# Nations Bank

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• Published : February 10, 2013

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Nations Bank

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,

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5

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%.

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...