Based on this general form of DDM, other forms of DDM have been established, such as the zero growth model (Moyer, McGuigan and Kretlow, 2009), the constant growth model (Gordon and Shapiro, 1956; Gordon, 1963), multi-stage model (Brealey, Myers and Allen, 2008), the EBO model (Edwards and Bell, 1961; Ohlson, 1995; Feltham and Ohlson, 1995), the H-model (Fuller and Hsia, 1984), the finite horizon expected return model (FHERM) (Gordon and Gordon, 1997), alternatives to EBO model (Gode and Mohanram, 2001; Gebhardt, Lee and Swaminathan, 2001; Ohlson and Juettner-Nauroth, 2005). These specific DDMs are derived from the basic DDM under certain assumptions as to facilitate the use of DDM to estimate the stock value or the cost of equity capital in practice. The following part of this essay will analyze three restricted forms of DDM: the zero growth model, the constant growth model and the multi-stage model.
Gordon and Shapiro (1956), Gordon (1963) offer the quantitative method for estimating the cost of equity for the stocks that have dividends projected to continuously grow at a constant rate (g). In this case, the shortcut of classic DDM equation is:
Where: is the expected dividend at the end of one year.
By rearranging this equation, the cost of equity capital can be calculated by divide the dividend at the end of one year with the present stock price then minus the growth rate of dividends. In particular, the employment of this model with g equal to zero is called the zero dividend growth model.
As dividend at the end of one year can be estimated by last year's dividend timing the growth rate, estimating the growth rate appears to be the major task when the constant growth model is employed. There are several ways of doing this: (1) Estimate g by considering related factors at the firm level (such as evaluation on the firm's strategic, management; analysis of financial record and ratios) as well as the economy level (changes in macroeconomic that affect the firm's operation) (Arnold, 2008); (2) Take arithmetic or geometric average of past dividend growth rates for g (Gordon and Shapiro, 1956; Ross, Westerfield and Jordan, 2006); (3) Using the analysts' forecasts (Brealey et al., 2008; Moyer et al., 2009); (4) Use the formula in which g is equal to the retention ratio (b) multiply by the rate of return on the book value of equity (r) based on the assumptions that (b), (r) and the debt to equity ratio are expected to remain constant as well as the firm plans to take no outside equity funding (Gordon and Shapiro, 1956; Gordon, 1963).
Under the situation where dividends are expected to grow neither at zero nor constant rate, the multi-stage DDM could be referred to calculate the cost of equity capital (Moyer et al., 2009; Brealey et al., 2008). In this model, dividends are anticipated to grow at differential rates over different periods (different stages) but tend to stabilize, approaching the overall average growth rate of the economy, therefore is expected to appear constant as time goes to infinite horizon (the last stage). As consequence, the cost of equity capital could be figured out by solving the equation where the current stock price is equal to the sum of present value of dividends paid in the first stages and the present value of the stock price at the begin of the last stage (using equation (2)).
Input data required by this multi-stage DDM are: the current stock price, last year's dividend and the growth rates of dividends at different stages. Therefore, it is crucial to come up with reliable expected growth rates of dividends. Again, this objective could be achieved by examining similar factors at the firm and the economy level as mentioned when estimating the constant growth rate of dividends. The multi-stage DDM could be two-stage model (such as H-model; FHERM), three-stage model and so on depending on how detailed the growth rate of dividends could be forecasted.
Example: Using DDM to calculate the cost of equity for PepsiCo
Assume that on average, PepsiCo's future dividends will grow in perpetuity at a constant rate equivalent to the geometric average growth rate over the past 30 years (1980 to 2009). Based on the data on PepsiCo's past dividends and current stock price available at the website of PepsiCo and Yahoo! Finance, the projected growth rate is 11% and the current stock price, last year dividend are $64.64 and $1.8 respectively (see Appendix 2). So according to the constant growth model, PepsiCo's cost of equity is 14% per annum.
However, due to the information about this year's dividend growth rate set at 7% and the growth rate of EPS over the past years is lower than 14% (see Appendix 2), it is supposed that PepsiCo's average future dividend growth rate is less than this figure.
Appendix 2.
PepsiCo's past dividend growth rates:
Year
Dividend
Annual growth rate
1980
0.08
1981
0.08
-
1982
0.08
-
1983
0.08
-
1984
0.08
-
1985
0.08
-
1986
0.12
0.50
1987
0.12
-
1988
0.16
0.33
1989
0.16
-
1990
0.2
0.25
1991
0.24
0.20
1992
0.28
0.17
1993
0.32
0.14
1994
0.36
0.13
1995
0.4
0.11
1996
0.48
0.20
1997
3.72
6.75
1998
0.52
(0.86)
1999
0.56
0.08
2000
0.56
-
2001
0.58
0.04
2002
0.6
0.03
2003
0.64
0.07
2004
0.92
0.44
2005
1.04
0.13
2006
1.2
0.15
2007
1.5
0.25
2008
1.7
0.13
2009
1.8
0.06
Arithmetic average growth rate
0.32
Geometric average growth rate
0.11
Source: http://uk.finance.yahoo.com; http://www.pepsico.com
The future dividend growth rate is assumed to be constant at the rate of 11%, equivalent to the geometric average growth rate over the period from 1980 to 2009.
PepsiCo's stock price is closed at $64.64 on November 12, 2010.
PepsiCo's 2009 dividend is $1.8 per share.
PepsiCo announced to raise annual dividend for the year of 2010 by 7%.
[http://www.pepsico.com/PressRelease/PepsiCo-to-Increase-Annual-Dividend-by-7-ercent-Authorizes-Share-Repurchases-up03152010.html].
PepsiCo's EPS growth rate:
Year
2005
2006
2007
2008
2009
Growth rate of EPS
Year over year
(2.05)
39.75
2.10
(5.87)
17.45
5-year average
10.06
17.84
13.01
9.38
9.09
Source: http://morningstar.co.uk
