# 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 a stable growth in the second stage which lasts forever. The first stage may have a positive, negative, or a volatile growth rate and will last for a finite period while 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 exact way i.e. in two such stages. Let us look at the example below for a better understanding of the concept of two-stage dividend discount model.

## Example Calculating Value of Stock/Share Using Two Stage Dividend Discount Model

Let us take an example of a company (ABC Ltd.) that has paid a dividend of \$ 4 this year. Assuming a higher growth for next 3 years at 15% and a stable growth of 4% thereafter; let us 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 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 dividend declared after 3 years will be \$ 6.0835 as calculated above

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

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* which an investor wants for the risk associated with the investment in equity as against investment in a risk-free security.

g = Growth rate

*One of the most commonly used ways of calculating 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 like 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 which in our example comes to \$92.35. Let us look at how does one interprets the value of the firm from an investor perspective?

## Interpreting Firm Value Using Two Stage Dividend Discount Model

Comparison of market price to the value of the firm can understand market the perception of the company. If the market price of the company’s share is lower than the calculated value using the model; this means the stock price is undervalued which could mean that our estimates of the growth of the company are higher than what market perceives. It can also be interpreted that one needs to revise the growth estimates in order 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 the stock price trading cheaper and can be a good investment to make.

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

Though the model has its own benefits and applications; it inherits some limitations too. Let us look at the limitations faced by two stage dividend discount model.

## Limitations of Two Stage Dividend Discount Model

• The model’s biggest limitation is the error in estimation that can come in due to 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 over valuation 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 a case of a high growth assumption in the first stage.
• Secondly, assuming a direct jump from say, 12% in expansion stage to say, a 4% stable growth in back to back years may not be a scenario closer to reality as in real world scenario the growth rates will stabilize gradually over a period of time in multiple stages and not just two.
• This model has its usage and applicability limited to companies which have higher growth rates during the 1st phase which is known and having stable growth rates thereafter. Also, the growth rates in 1st phase should be closer to growth rates in stage two- so essentially if there is not much difference between the two stages; is when the model will yield appropriate results.

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

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Last updated on : December 31st, 2016

1. Ronald