## What is the H-Model?

The H-model is a quantitative method of valuing a company’s stock price. This model is very similar to the two-stage dividend discount model however it attempts to smooth out the growth rate over time, rather than abruptly changing from the high growth period to the stable growth period. This model assumes that the growth rate will fall linearly towards the terminal growth rate.

### Quick Summary of Points

- The H-model is a quantitative method of valuing a company’s stock price
- This model is similar to the two-stage dividend discount model, however, it differs by attempting to smooth out the high growth rate period over time
- The H-model formula is given by: ((D
_{0}(1+g_{2}) + D_{0}*H*(g_{1}-g_{2}))/(r-g_{2})

### What is the purpose of the H-Model?

The H-model is used to assess and value a company stock. This model, similarly to the dividend discount model theorizes the stock is worth the sum of all future dividend payments discounted to the present value.

One potential problem with the two-stage dividend discount model is that it assumes a high growth rate, then an abrupt drop-off in growth to the terminal growth rate when the company reaches stable growth. The H-model instead smooths out the growth rate linearly towards the terminal growth rate. The H-model thus provides a more realistic approach in most scenarios when valuing a company’s stock.

### What is the H-Model Formula?

The H-model formula consists of two parts. The first component of the formula considers the value of the stock based on the long-term growth rate. This component ignores the high growth rate period. The second component of the equation adds the value from the high growth rate period. The formula is given as:

Stock Value = (D_{0}(1+g_{2}))/(r-g_{2}) + (D_{0}*H*(g_{1}-g_{2}))/(r-g_{2})

= ((D_{0}(1+g_{2}) + D_{0}*H*(g_{1}-g_{2}))/(r-g_{2})

Where:

- D
_{0}= The most recent dividend payment - g
_{1}= The initial high growth rate - g
_{2}= The terminal growth rate - r = The discount rate
- H = The half-life of the high growth period

Visually we can see how the components of the H-model formula add up to the total value of the stock:

From the initial high growth rate (g_{1}) to the stable growth rate (g_{2}) we can see that under the H-model, the growth rate drops linearly until it hits the terminal growth rate. From there the terminal growth rate is expected to hold indefinitely. The two components of the H-model formula make up the two parts that are considered in the stock valuation.

### H-Model – Worked Example

Let us now work through a hypothetical situation that involves the H-model. A company has just issued a dividend of $3. The expected growth rate is 10% and you expect this rate to fall to a stable growth rate of 2% over the next twelve years. If the required rate of return is 11%, what would the value of a share in this hypothetical company be under the H-model?

We are given all the components that would be used in the H-model, so using the formula we get:

Stock Value = (D_{0}(1+g_{2}))/(r-g_{2}) + (D_{0}*H*(g_{1}-g_{2}))/(r-g_{2})

Stock Value = ($3(1+0.02))/(0.11-0.02) + ($3*(12/2)*(0.10-0.02))/(0.11-0.02)

Stock Value = $50.00

This calculation can also easily be done in Excel. Below shows how Excel was used to calculate this value. To the right of the calculation this value is sensitized based on the discount rate and terminal growth rate. Below the calculation, the graph shows the growth rate under the H-model:

Here we can see that the component corresponding to the terminal growth rate is $34. The component corresponding to the high growth is $16. These two parts combined give a per share value of $50. To the right of the graph, this value has been sensitized based on the terminal growth rate and the discount rate used. In the top left corner, we can see that the value could be as low as $42.27 if the discount rate was 12% and the terminal growth rate was 1%. Alternatively, if the discount rate was as low as 10% and the terminal growth rate was 3% the value of the stock under the H-model would be $62.14.

### Additional Resources

Thank you for readings CFI’s article on the H-model. If you would like to learn more about related concepts check out CFI’s other resources: