Question

4. Brennan's just paid a dividend of $1.50 per share. This is expected to grow at an 8% annual rate for the next three years, then it will grow at 2% in perpetuity. The coefficient of correlation of Brennan's with the market portfolio is 0.3 and its standard deviation is 24%. The expected return and standard deviation for the market are 12% and 9% respectively. a. What is the beta for Brennan's? b. If the risk-free rate of return is 5%, what is the required rate of return for Brennan's? c. What is the price of a single share of Brennan's?

Answer 1

a. Beta for Brennan's =Correlation of Market*Standard Deviation of Portfolio/Standard Deviation of Market =0.3*24%/9% =0.8

b. The Required rate of stock =Risk free Rate+Beta*(Market Return-Risk free Rate)=5%+0.8*(9%-5%)=8.2%

c. Dividend Year 1(D1)=1.50*(1+8%)
D2=1.50*(1+8%)^2
D3=1.50*(1+8%)^3
D4 =1.50*(1+8%)^3*(1+2%)
Terminal Value=D4/(r-g)=1.50*(1+8%)^3*(1+2%)/(8.2%-2%)=31.0864
Price of Stock =1.50*(1+8%)/(1+8.2%)+1.50*(1+8%)^2/(1+8.2%)^2 +1.50*(1+8%)^3/(1+8.2%)^3+31.0864/(1+8.2%)^3
=29.02