Philadelphia Corporation's stock recently paid a dividend of $2.00 per share (D0 = $2), and the stock is in equilibrium. The company has a constant growth rate of 5 percent and a beta equal to 1.5. The required rate of return on the market is 15 percent, and the risk-free rate is 7 percent. Philadelphia is considering a change in policy which will increase its beta coefficient to 1.75. If market conditions remain unchanged, what new constant growth rate will cause the common stock price of Philadelphia to remain unchanged?

Question

Quizplus · Accepted Answer

First, we can solve for the current stock price using the dividend discount model:
P0 = D1 / (r - g)
where P0 is the current stock price, D1 is the next dividend (which can be found using the constant growth rate formula: D1 = D0 * (1 + g)), r is the required rate of return, and g is the constant growth rate.
D1 = $2 * (1 + 0.05) = $2.10
P0 = $2.10 / (0.15 - 0.05) = $21.00

Next, we can solve for the new required rate of return using the capital asset pricing model (CAPM):
r = rf + beta * (rm - rf)
where rf is the risk-free rate, beta is the beta coefficient, and rm is the required rate of return on the market.
r = 0.07 + 1.75 * (0.15 - 0.07) = 0.07 + 0.14 = 0.21, or 21%

Finally, we can solve for the new constant growth rate using the dividend discount model again, but with the new required rate of return and the current stock price:
g = r - (D1 / P0)
g = 0.21 - ($2.10 / $21.00) = 0.10, or 10%
But, we want to find the growth rate that will keep the stock price unchanged, so we need to use the current dividend and the new required rate of return:
P1 = D1 / (r - g)
$21.00 = $2.10 / (0.21 - g)
g = 0.0677, or 6.77%

Therefore, the answer is (C) 6.77%.

Philadelphia Corporation's Stock Recently Paid a Dividend of $2