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# Two-Stage Growth Model – Dividend Discount Model

The two-stage dividend discount model takes into account two stages of growth. This method of equity valuation is not a model based on two cash flows but is a two-stage model where the first stage may have a high growth rate and the second stage is usually assumed to have a stable growth rate.

## Two-Stage Dividend Discount Model

The two-stage model can be used to value companies where the first stage has an unstable initial growth rate and there is stable growth in the second stage, which lasts forever. The first stage may have a positive, negative, or volatile growth rate and will last for a finite period, whereas the second stage is assumed to have a stable growth rate for the rest of the life of the company. In this model, it is assumed that the dividend paid by a company also grows in the same way, i.e., in two stages. Now, let’s look at the example to get a better understanding of the concept of the two-stage dividend discount model. ## Example Calculating Value of Stock/Share Using Two-Stage Dividend Discount Model

Let’s take the example of a company (ABC Ltd.) that has paid a dividend of \$4 this year. Assuming a higher growth for the next 3 years at 15% and stable growth of 4% thereafter, let’s calculate the value using a two-stage dividend discount model.

We need to do an adjustment here to arrive at the dividend amount that needs to be discounted after adjusting for the different rates in the different stages. Continuing with the above example and assuming a required rate of return of 10%, we can calculate the value of the stock/firm as follows:

Current Dividend                             = \$ 4.00

Dividend after 1st year will be     = \$ 4.60 (\$ 4 x 1.15 – growing at 15 %)

Dividend after 2nd year will be    = \$ 5.29 (\$ 4.60 x 1.15 – growing at 15%)

Dividend after 3rd year will be     = \$ 6.0835 (\$ 5.29 x 1.15 – growing at 15%)

Since the growth in the first three years was 15%, the value of the dividend declared after 3 years will be \$6.0835, as calculated above.

The second stage has a growth rate of 4%, so the dividend value after the 4th year will be \$6.0835 x 1.04 = \$6.3268. Assuming this as the constant dividend for the rest of the company’s life, we arrive at the present values, as follow:

P0 = D / (i – g)

Where P0 = Value of the stock/equity

D = Per-Share dividend paid by the company at the end of each year

i = Discount rate, which is the required rate of return* that an investor wants for the risk associated with the investment in equity against investment in risk-free security.

g = Growth rate

*One of the most commonly used ways of calculating the required rate of return is by using the Capital Asset Pricing (CAPM) model.

(Note: The formula for arriving at the present value remains similar to earlier methods, such as single period dividend discount method, Gordon growth model, etc.)

Now, using the formula for calculating the value of the firm, we can arrive at the present value at the end of 3rd year for all future cash flows as follows:

Value    = \$6.3268 / (10% – 4%)

= \$105.45

Table Showing Present Values

 Tenor Cash Flow Discount Rate Present Value 1 4.6 10% 4.18 2 5.29 10% 4.37 3 6.0835 10% 4.57 3 105.45 10% 79.23 Total Present Value 92.35

Present value calculations in the above table are arrived at as follows:

\$4.18 = \$4.60 / (1 + 10%) ^1

\$4.37 = \$5.29 / (1 + 10%) ^2

\$4.57 = \$6.0835 / (1 + 10%) ^3

\$79.23 = \$105.45 / (1 + 10%) ^3

The sum of all the present values will be the value of the firm; in our example, this comes to \$92.35. Let’s look at how one should interpret the value of the firm from an investor perspective.

## Interpreting Firm Value Using Two-Stage Dividend Discount Model

The comparison of the market price to the value of the firm can help you understand the market perception of the company. If the market price of the company’s share is lower than the calculated value using the model, the stock price is undervalued, which could mean that our estimates for the growth of the company are higher than what the market perceives. It can also be interpreted that one needs to revise the growth estimates to align the model value closer to the market price of the stock; this is called the implied growth rate. However, if prices are marginally lower than the model price, one could assume that the stock price is trading cheaper and could be a good investment to make.

On the other hand, if the market price is higher than the model output, it means that the market expects the company to grow faster than our estimates.

Although the model has its benefits and applications; it inherits some limitations as well. Let’s look at the limitations faced by the two-stage dividend discount model.

## Limitations of the Two-Stage Dividend Discount Model

• The model’s biggest limitation is the error in estimation that can occur due to the incorrect estimation of the length of the first stage. It is very difficult to estimate the length of the first stage, which could lead to overvaluation or undervaluation of the stock under consideration. A shorter first stage will cause the valuation to be undervalued, while a longer first stage could lead to overvaluation, in the case of a high growth assumption in the first stage.
• Secondly, assuming a direct jump from, for example, 12% in the expansion stage to 4% stable growth in back-to-back years may not be a scenario closer to reality, as, in the real-world scenario, the growth rates will stabilize gradually over a period of time in multiple stages, not just two.
• This model has its usage and applicability limited to companies that have higher growth rates during the 1st phase, which is known and has stable growth rates thereafter. Also, the growth rates in the 1st phase should be closer to growth rates in stage two. Essentially, if there is not much difference between the two stages, the model will yield appropriate results.

There have been other models in use that tend to reduce the estimation error of the two-stage model dividend discount model, such as the H model and three-stage models, such that the valuation could be calibrated close to the market reality. However, the two-stage model is still worthy of application to specific cases and scenarios, as lesser stages require less estimation and business models where high growth lasts only for a few years, after which the reasons for high growth are lost. In the case of an innovation/idea/product, a firm may enjoy high growth rates until the patent expires or competitors jump in. For such cases, a two-stage model is appropriate for use and application.12,3

1.
C. Spaulding W. DIVIDEND DISCOUNT MODELS. thismatter.com. August 2019. [Source]
2.
fmvaluation. moneychimp. January 2019. [Source]
3.
DIVIDEND DISCOUNT MODELS. NYU | STERN. August 2019. [PDF]
Last updated on : August 31st, 2019
1. Ronald