101 Concepts for the Level I Exam

Essential Concept 50: Multistage Dividend Discount Models

Companies with varying growth prospects must be valued using multistage DCF models such as the two-stage DDM, H-model, three-stage DDM or spreadsheet modeling. The assumptions of these models are:

Two-stage DDM: this model assumes different growth rates in stage 1 and stage 2. A supernormal growth in stage 1 is followed by a lower, sustainable growth rate in second stage.
H-model: the dividend growth rate declines linearly from a high supernormal rate to the normal growth rate in stage 1, and becomes constant and normal in stage 2.
Three-stage DDM: There are two variations of this model.
- In one version, the growth in the middle stage is constant.
- In the second version, the middle stage is similar to the first stage in the H-model. Dividends grow at a constant high rate in the second stage, and declines linearly to a sustainable, mature growth rate in the third stage. The second and third stages can be valued as an H-model.

The value of a stock using two-stage DDM is:

${\mathrm{V}}_0\mathrm{=\ }\sum\limits_{t=1}^{N}{\frac{{\mathrm{D}}_{\mathrm{0\ }}{\left(\mathrm{1+}{\mathrm{g}}_{\mathrm{s}}\right)}^{\mathrm{t}}}{{\left(\mathrm{1+r}\right)}^{\mathrm{t}}}}\mathrm{+}\frac{{\mathrm{D}}_{0\mathrm{\ }}{\left(\mathrm{1+}{\mathrm{g}}_{\mathrm{s}}\right)}^{\mathrm{n}}\left(\mathrm{1+}{\mathrm{g}}_{\mathrm{L}}\right)}{{\left(\mathrm{1+r}\right)}^{\mathrm{n}}\mathrm{\ }\left(\mathrm{r-}{\mathrm{g}}_{\mathrm{L}}\right)}$

where:

g_s = short-term high growth rate

g_L = long-term sustainable growth rate

n = number of years of high growth rate

The value of a stock using the H-model is:

${\mathrm{V}}_0\mathrm{=}\frac{{\mathrm{D}}_0\left(\mathrm{1+}{\mathrm{g}}_{\mathrm{L}}\right)\mathrm{+}{\mathrm{D}}_0\mathrm{*}\mathrm{H*}\left({\mathrm{g}}_{\mathrm{s}}\mathrm{-}{\mathrm{g}}_{\mathrm{L}}\right)}{\mathrm{r-}{\mathrm{g}}_{\mathrm{L}}}$