Your Company Doesn't Face Any Taxes and Has $750 Million

Your company doesn't face any taxes and has $750 million in assets, currently financed entirely with equity. Equity is worth $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 shown as follows:
$$\begin{array} { c c c c } \text { State } & \text { Recession } & \text { Average } & \text { Boom } \\\text { Probability of state } & 0.15 & 0.65 & 0.20 \\\text { Expected EBIT in state } & \$ 100 \text { million } & \$ 175 \text { million } & \$ 235 \text { million }\end{array}$$
The firm is considering switching to a 30 percent debt capital structure, and has determined that they would have to pay a 9 percent yield on perpetual debt in either event. What will be the standard deviation in EPS if they switch to the proposed capital structure?

A) 3.76
B) 9.15
C) 14.17
D) 83.79