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:

Bond Valuation

We know that when a government or a company borrows money from the public, it does so by issuing bonds. Naturally, a bond is a piece of paper (legal of course), that signifies debt.

Bonds are usually long - term borrowings, say 10 - 15 years. Needless to say that during the term of a bond, the borrowing party will pay interest to the lending party. The rate of interest at which this interest is paid is known as the coupon rate of interest and it remains the same for the term of the bond (at least for a straight bond). The principal amount on which the interest is calculated is called the Face Value or the Maturity Value of the bond. The interest payments are made periodically, either annually or semi - annually and are called coupon payments.

The value (or price) of a bond responds to the market interest rate. If market interest rates rise, the value of a bond falls and vice - versa. This is pretty intuitive. Suppose, you have a bond that pays you a 7% p.a. interest rate. You are quite happy with it until one day you find that the going market interest rate on similar financial instruments is 8.5% p.a. You get grumpy and want to sell off your bond and re - invest your money at the higher interest rate. The only problem is that you may not find a ready buyer for a bond that pays 7% at a time when other instruments are offering 8.5%. Since you want to sell and the buyers are not that forthcoming, you may have to plead the buyers and maybe give them a bargain price for your bond. The price would therefore fall. The reverse is true for when the market interest rates are lower than the coupon rate on your bond. Then, you have something valuable because you have a financial instrument that gives you more interest income as compared to other instruments on the market. Should you need to sell such a bond, it can fetch you a lucrative price.

Simply put, the market interest rate can also be called  the Required rate of return.  Let us call it k. If the coupon rate is higher than k, the price of a bond rises and is above the Face value of the bond.(Premium Bond). If the coupon rate is less than k, the price of a bond falls and is below the Face value of the bond. (Discount Bond) And if by chance, the coupon rate is equal to k, the bond sells for its face value.

The premium or discount on a bond reduces with time, i.e.; as we move closer to the maturity date, the price of the bond gets closer and closer to its face value, such that on the maturity date, the price is equal to the face value.

Mathematically speaking, the value of a bond is the present value of its coupon payments and face value (maturity value). The video below demonstrates how to find a bond's value: