying Graham and Dodd we average this with the 15 from the historical P/E study to get an estimated market multiplier of 16.4. With the latest S and P P/E at 17.10 or so the market as of June 06 would appear to be near historic fair value.

Note about kM. If (kM–gM) = .0354 and gM = .0711 then kM = .1065.

USING THE MULTIPLIER TWO STAGE MODEL TO ANALYZE GOOGLE

The pure dividend model gives a value of zero to Google because the current dividend is zero. But the multiplier model can be used. It is simple because the first stage is zero. The formula is: P/Eo = MM [1+g / 1+k] T. (7) The first task is to pick an appropriate multiplier MM. If we were analyzing Lennar in the home construction business and use the 16.4 multiplier we would find it a super buy because it has a current P/E of only 5.35 (industry 5.00) and for all reasonable values of g, k, and T the formula gives a higher value. The 16.4 is for an average stock in average times. Industry characteristics must be taken into account. As for Google it is a unique company. Its only real competitor at the moment is Yahoo which has a P/E of 29.8 at this time (Yahoo Finance has an industry P/E of 41 but who else is in the industry?). Graham and Dodd have a comment about P/E targets for individual stocks, p. 514. An upper limit would be 20 times earnings 4 years hence. Judgment is used to set the multiplier between 7 and 20. Being a little conservative let us say that even Google does not deserve a 20, let us use 19. Setting T. Reilly and Norton used 9 years for Walgreen. Graham and Dodd and set T at a maximum of 4 as mentioned several times above. As an experiment we will try T = 9 to see what happens. Then we will use T = 4.

Finding k. We use the security market line approach where k = krf + [kM–krf] . Above we found k = .1065. Many analysts use the rate on the 10 year Treasury for k. It is .0463 currently (Oct. 1). Yahoo Finance gives Google a beta of .66, Reuters .89. Being conservative we use Reuters. Hence k for Google is estimated to be .0999.

Finding g. Google’s sales and EPS growth rates have been in the 70-90+% range but let us assume 55%. Eo = 6.85. Using T = 9: P/6.85 = 19 [1.55 / 1.0999]9 P = 2852.66 (8) T = 9 gives an answer reminiscent of the dot.com days of 1999. Using T = 4 gives a fair value price of $513.28. The Impact of Excluding 1994-04 Data. If we had included the bubble, aftermath, and accounting problem years 1994-04 in the analysis the historic multiplier would have been about 18 rather than 16.4, a difference of 1.6. If we increase Google’s multiplier proportionally by the same amount it becomes 20.85 and Google’s estimated fair value becomes $567.26. This is an aggressive estimate; the $513.28 estimate is more conservative. In general there are costs of being too conservative or aggressive. If an is too conservative or selective stocks that go up will not be bought, an opportunity cost. An aggressive investor will buy more stocks that go down. This situation is similar to the Type I and Type II errors in sampling theory. Case of XTO Energy. This is a company with dividends but the payout ratio is only 6% or .06. It gives us a chance to compare the results of the pure dividend model versus the multiplier model. Parameter values: Beta = .94 giving a k of .1029. Growth g is measured by projections of real product production of natural gas of 21% which it has been doing for the past decade. The value of the first stage of both models is: .06 (1.21 / [.1029 – .21]) (1 – [1.21 / 1.1029]4) = .3042 (9) The Multiplier Model Result.The industry multiplier is less than 16.4 at 13.1 (Yahoo Finance). Natural gas being quite volatile to be conservative we drop the multiplier to only 9. The +second stage is: 9 [1.21 /1.1029]4 = 13.039 (10) The estimated value is P / 4.94 = .3042 + 13.039. P = $65.91 (11) The Pure Dividend Model. The second stage is from Equation 5 of Exhibit 3. It keeps the POR of .06. We assume a terminal growth rate of .0711. Substituting: .06 (1.0711 / [.1029 – .0711]) (1.21 / 1.1029)4 = 2.9279 (12) The estimated value is P / 4.94 =.3042 + 2.9279. P = $15.97. (13)

Case of Walgreen Reilly and Norton found a value of $27.05 (27.25 without rounding errors) using the dividend model. We use the following for the multiplier analysis. As Reilly and Norton assume g = .13. They say that WAG deserves a premium multiplier, we agree so MM = 20 (even higher than Google). Reilly and Norton assumed a risk free rate of .05 and a beta of .90 which, using kM = .1065 gives a k of .05 + (.1065 – .05) .90 = .10085. Their 2004 Do was .17 and the implied Eo was 1.264 (it was 1.31 actually from the 2005 10K) giving a current POR of .1345. (k–g) = .02915. Then: P/1.264 =.1345 (1.13 / -.02915) [1 – (1.13 / 1.10085)4] + 20 (1.13 /1.10085)4. (14) P = $28.79 which is fairly close to Reilly and Norton. The pure dividend model can work for companies with a payout ratio in double digits, just not for zero payers like Google or nominal payers like XTO.

CONCLUSION

The pure dividend model cannot be used to analyze stocks with a zero or nominal dividend payout. The multiplier model redeveloped here is a general model capable of analyzing such stocks. Two stage models can give the same results as multistage models with fewer assumptions. Graham and Dodd (1962) estimated a multiplier of about 15 for the average S and P stock. Our update of their results gives a multiplier estimate of 16.4. Graham and Dodd (1962) used data from 1871 to 1960 for their estimate. We added 1961-94 and 2005-1H06 in our update excluding 1995-2004 which was distorted by the dot.com bubble and aftermath along with massive accounting problems. Excluding 1994-04 is a conservative assumption.

Two useful byproduct are that the estimated historic value of (kM–gM) is .0354 and the terminal market growth rate gM was .0711. Combining these two estimates gives an estimate of .1065 for kM which is a key number in the security market line equation.

It appears that the market has returned to more normal levels in 2005-1H06. But one factor has not, the dividend payout ratio. Silverblatt (2006A-C) has created the dividend plus buyback yield which we transformed into a dividend plus buyback payout ratio. and then modified that to a dividend plus .4 buyback payout ratios. More work remains to be done on this problem. Given the recent global financial crisis, this deficiency could exacerbate future global crises.

IMPLICATIONS FOR FURTHER RESEARCH

More test cases would help build an actuarial basis for predicting how often the existing approach gets the wrong answer. More investigation of potential added variables that could reconcile the approaches is needed.

REFERENCES

Graham, B. and D. Dodd (1962), Security Analysis: Principles and Techniques, Leisman, S. and J. Weil (2001), Disappearing Act, Wall Street Journal, (July 13). Nybert, A. (2001) Buybacks at Ultramar Diamond Shamrock, CEO Magazine, (April). Reilly, F. and E. Norton (2007), Investments, Englewood Cliffs, NJ: Prentice-Hall. Silverblatt, H. (2006A), “Buybacks and the Impact of Share Count Reduction”, Wall Street Journal, (March 24). Silverblatt, H., (2006B), S&P 500 Buyback Activity Continues “, Wall Street Journal, (June 12). Silverblatt, H. (2006C), The buyback section of “Record” Company Cash Levels Producing Significant Interest Income”, Wall Street Journal, (May 24).