# Implied Dividend Growth Rate

We are now aware of the various models that are used for equity valuation like Gordon model, H model, 2 stage model etc. in each of these models, we were assuming that the given inputs are dividend, dividend growth rates and time horizon, The output that we expected from these models was the current stock price. While this is true most of the time, it may not always be correct.

The very same model that can be used to calculate share price can also be used in the reverse to figure out the rate of dividend growth that is being implied in the calculation. This may be a handy calculation to undertake. Let’s have a closer look at this concept in this article.

### Backward Calculation:

The logic behind the calculation is simple. If all inputs except the growth rate are available then we can solve for the growth rate. This growth rate will be called the implied dividend growth rate as it is not directly mentioned. Instead it is included in the price. Instead of using the growth rate to move forward towards the share price, we can use the share price to move backwards towards the growth rate.

### Sanity Check:

The implied dividend growth rate provides a great mechanism to check for sanity behind our assumptions and calculations. This is because it is empirically known that in the long run no company can grow at a rate which is much faster than the GDP. For instance, if the GDP growth is expected to be 4% over a long period of time, companies may grow at 3% of 6% i.e. one or two percentage points here and there.

However it would be downright impossible for any company to grow at 25% over an extended period of time when the GDP is growing at 4%. Hence if we take the current stock price from the market and solve for implied growth rate to find it at exorbitant levels like this, we immediately know that the share is overvalued. This provides an efficient sanity check mechanism and allows us to rule out obvious asset bubbles.

### Calculation:

It is possible to calculate the implied rate of dividend growth, no matter which dividend discount model is being used.

- In case of Gordon model, the calculation is pretty straightforward. The formula can be easily remembered and is very convenient to use
- In case of H model, the formula becomes considerably more complex. To derive this formula, we will have to re-arrange the H model equation in such a way that r is on the left hand side and everything else is on the right hand side. This formula may be complex to remember. However, it is still easy to use and accurate.
- Lastly, in case of a multi stage dividend discount model, it becomes a little more difficult to apply this backward calculation. The formula is difficult to remember as well as difficult to use since it requires iterations to derive the correct answer.

The bottom line, therefore is that regardless of the type of model that has to be used, backward calculations are possible. Also, it does make sense to conduct these calculations. It reveals one of the fundamental assumptions built in the market price and therefore reveals its sanity!

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