## Two Stage Growth Model

This two-stage growth model is split into two stages. The first one is the high growth stage or high growth rate period and the second one is the stable growth rate period. Initial years tend to be a high growth rate period until the company starts earning a stable and constant rate. When an existing or new company enters into the market with an innovative idea or project, it earns a higher growth rate. However, the moment there is an upgrade to the technology or the competition hots up in the industry segment or quota relaxation is there. For any such reason, the unhindered growth of the company takes a halt after the company enters into a period where its earnings grow in a stable manner as long as the company continues to upgrade and remain relevant to the industry.

This model is also based on the limited assumption that the value of the stock is equal to the sum of all future dividend flows to investors. That could be loosely indicated as his cash flows from the investments in the form of dividends only.

## Example

Assume that a company X launches an electronic gadget with the most innovative features. Now, the company will enjoy and earn at a higher growth rate. But after a period of 3 years, another company, Y, comes up with more innovative features. This will make a dent in the volume of the company. And that will cause a reduction in the earnings of company X as customers will demand recent technology. Hence, even if company X updates the features of its product to compete with company Y, the customers are now divided between both the companies. Earlier, there was no competitor due to which company X was able to earn a higher rate. However, after three years, the company enters a stable growth rate period due to the entry of competitors with newer ideas.

## 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

r = required rate of return

## Calculator

## How to Calculate using Calculator

The user has to enter the following figures into the calculator, which will provide the present value after discounting all the dividends of both the time periods – the high growth rate period and the stable growth rate period.

### Dividend

The user is supposed to enter the dividend of 0 periods or the base year in the calculator, and it will calculate the value of dividends for the rest of the periods. It is denoted by D_{0}. To determine the value of D_{1}, that is, dividend at 1 period, we add the growth rate in D_{0} by applying the formula: D_{1} = D_{0}(1+g). For calculating values of D_{2}, D_{3}, and so on, we have to simply compound the growth rate by the number of periods by a similar formula.

### High Growth Rate

This is the growth rate of the high growth rate period or the initial period.

### Number of Years in High Growth Rate Period

Provide the number of years in the high growth rate period. This means the number of years till the company is expected to earn at a higher than normal growth rate.

### Growth Rate of Stable Period

This is the rate of earnings of a stable growth rate period. And, it is always less than the rate of high growth rate period.

### Required Rate of Return

This is the rate by which dividends are discounted. The most appropriate method to calculate this rate is CAPM.

## Example

Assume that the dividend paid by company T is $7. And the company will earn at a growth rate of 25% for three years, and after that, it will earn at a stable rate of 8%. The required rate of return of the company is 11.5%. Now, let us calculate the current value of its stock.

In the above example, the company is earning at a growth rate of 25% for the initial 3 years. And, after that, the growth rate reduces to 8%. This period of the initial 3 years is the high growth rate period, and when the growth rate reduces to 8% till infinity, it enters the stable growth rate period. Hence, the cash flow for the rest of the life of the company will be discount at the end of the third year as per the assumption of the Dividend Discounting Model.

Dividend | Amount | Present Value | Remarks |
---|---|---|---|

D_{1} | 8.75 | 7.85 | 8.75/(1+0.115) |

D_{2} | 10.94 | 8.80 | 10.94/(1+0.115)^{2} |

D_{3} | 13.67 | 9.86 | 13.67/(1+0.115)^{3} |

Dividend for Stable GrowthRate Period | 421.88 | 303.51 | 421.88/(1+0.115)^{3} |

Total | 330.02 |

### Calculation of Dividend

D_{1} = D_{0}*(1+g) = 7*(1+0.25) = 8.75

D_{2} = D_{1}*(1+g) = 8.75*(1+0.25) = 10.94

And, D_{3} = D_{2}*(1+g) = 10.94*(1+0.25) = 13.67

Dividend for Stable Growth Rate Period = D_{3}*(1+g)/(r-g_{n})

= 13.67*(1+0.08)/(0.115-0.08) = 421.88

And these dividends are then discounted by the required rate of return to arrive at the value.

Hence, the value is equal to **$330.02**

## Interpretation

The value derived from this model helps in comparing the current market value of the stock. If the market value of the stock is more than this value, it indicates that it is overvalued and vice-versa. Investors go for such stocks which fulfill their required rate of return criteria where the discounted stream of dividends is more than the prevailing stock price or can wait for the price to come to that level.

Assume, in this case, that the market value is $297.05. This means that the company is undervalued. In such a case, it is advisable to make an investment in such a company as per this model.