Purpose: The purpose of this case is to calculate a stock’s price using its past dividends as an indicator of future dividend growth rates. The student must determine the stock’s required rate of return (CAPM) and future expected dividend growth rate and use the Gordon Growth Model to calculate a current price.
1. The equation for CAPM is kj = Rf + [bj x (Rm – Rf)] where,
kj = required return on asset j,
Rf = risk-free rate of return,
bj = beta coefficient for asset j,
Rm = market return.
kj = 6% + 1.75(10% – 6%)
kj = 13%
2. The equation for the Gordon Growth Model is, where,
P0 = price of the common stock,
D1 = per share dividend expected at the end of year 1,
D0 = most recently paid dividend,
Ks = required return on common stock,
g = growth rate in dividends.
To calculate g, we have to assume that future dividend payments will grow at a constant rate into the future forever. This constant rate can be estimated
by examining the average growth rate in the past. On a calculator,
Let,
PV = $ .86,
FV = $2.00,
n = 8.
Solve for i. i = the average growth rate. In this case i = g = 11.13%.
The Essay on Dividend Growth Model
... a company may not exceed the market growth rate. In addition, since the dividend growth rate is expected to remain constant indefinitely, the ... same rational expectations of returns, and that these returns are in line with the best prediction for future returns as based on ... using the Dividend Growth Model, we simply adjust the model’s equation for estimating the price of a stock, given as ...
Plugging this growth rate into the Gordon Growth Model,
P0 = $2.00(1 + .1113) = $118.86.13 – .1113
3. This time,
Let,
PV = $1.42,
FV = $2.00,
n = 5.
Solve for i. i = g = 7.09%.
Plugging this growth rate into the Gordon Growth Model,
P0 = $2.00(1 + .0709) = $36.24
.13 – .0709
4. The Gordon Growth Model, or any other dividend based pricing model, has major drawbacks in that we are not sure what the true future growth rate in dividends is. As we have just demonstrated, depending on the period we consider, the stock’s price can fluctuate wildly.
5. The required rate of return calculation has an enormous effect on the stock’s price using these types of models. If we assume that Nations Bank’s required rate of return on its common stock is 12% instead of 13%, the Gordon Growth Model will yield a price of
P0 = $2.00(1 + .0709) = $43.62
.12 – .0709
This value is not much different, but consider the result when the growth rate in dividends is near the required rate of return on the common stock as is the case from 1987-1995.
P0 = $2.00(1 + .1113) = $255.47
.12 – .1113
In general, the calculated stock price will be extremely sensitive to the required rate of return when the required rate of return is close to g.
6. This would be an example of a zero growth stock. The stream of payments would be constant (annuity) and they would last forever (perpetuity).
When this special case occurs, a simplified equation can be used.
P0 = D1/Ks = $2.00/.13 = $15.38
7. The further out into the future the dividend payments are received, the less valuable they are in today’s dollars. Using a dividend amount of $1.00 and a discount rate of .13, the present value of these three dividends are $.88, $.29, and $.000004922, respectively.
