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There are several assumptions of the first version of the two-stage DDM:

- The first stage represents a period of abnormal growth.
- The second stage represents a period of sustainable growth.
- There is a sudden transition from abnormal growth to mature growth.

$$\text{V}_0= ∑_{(\text{t}=1)}^{\text{n}}\frac{\text{D}_0(1+\text{g}_{\text{S}})^\text{t}}{(1+\text{r})^\text{t}} +\frac{\text{D}_0 (1+\text{g}_{\text{S}})^\text{n}(1+\text{g}_{\text{L}})}{(1+\text{r})^\text{n}(\text{r}-\text{g}_{\text{L}})}$$

Where:

\(\text{g}_{\text{S}}=\) Supernormal growth rate at the first stage.

\(\text{g}_{\text{l}}=\) Mature growth rate at the second stage.

\(\text{r}=\) Required rate of return.

\(\text{n}=\) Length of the extraordinary growth rate.

The assumptions of the H-Model include:

- There are two stages similar to the general two-stage model.
- An initial high growth rate
over a particular duration until it reaches a sustainable long-term rate that exists in perpetuity.**declines linearly** - The transition from supernormal growth to the sustainable growth rate is relatively smooth.

$$\text{V}_0= \frac{\text{D}_0 (1+\text{g}_\text{L})+\text{D}_0\text{H}(\text{g}_{\text{S}}-\text{g}_{\text{L}})}{\text{r}-\text{g}_{\text{L}}}$$

Where:

\(\text{H}=\) Half-life (years) of the high growth period.

\(\text{g}_{\text{S}}=\) Initial short term high dividend growth rate.

\(\text{g}_{\text{l}}=\) Sustainable long-term dividend growth rate.

\(\text{r}=\) Required rate of return.

This model is more suitable for companies that are expected to have three separate stages of earnings growth. It is a more complex refinement of the two-stage model.

- The initial stage of growth.
- The second stage of growth.
- The stable phase of growth.

- The firm is assumed to have three phases.
- The growth rate during each phase is different but constant.

Calculation steps under this model are:

- Estimate the dividends over the first two stages of growth.
- Discount estimated dividends to the present.
- Estimate the dividends for the first year of the 3
^{rd}stage. - Calculate the terminal value at the beginning of the 3
^{rd}stage. - Calculate the present value of the terminal value.

- The second stage is similar to the first stage of the H-model.

The steps under this model are:

- Calculate the yearly dividends and the present values in stage 1.
- Apply the H-model to the 2
^{nd}and 3^{rd}stages to determine the value of the share at the beginning of stage 2 (H-model value). - Determine the present value of the H-model value.
- Sum the present value from stage 1 and the present value of the H-model value.

Spreadsheet modeling is used to build complicated models that would require different patterns of dividend growth. Built-in spreadsheet functions also make the calculation simpler. In addition, they allow several analysts to share their spreadsheet models, thus exchanging information.

Spreadsheet models also reduce the probability of computational inaccuracies.

## Question

Which of the following is the

least likelyan assumption of the H-model?

- There are two stages in the H-model.
- A supernormal growth rate characterizes the final stage of the H-model.
- A sustainable long term growth rate characterizes the final stage of the H-model.
## Solution

The correct answer is B.A supernormal growth rate does not characterize the final stage. It is during the first stage of the H-model that the growth rate is expected to be high.

A is incorrect.The H-model assumes there are two stages.

C is incorrect.The final stage of the H-model is characterized by a sustainable long-term growth rate that is expected to continue into perpetuity.

Reading 23: Discounted Dividend Valuation

*LOS 23 (j) Explain the assumptions and justify the selection of the two-stage DDM, the H-model, the three-stage DDM, or spreadsheet modeling to value a company’s common shares.*