The investor is expecting two types of cash flows from their investment 1) dividends while they hold their shares (Div1) and 2) the expected price they receive when they sell their share (P1). The valuation principle implies that the value of any share will be equal to the expected future cash flows from that share. It is however difficult for any investor to know with certainty the future dividend and share price. These are based on the share holders expectations when they purchase the share (P0). P0 should be up to a point where there is a zero net present value (NPV). The NPV rule states that the value of any asset is the present value of expected future cash flows discounted at a rate appropriate to the riskiness of the cash flows.
As the dividends and the future price of the share is unknown there is an element of risk associated with the investment that is greater than a risk free investment such as putting your money into a term deposit with a bank. This is also known as the equity cost of capital (re).
We must consider that our investor is expecting to gain cash flows from two sources 1) the expected dividends and 2) the sale of the share at some point in time Pn. If Pn is greater than P0 then we would say that the investor has made a capital gain. We would expect that our model would have to take this into consideration at some point which it does. The valuation principle says that the value of a share is equal to the present value of the dividend and future sale price. As per the above equation n can be a number that goes on forever. An investor with the same expectations of the future would therefore attach the same value to the shares, no matter how long they hold the shares. Under the dividend discount model a company that has an infinite life, will have an infinite cash flow stream. So this being the case the value of the share is simple the value of the future discounted cash flows. The value of the shares is solely determined by these cash flow streams. The dividend discount model implies that the share price equals the present value of all future dividends. The formula for the dividend discount model is:
P0 = Div1 / 1 + re + Div2 / (1 + re)^2+ ... + Divn / (1+re)^n + Pn / (1 + re)^n
The simplest form of the dividend growth model is the constant growth model or also known as the Gordon Growth Model named after its founder. The major assumption that is made in the Gordon growth model is that the dividends will grow at a constant growth rate (g). The constant growth rate cannot be greater than re otherwise the dividends would eventually exceed the earnings. By making this assumption we can then value the stock by using the following equation:
Po = Div1 / re - g
A further assumption is that the growth rate has to be less than the growth rate of the economy in which the company operates. We do know however that this is not always the case in reality. When a firm starts out it may and tends to experience rapid growth before becoming stable. During this time the growth rate may exceed the growth rate of the economy. The Gordon growth model can be used as a two stage model where a firm experiences high stable growth and then stable normal growth. This is known as the "Two stage Dividend discount model" and also adapted to a firm that experiences high…