WARM-UP: THE GENERAL DIVIDEND DISCOUNT MODEL
LOS 27.i: Explain the assumptions and justify the selection of the two-
modeling to value a company’s common shares.
CFA® Program Curriculum: Volume 4, page 226 For most companies, the Gordon growth model assumption of constant dividend growth that continues into perpetuity is unrealistic. For example, many companies experience growth rates in excess of the required rate of return for short periods of time as a result of a competitive advantage they have developed. We need more realistic multistage growth models to estimate value for companies with several stages of future growth. The appropriate model is the one that most closely matches the firm’s expected pattern of growth. However, whichever multistage model we use, there are two important points to keep in mind:
We’re still just forecasting dividends into the future and discounting them back to today to find intrinsic value.
Over the long term, growth rates tend to revert to a long-run rate approximately equal to the long-term growth rate in real gross domestic product (GDP) plus the long-term inflation rate. Historically, that number has been between 2% and 5%. Anything higher than 5% as a long-run perpetual growth rate is difficult to justify.
PROFESSOR’S NOTE
The required rate of return applicable to each stage might also be different. For instance, a firm with a supernormal growth rate is probably more risky (should have a higher required return) than a stable, mature firm with a slower growth rate. In most cases on the exam, however, a single required return is applied to all of the stages.
Two-Stage DDM: The most basic multistage model is a two-stage DDM in which we assume the company grows at a high rate for a relatively short period of time (the first stage) and then reverts to a long-run perpetual growth rate (the second stage). The length of the high-growth phase is a function of the visibility of the company’s operations; in other words, it tells how far into the future the analyst can predict growth rates with a certain degree of confidence. An example in which the two-stage model would apply is a situation in which a company has a patent that will expire. For example, suppose a firm is expected to grow at 15% until patents expire in four years, then immediately revert to a long-run growth rate of 3% in perpetuity.
This stock should be modeled by a two-stage model, with dividends growing at 15% before the patent expires and 3% thereafter (see Figure 27.1).
Figure 27.1: Example of a Two-Stage DDM
H-Model: The problem with the basic two-stage DDM is that it is usually unrealistic to assume that a stock will experience high growth for a short period, then immediately fall back to a long-run level. The H-model utilizes a more realistic assumption: the growth rate starts out high and then declines linearly over the high-growth stage until it reaches the long-run average growth rate. For example, consider a firm that generates high profit margins, faces little competition from within its industry, and is currently growing at 15%. We might forecast that the firm’s growth rate will decline by 3% per year as competitors enter the market until it reaches 3% at the end of the fourth year, when the industry matures and growth rates stabilize (see Figure 27.2).
Figure 27.2: Example of an H-Model
Three-stage DDM: Three-stage models are appropriate for firms that are expected to have three distinct stages of earnings growth. A three-stage model is a slightly more complex refinement of a two-stage model. For example, suppose we forecast that a biotech company will experience supernormal growth of 25% for three years, then 15% growth for five years, and finally slow down to a stable, long-run rate of 3% (see Figure 27.3). Alternatively, in stage 2, the growth rate may also linearly decay to the stage 3 stable, long-run growth rate.
Figure 27.3: Example of a Three-Stage DDM
Spreadsheet modeling: The two and three stage models we’ve discussed so far are really just models in which we’ve simplified the growth pattern to make the calculations doable.
Obviously that’s an important consideration on the exam. However, in practice we can use spreadsheets to model any pattern of dividend growth we’d like with different growth rates for each year because the spreadsheet does all the calculations for us. Spreadsheet modeling is applicable to firms about which you have a great deal of information and can project different growth rates for differing periods, such as construction firms and defense contractors with many long-term contracts. Figure 27.4 is an example of three different spreadsheet models.
Figure 27.4: Examples of Spreadsheet Modeling Growth Rates
Year 1 2 3 4 5 6 7 and after
Scenario 1 20% 19% 13% 5% 5% 5% 5%
Scenario 2 20% 19% 13% 11% 5% 5% 5%
Scenario 3 20% 19% 13% 11% 8% 7% 5%