Philadelphia Corporation\'s stock recently paid a dividend of $2.00 per share (D
ID: 2733197 • Letter: P
Question
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?
Explanation / Answer
Current Dividend = D0
Growth Rate= g
Required rate of return on the market = Rm
Risk-free rate = Rf
Required rate of return = Ke
Expected Dividend = D1
D1= D0 (1+g) + D0
= $2.1
Solution
D0= $2
g= 5%
Beta = 1.5
Rm = 15%
Rf= 7%
Ke= Rf+ (Rm-Rf)Beta
= 19%
Price (P0)= D1/ Ke- g
= $2.1/ 19%- 5%
= $ 15
When Beta changes to 1.75,
Beta = 1.75
Rm = 15%
Rf= 7%
Ke= Rf+ (Rm-Rf)Beta
=21%
Price (P0)= D1/ Ke- g
or $15 = [2(1+g) ] / 0.21- g
or g= 6.8%
Hence, the new constant growth rate will cause the common stock price of Philadelphia to remain unchanged is
6.8%