APPENDIX 10-A THE CONSTANT GROWTH VERSION OF THE DDM
Table 10A-1 illustrates the case of Summa's growth stock with a current dividend of $1 per share (D0), an expected constant-growth rate of 7 percent, and a required rate of return, k, of 15 percent.
TABLE 10A-1 GOES ABOUT HERE {FROM 9th ed.}
As Table 10A-1 shows, the expected dollar dividend for each period in the future grows by 7 percent. Therefore, D1 = $1.07, D2 = $1.14, D10 = $1.97, and so forth. Only the first 60 years of growth are shown, at the end of which time the dollar dividend is $57.95. The last column of Table 10A-1 shows the discounted value of each of the first 60 years of dividends. Thus, the present value of the dividend for Period 1, discounted at 15 percent, is $0.93, while the present value of the actual dollar dividend in Year 60, $57.95, is only $0.01 today. Obviously, dividends received far in the future, assuming normal discount rates, are worth very little today.
Figure 10A-1 shows this growth in the dollar dividend for only the first 30 years in order to provide some scale to the process. Because k is greater than g, the present value of each future dividend is declining--for example, the present value of D1 = $0.93, the present value of D2 = $0.87, and the present value of D10 = $0.49. Therefore, the present-value-of dividends curve at the bottom of Figure 10A-1 is declining more rapidly than the growth in-dividends-over-time curve above it is growing.
FIGURE 10A-1 GOES ABOUT HERE {FROM 9th ed.}
The estimated price of Summa, as illustrated in Table 10A-1 and Figure 10A-1, is the sum of the present values of each of the future dividends. Adding each of these present values together from now to infinity would produce the correct estimated value of the stock. Note from Table 10A-1 that adding the present values of the first 60 years of dividends together produces an estimated value of $13.20. The correct answer, as obtained from adding all years from now to infinity, or using Equation 10-5, is:
$1.07
P0 = Estimated price = ------= $13.38
0.15 - 0.07
Thus, years beyond 40 to 50 typically add very little to the estimated value of a stock. Adding all of the discounted dividends together for the first 60 years produces a present value, or estimated value for the stock, of $13.20, which is only $0.18 different from using Equation 10-5. Therefore, years 61 to infinity add a total value of $0.18.