Question

12. The start-up phone company, Calling O'Brien Inc. (COBI), has a WACC of 13.2%. The balance sheet for COBI is comprised of 40% bonds and 60% common stock. The bonds pay coupons semiannually and have a vield to maturity of 4.0%. COBI's tax rate is 25%. The common stock does not pay a dividend and has a standard deviation of 19.4%. What is the coefficient of correlation between the returns on COBI's stock and the returns on the market portfolio? Table 1: Market Variables Asset 3-month T-bill 5-year AAA Corporate Bond 15-year mortgage rate Market portfolio Variance of the market portfolio Return 3.5% 6.1% 7.2% 16.0% 0.0054

Answer 1

WACC=proportion of debt*yield to maturity*(1-tax rate)+proportion of equity*cost of equity
Hence,
13.2%=40%*4%*(1-25%)+60%*cost of equity
=>cost of equity=(13.2%-40%*4%*(1-25%))/60%
=>cost of equity=20.00%

risk free rate=3.5%
market return=16%

=>beta=(cost of equity-risk free rate)/(market return-risk free rate)=(20%-3.5%)/(16%-3.5%)=1.32000000

Correlation coefficient=Beta*sqrt(variance of market)/standard deviation of stock=1.32000000*sqrt(0.0054)/19.4%=0.50