The Dividend Discount Model (DDM) was first developed by Williams (1938). This model allows the cost of equity capital to be estimated based on the premise that in the equilibrium market the stock price is equivalent to the sum of present values of all expected future dividends generating from holding the stock. The discount rate that equates the stock price with the sum of discounted future dividends is the required rate of return on equity investment or the cost of equity capital.
Where:
Po: Current stock price.
Dt: Expected dividend at time t.
: The cost of equity capital.
As long as the data of current stock price and expected dividend payments are available, the cost of equity capital can theoretically be calculated by solving this equation.
Based on the above general form of DDM, other forms of DDM have been established, such as the DDM with dividends remain unchanged (Moyer, McGuigan and Kretlow, 2008), the DDM with constant dividend growth rate (Gordon and Shapiro, 1956; Gordon, 1963), multi-stage DDM (Brealey, Myers and Allen, 2008), the model which is often referred as EBO model constructed by Edwards and Bell (1961), Ohlson (1995) and Feltham and Ohlson (1995), the finite horizon expected return model (Gordon and Gordon, 1997), alternatives to EBO model (Ohlson and Juettner-Nauroth, 2000; Gode and Mohanram, 2001; Gebhardt, Lee and Swaminathan, 2001). 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.
This essay analyzes the employment of three restricted forms of DDM to calculate the cost of equity capital: the zero dividend growth model stated by Moyer et al. (2008), the constant dividend growth model proposed by Gordon and Shapiro (1956) and Gordon (1963) and the multi-stage model suggested by Brealey et al. (2008).
Moyer et al. (2008) suggest that for the corporations that exhibit stable expected dividends stream, the formula of general DDM can be written as:
As a result, the cost of equity capital is equal to the dividend divided by the stock price. Both of these data are publicly available so as can be collected to calculate the cost of equity for this dividend pattern.
Gordon and Shapiro (1956) 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 should be as followed:
Where: is the expected dividend at the end of one year.
By rearranging this equation, the cost of capital can be calculated by the dividend at the end of one year divided by the present stock price then minus the growth rate of dividends.
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. While numerous 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) should be consider in order to get a reasonable estimate of growth rate of dividend (Alen Arnold, 2008), the growth rate could also be derived from simply taking arithmetic or geometric average of past dividend growth rates (Gordon and Shapiro, 1956; Ross,…..) or using the analysts' forecasts (Brealey et al., 2008; Moyer et al., 2008). In addition, inevitable errors generated in using these two approaches could be diminished by the use of large sample of past or analysts' expected dividend growth rates (Brealey et al., 2008; Ross,….). What is more, based on the assumptions that a firm's earnings retention ratio (b), rate of return on the book equity (r) and the debt to equity ratio are expected to remain constant as well as the firm plans to take no outside equity funding, the growth rate of dividend can be calculated by multiplying retention ratio with rate of return on the book value of equity (Gordon and Shapiro, 1956; Gordon, 1963).
In 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., 2008; Brealey et al., 2008). In this form of DDM, dividends are anticipated to grow at differential rates over different periods (different stages) but tend to stabilize, therefore the growth rate is expected to be constant and approach the overall average growth rate of the economy as time going to infinite horizon (the last stage). Based on this assumption, 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, which are expected to grow at various growth rates, paid in the first stages and the present value of dividends, which are projected to grow at a constant rate, paid in the last stage.
Input data required by this multi-stage DDM include: the current stock price, last year's dividend and the growth rates of dividends at different stages. Therefore, to calculate the cost of equity capital, 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 in the process of estimating constant growth rate of dividends. In particular, the multi-stage DDM could be two-stage model (such as Fuller and Hsia 1984; FHERM (1997)), three-stage model and so on depending on how detailed the growth rate of dividends could be estimated.
Take the example of how DDM is applied to estimate the cost of equity of Pepsico listed on NYSE, data for dividends paid by PepsiCo within the past thirty years (1980 to 2009) are collected from the website of PepsiCo (for the period from 2000 to 2009) and Yahoo! Finance (for the period from 1980 to 1999) as shown in the table below. The cost of equity capital of PepsiCo is calculated by employing the constant growth model with the expectation that future dividend payments will grow at a constant rate which is estimated based on past data of dividend growth rates. By taking geometric average of annual growth rates over thirty years, the expected growth rate of dividend for PepsiCo is set at the rate of 11% per annum. As the PepsiCo's current stock price (close price on November 12, 2010) and last year dividend are $64.64 and $1.8 per share, the expected cost of equity capital of PepsiCo is 14% per annum.
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 growth rate
0.32
Geometric growth rate
0.11
