Stock Valuation: The Variable Growth Case (Gordon Model)

Financial Instruments are valuable because we derive some benefit from them in the form of return. It goes to say that higher the expected benefit from an asset, higher should be its value. Shares of stock are no exception. We expect to earn a return on them in two ways: 1) Dividends and 2) Capital gains (difference between the buying and selling prices).

We can see capital gains also as a function of expected future dividends. We know that a capital gain arises if the selling price of a stock is more than its buying price. It should lead us to think in terms of what affects the price of a stock. Well, there can be a host of factors, one of which is the dividend that we expect to get on it. Intuitively, if we expect to earn a higher dividend, we believe that perhaps the company in which we have invested is a profitable one. How else would it be able to afford a higher dividend payment? This perception can have a favorable impact on the stock price of the company, thereby creating an opportunity for a capital gain.

In essence therefore, we can look at the value (price) of a stock as simply a function of its expected dividends. Higher expected dividends create an upward pressure on the price and vice - versa.

We also know that expected dividends are receivable on future dates. Therefore, the value (price) of a stock should be the discounted value of these dividends. What we have now is the understanding that if we find the present value of expected dividends of a company, we can have an estimate of the current stock price. It should be kept in mind that this argument is valid only for dividend paying companies and for this post, I am sticking to a dividend paying company.

Of course, the price estimate can vary from person to person because people have different estimates of expected dividends and the required return (discount rate). Therefore, what we get from a stock valuation model of this type is an estimate of the intrinsic value of a stock, which can differ from its market value. Depending on who had a better idea about future expectations and the required rate of return, he / she will be that much closer to the real intrinsic worth of the stock. Needless to say that if we provide inputs to a model that are not in touch with the pulse of the company and the market, we will find ourselves gaping at some strange results. The fault may not be that of the model but in the inputs provided to the model. It works the same way as a computer does, that is, on the GIGO (garbage - in - garbage - out) principle.

We also know that the world is a flux. Therefore, like everything else, dividends also keep on changing over time. For a given time period, they grow (or fall) at a certain rate and then this rate can change as we move into another time period. In short, the growth rate (either positive or negative) keeps varying and when that happens, we start talking in terms of a stock valuation model that can account for changing growth in dividends.

For the sake of simplicity, let us assume that the dividends on a certain stock grow at a 5% p.a. rate for the first two years from now. After the first two years, the growth rate will change to 7% p.a. for an indefinite period of time.

Let us say that the current year's dividend was $1 per share. It will mean that the dividend at the end of the next year will be 1 x 1.05 = $1.05 and the dividend at the end of the second year will be 1.05 x 1.05 = $1.1025. If we find out the present value of these two dividends at some discount rate k, we will get a part of our answer. Why a part? Because we still need to account for 7% growth in dividends from the third year onwards. Once we do that, we can have the final answer for what is the value of this stock.

In the following video, we take up some data and arrive at the value of a stock assuming varying growth rates in dividend: