Your company doesn\'t face any taxes and has $760 million in assets, currently f

Question

Your company doesn't face any taxes and has $760 million in assets, currently financed entirely with equity. Equity is worth $51.00 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:

The firm is considering switching to a 15-percent debt capital structure, and has determined that they would have to pay a 11 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.)

State Recession Average Boom   Probability of State .10 .75 .15   Expect EBIT in State $110 million $185 million $245 million

Explanation / Answer

Number of shares=Enterprise Value/Market Value=760/51=14.90196 million
Number of shares in case of 20% capital strucutre=80%*14.90196=11.92157 million

Probability: 0.1 EBIT=110..Debt=15%*760=114 Interest=11%*114=12.54 Net Income=110-12.54=97.46 million EPS=97.46/11.92157=8.175098

Probability: 0.75 EBIT=185..Debt=15%*760=114 Interest=11%*114=12.54 Net Income=185-12.54=172.46 million EPS=172.46/11.92157=14.46622

Probability: 0.15 EBIT=245..Debt=15%*760=114 Interest=11%*114=12.54 Net Income=245-12.54=232.46 million EPS=232.46/11.92157=19.49911

Mean EPS=0.1*8.175098+0.75*14.46622+0.15*19.49911=14.59204

Standard Devaition EPS=sqrt(0.2*(8.175098-14.59204)^2+0.6*(14.46622-14.59204)^2+0.2*(19.49911-14.59204)^2)=3.614

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