Your company doesn\'t face any taxes and has $755 million in assets, currently f

Question

Your company doesn't face any taxes and has $755 million in assets, currently financed entirely with equity. Equity is worth $50.50 per share, and book value of equity is equal to market value of equity. Also, let's assume that the firm's expected values for EBIT depend upon which state of the economy occurs this year, with the possible values of EBIT and their associated probabilities as shown below: State Recession Average Boom Probability of State .20 .60 .20 Expect EBIT in State $105 million $180 million $240 million The firm is considering switching to a 20-percent debt capital structure, and has determined that they would have to pay a 10 percent yield on perpetual debt in either event. What will be the standard deviation in EPS if they switch to the proposed capital structure? (Round your intermediate calculations and final answer to 2 decimal places except calculation of number of shares which should be rounded to nearest whole number.)

a) 13.54

b) 3.58

c) 13.37

d) 6.33

Explanation / Answer

Number of shares=Enterprise Value/Market Value=755/50.5=14.9505 million
Number of shares in case of 20% capital strucutre=80%*14.9505=11.9604 million

Probability: 0.2 EBIT=105..Debt=20%*755=151 Interest=10%*151=15.1 Net Income=105-15.1=89.9 EPS=89.9/11.9604=7.51647

Probability: 0.6 EBIT=180..Debt=20%*755=151 Interest=10%*151=15.1 Net Income=180-15.1=164.9 EPS=164.9/11.9604=13.78716

Probability: 0.2 EBIT=240..Debt=20%*755=151 Interest=10%*151=15.1 Net Income=240-15.1=224.9
EPS=224.9/11.9604=18.80372

Mean EPS=0.2*7.51647+0.6*13.78716+0.2*18.80372=13.53633

Standard Devaition EPS=sqrt(0.2*(7.51647-13.53633)^2+0.6*(13.78716-13.53633)^2+0.2*(18.80372-13.53633)^2)=3.58 million

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