Question 8.3: The next dividend for the Gordon Growth Company will be $4 p...
The next dividend for the Gordon Growth Company will be $4 per share. Investors require a 16 percent return on companies such as Gordon. Gordon’s dividend increases by 6 percent every year. Based on the dividend growth model, what is the value of Gordon’s stock today? What is the value in four years?
The only tricky thing here is that the next dividend, D_{1}, is given as $4, so we won’t multiply this by (1 + g). With this in mind, the price per share is given by:
P_{0} = D_{1}/(R – g)
= $4/(.16 – .06)
= $4/.10
= $40
Because we already have the dividend in one year, we know that the dividend in four years is equal to D_{1} × (1 + g)³ = $4 × 1.06³ = $4.764. The price in four years is therefore:
P_{4} = D_{4} × (1 + g)/(R – g)
= $4.764 × 1.06/(.16 – .06)
= $5.05/.10
= $50.50
Notice in this example that P_{4} is equal to P_{0} × (1 + g)^4.
P_{4} = \$50.50 = \$40 × 1.06^4 = P_{0} × (1 + g)^4
To see why this is so, notice first that:
P_{4} = D_{5}/(R – g)
However, D_{5} is just equal to D_{1} × (1 + g)^4, so we can write P_{4} as:
P_{4} = D_{1} × (1 + g)^4/(R – g)
= [D_{1}/(R – g)] × (1 + g)^4
= P_{0} × (1 + g)^4
This last example illustrates that the dividend growth model makes the implicit assumption that the stock price will grow at the same constant rate as the dividend. This really isn’t too surprising. What it tells us is that if the cash flows on an investment grow at a constant rate through time, so does the value of that investment.