P7-21. a) The risk premium on the stock is Ra — Rf, so 14.8 — 10 = 4.8%
b) The first step is to calculate the . This is done by taking the growth rate for each year, adding them to find a sum then dividing the sum by the number of periods (6):
The Gordon dividend growth model shows that the required rate of return for the company should be:
P = D / (k-g) where k is the discount rate and g is the dividend growth rate.
P = 2.60 / (14.8 — 5.61)
P = 2.60 /
P = $28.29
c) A decrease in the risk premium would increase the value of the stock. If the risk premium were decreased, for example to 3%, that would change k. The value of k would now be .13. When plugged into the , this would give the following result:
P = 2.60 / (13% – 5.61%)
P = 2.60 / (.0739)
P = $35.18
This example clearly shows that by reducing the risk premium, the denominator is lowered and this will have the impact of increasing the stock’s price.
P7-23. a) The company’s dividend apparently is not growing. The stock price would then be as follows:
P = 5.00 / .11
P = $45.45
b) The credibility issue adds 1% to the required rate of return. Thus, the new rate of return is .11 + .01 = .12
P = 5.00 / .12
P = $41.67
The company’s stock is worth less as the result of its credibility problem.
c) The value difference is $45.45 – $41.67 = $3.78. The difference can be interpreted as the investor needs to earn a greater return on the investment in order to be willing to make that investment. The only way to achieve a greater return on the investment, given the , is if the price falls. When the price falls to $41.67, this is a company with the equivalent risk to the same company with no credibility problem at $45.45. The lower price is the result of a shakier company and the reduced demand from investors that results from the company’s credibility problems.