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 (k M–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.
Year
1-3
4-6
7-9
10+
Exhibit 1: Bourke Company
Dividend Growth Rate
25%
20%
15%
9%
Current Dividend Do
$7.00/share
V1 = 2.00 (1.25) + 2.00 (1.25)2 + 2.00 (1.25)3
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)
(1.14)9
= 94.21
(15)
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.
Year
-7
8
9
10
11
12+
Exhibit 2: Walgreen Summary
Dividend Growth Rate
13%
12%
11%
10%
9%
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
_____________________________________________________
Current Dividend Do
$.17
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
1.0912
1.08
.09-.08
= 27.24
(16)
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.
(1)
Exhibit 3: TWO STAGE EQUIVALENT DDM FUNCTION
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)
2
P = .17
1.13 +
1.09
1.13
1.09
+ .17
1.139
1.099
1.08 + 1.08
1.09
1.09
(3)
P = .17
1.13
.09-.13
1 - 1.13
1.09
(4)
P = Do 1 + g
k–g
(5)
P = POR 1 + g
Eo
k–g
1 -
+ ....
1+g
1+k
1 -
2
9
9
+ . . . . + 1.08
1.09
+ .17
T
1+g
1+k
1.13
1.09
1.13
1.09
+ Do 1 + gT
k – gT
T
+ POR
9
00
1.08
.09-.08
1+g
1+k
1 + gT
k – gT
= 27.23
T
1+g
1+k
T
The 4th equation is the dividend model in symbolic form. The only variable that changes value is g, the growth
rate. In Stage 1 it has the high growth value g. Then it declines to g T in the terminal or 2nd stage. Reilly and Norton do
not discuss how to find the terminal value of g in any detail. Since g T 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 position 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 earnings per share 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 g T
(.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 POR M, 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.
(1) P =
D1 +
1+k
D2
+
(1 + k)2
D3
+
(1 + k)3
Exhibit 4:
D5
+
D6
+…
(1 + k)4 (1 + km) (1 + k)4 (1+km)4
D4
+
(1 + k)4
(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
(1 + k) (1 + k)2 (1 + k)3
(1 + k)4 (1 + k)4 (1 + km) (1 + k)4 (1 + km)2
(3) P = PORE1 +
E 2 + E4
+
+ k (1 + k)2
PORm
(1 + k)4
E5
+…
+
E6
+…
(1 + k)4(1 + km) (1 + k)4 (1+km)
(3a) E1=Eo(1+g) E2=Eo (1+g)2. . E4=Eo (1+g)4 E5=Eo (1+g)4 (1+gm) E6=Eo (1+g)4 (1+gm)2
(4) P = POR Eo (1+g)+Eo(1+g)2+.Eo(1+g)4 +PORm
1+k
(1+k)2
(1+k)4
(5) P = POR 1+g + 1 +g
Eo
1+k 1+k
(5a)
2
1+g
k-g
(6)
P = POR 1+g
Eo
k-g
(6a)
PORm
(7)
+.. 1+g
1+k
1+gm =
km-gm
P = POR 1+g
Eo
k-g
4
+ PORm 1+g
1+k
1- 1+g
l+k
l - 1+g
1+k
P
4
=
Eo
4
1+gm + 1+gm2 +…1+gm oo
1+km 1+km
1+km
4
1 + gm
km - gm
+ PORm 1+gm
km-gm
1+g
1+k
4
P of the market = market multiplier MM
E
m
l - 1+g
1+k
Eo(1+g)4(1+gm) +Eo(1+g)4(1+gm)2+.
(1+k)4 (1+km)
(1+k)4(1+km)2
4
+ MM
1+g
1+k
4
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.
P/Eo = POR (1+g / k–g) [1 – (1+g / 1+k) T] +POR (1+gT / k–gT) (1+g / 1+k) T. (1)
P/Eo =POR(1+g / k–g) [1 – (1+g / 1+k) T] +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 g M 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:
P/Eo = PORM (1+gM) / (kM–gM) [1+g /1+k] T
(5)
T
P/Eo = MM [1+g /1+k]
(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 Alan Greenspan. 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 “irrational exuberance” in December 1996 and many consider
that this period was a stock market “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 writeoffs 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.
Years
1871-80
to 1890
1900
1910
1920
1930
1940
1950
1960
1871-1960
Table 1: P/E RATIOS-HISTORICAL
P/E
Years
P/E
11.2
1960-72
17.85
16.0
to 1982
9.26
16.1
1994
16.25
13.2
9.7
1960-94
14.76
11.0
16.3
1995-99
24.96
9.7
to 2004
25.19
13.2
2005
17.85
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
modified to P = EPS / 1.33333 iAaa in their 4th Edition. Dividing by EPS and inverting we get E/P = 1.333 iAAA. E/P is
the earnings yield. 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 i Aaa 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 “Fed Model” 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.
Year
1925
1926-29
1930-39
1940-49
1950-60
1961-72
1973-82
1983-94
1995-99
2000-04
2005
Jun 2006
P/Eo
14.855
16.523
10.933
12.847
17.847
9.262
16.247
24.962
25.190
17.850
17.050
Table 2: PARAMETER ESTIMATES
DivYield
PORM
End EPS
gM
Implied (kM–gM)*
1.22e
4.228%
61.715%
1.61
7.180%
4.453%
5.675
90.106
.90
–5.650
5.153
5.719
59.366
2.32
9.932
5.969
4.610
55.025
3.27
3.169
4.419
3.121
55.337
6.42
5.783
3.280
4.344
43.045
12.64
7.009
4.973
3.430
53.757
30.60
7.646
3.562
1.662
39.504
48.17
9.499
1.733
1.518
38.126
58.55
3.980
1.574 **2.24
1.780
31.774
69.93
19.436
2.126 **3.63
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 shares outstanding 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 dividend yield 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 POR M (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
of .51219 is about .50840. The compounded growth rate of EPS from 3.27 (1+gM)45.5 = 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 = k rf + [kM–krf] Beta. 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 investor 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 k M 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).