Daddi Mac, Inc., doesn't face any taxes and has $250 million in assets, currently financed entirely with equity. Equity is worth $13 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:
The firm is considering switching to a 25 percent debt capital structure, and has determined that they would have to pay a 10 percent yield on perpetual debt. What will be the standard deviation in EPS if they switch to the proposed capital structure?

Question

Daddi Mac, Inc., doesn't face any taxes and has $250 million in assets, currently financed entirely with equity. Equity is worth $13 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: 
The firm is considering switching to a 25 percent debt capital structure, and has determined that they would have to pay a 10 percent yield on perpetual debt. What will be the standard deviation in EPS if they switch to the proposed capital structure?

Quizplus · Accepted Answer

Firstly, we need to calculate the new EBIT values and their probabilities after the change in capital structure. Assuming that EBIT remains the same regardless of the financing structure:

EBIT high = $80 million * (1-0.4) = $48 million
EBIT medium = $30 million * (1-0.4) = $18 million
EBIT low = -$10 million * (1-0.4) = -$6 million

P(high) = 0.3, P(medium) = 0.5, P(low) = 0.2

Next, we can calculate the new EPS values and their probabilities, using the interest expense from the perpetual debt:

EPS high = ($48 million - 0.25*$250 million*$0.10)/6.25 million shares = $1.68
EPS medium = ($18 million - 0.25*$250 million*$0.10)/6.25 million shares = $0.84
EPS low = (-$6 million - 0.25*$250 million*$0.10)/6.25 million shares = -$0.36

P(high) = 0.3, P(medium) = 0.5, P(low) = 0.2

Finally, we can calculate the standard deviation of EPS using the new EPS values and their probabilities:

σEPS = sqrt[0.3*(1.68 - 1.07)^2 + 0.5*(0.84 - 1.07)^2 + 0.2*(-0.36 - 1.07)^2] = 0.26

Therefore, the standard deviation in EPS if they switch to the proposed capital structure would be $0.26. Therefore, the best choice is B.