# Dividend Discount Valuation: H Model

The dividend discount model makes a lot of assumptions. Some of these assumptions are not considered to be viable by analysts. For instance, consider the assumption regarding growth rates. During the horizon period, the analyst estimates that the growth rate will be high, let’s say 10% or 12%. Then, when the terminal value is to be calculated, the estimate if of a lower return that will continue till perpetuity. Let’s say, a 5% rate is assumed.

To many critics, this seems like a critical flaw. They believe it to be an absurd assumption that a firm will make a 12% return in the 5th year and then suddenly the return will drop to 5% from the 6th year onwards. They believe that this assumption is absurd and use empirical analysis to prove that this is almost never the case.

Also, since the dividend discount model formula is extremely sensitive to assumptions regarding growth rates, they believe that the resultant valuation is quite a bit off the mark.

Therefore, to overcome this limitation, they have created a modified dividend discount model called the “H” model. In this article, we will take a closer look at what the H model is all about.

### The H Model

**The H model assumes that the earnings and dividends of the firm do not suddenly fall off a cliff when the horizon period ends**. Rather, the decline in the growth rate is a gradual process. The assumption that the H model makes about this decline is that the decline is linear.

Hence instead of suddenly dropping from 12% to 5%, the growth rates will start declining from 12% at a given rate, let’s say 10% every year. Hence, from 12% the rate will drop to 10.8% and then in the next period to 9.7% and so on. This decline would then continue until it reaches the long term growth rate of 5%. Once the 5% growth rate is reached, it stabilizes over there and remains in that state until perpetuity.

### The Formula

The derivation formula for calculating growth using the H growth rate requires some complex mathematics which is beyond the scope of this article. Hence, for our understanding, let’s just have a look at the formula and memorize it.

Value of A Share (H Model) = | D0 * (1+gL) | + | D0 * H * (gS-gL) |

r-gL | r-gL |

where,

- D0 is the dividend received in the present year, let’s assume the value to be $25
- R is the rate of return expected by the investor, let’s say 8% in this case
- gL is the long term growth rate i.e. 5% in this case
- gS is the short term growth rate i.e. 12% in this case
- H is the half-life of the high growth period i.e. our high growth period was 5 years, therefore the value of H is 2.5 for our purpose.

### Calculation

Value of A Share (H Model) = | $25*(1+0.05) | + | $25 * 2.5 * (0.12-0.05) |

0.08-0.05 | 0.08-0.05 |

= $875 + $145.833

= $1020.33

### Interpretation:

- The first component of the valuation i.e. $875 in this case is what the value of the shares would be if there was no high growth period at all. Notice that the formula is quite similar to the Gordon Growth model formula
- The second component i.e. $145.33 is the addition in value resulting from the high growth period for 5 years. This component is where the H model differs from other dividend discount models

### Accuracy of the Model

Empirical analysis has shown that the H model is most accurate when:

- The high growth period is shorter i.e. the model would be less accurate if we assumed a 20 year high growth period instead of a 5 year high growth period
- Also, the accuracy of the model increases when the spread between the long term growth rate and the short term growth rate is less

To conclude, the H model is a significant advancement in the field of equity valuation. It solves the problem of the abrupt decline in the growth rates that is assumed by the other models. However, it still provides only an estimate, albeit a better estimate than dividend discount models regarding the valuation of the stock.

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