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An Alternative to the Pure Dividend Discount Model

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An Alternative to the Pure Dividend 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 stocks 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 stock. 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 security market line equation. Keywords: Dividend policy, dividend models INTRODUCTION The simple (DDM) dividend discount model 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 valuation 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 3 3 3 2.00 (1.25) (1.20) (1.15) (1.09) + (0.14 – 0.09) = 94.21 (15) 9 (1.14) 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 dividends 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 long 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 yield 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 terminal value 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.
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