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. At the same time, the second stage is assumed to have a stable growth rate for the rest of the company’s life. This model assumes 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 better understand the concept of the two-stage dividend discount model.

## Formula

To calculate the value using a two-stage growth model, one has to discount the dividends of all the years of a high growth rate period plus discounted value of dividends of a stable growth rate period. The formula is as follows:

Where D = dividend of different periods (like D_{0}, D_{1}, and so on)

g = higher growth rate

n = number of years in a high growth rate period

g_{n} = growth rate of the stable growth rate period

## 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.

**Also Read: **H Model – Dividend Discount Model

We need to make 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 1^{st} year will be = $ 4.60 ($ 4 x 1.15 – growing at 15 %)

After 2^{nd} year will be = $ 5.29 ($ 4.60 x 1.15 – growing at 15%)

After 3^{rd} 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.

You can also use the Two-Stage Growth Model Calculator.

### Second Stage

The second stage has a growth rate of 4%, so the dividend value after the 4^{th} 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 follows:

P_{0} = D / (i – g)

Where P_{0} = 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.

**Also Read: **Two Stage Growth Model Calculator

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 the 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 3^{rd} 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 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.

Get quick help with the Dividend Discount Model Calculator

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

The comparison of the market price to the firm’s value 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 this model, the stock price is undervalued. This could mean that our estimates for the company’s growth 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 stock’s market price; this is 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, it could be a good investment to make.

On the contrary, 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 also inherits some limitations. 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 isn’t easy 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 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 with 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 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 there are no reasons for high growth. 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.

Quiz on Two-Stage Growth Model

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( Two stage growth Model)

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