Ultras Inc. has a 20 percent tax rate and has $350 million in assets, currently financed entirely with equity. Equity is worth $80 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 20 percent debt capital structure, and has determined that they would have to pay a 7 percent yield on perpetual debt in either event. What will be the standard deviation in EPS if the firm switches to the proposed capital structure?

Question

Ultras Inc. has a 20 percent tax rate and has $350 million in assets, currently financed entirely with equity. Equity is worth $80 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 20 percent debt capital structure, and has determined that they would have to pay a 7 percent yield on perpetual debt in either event. What will be the standard deviation in EPS if the firm switches to the proposed capital structure?

Quizplus · Accepted Answer

First, we need to calculate the new capital structure of the firm if they switch to a 20 percent debt capital structure. Since they currently have no debt, the entire $350 million in assets is financed with equity. After the switch, only 80 percent of the assets will be financed with equity, which gives us:

Debt = 0.2 x $350 million = $70 million
Equity = $350 million - $70 million = $280 million

The number of shares outstanding is:

Shares Outstanding = $280 million / $80 per share = 3.5 million shares

Next, we need to calculate the expected EPS under the new capital structure. We'll use the EBIT values from the table and the new capital structure's interest expense:

Interest Expense = 0.07 x $70 million = $4.9 million

We then calculate the expected EPS for each EBIT state:

EPS($80) = ($155 million - $4.9 million) x (1 - 0.2) / 3.5 million shares = $33.88
EPS($60) = ($120 million - $4.9 million) x (1 - 0.2) / 3.5 million shares = $22.46
EPS($40) = ($85 million - $4.9 million) x (1 - 0.2) / 3.5 million shares = $11.04

Now, we can calculate the standard deviation of EPS using the formula for levered standard deviation:

σEPS = [EBIT($155m) - EBIT($120m)] / [EBIT($155m) - Interest Expense] x σEBIT($80)
       + [EBIT($120m) - EBIT($85m)] / [EBIT($155m) - Interest Expense] x σEBIT($60)
       + [EBIT($85m) - EBIT($40m)] / [EBIT($155m) - Interest Expense] x σEBIT($40)

Plugging in the values, we get:

σEPS = [(155 - 120) / (155 - 4.9)] x 0.12
       + [(120 - 85) / (155 - 4.9)] x 0.17
       + [(85 - 40) / (155 - 4.9)] x 0.21
      = 0.0258

Therefore, the standard deviation in EPS if the firm switches to the proposed capital structure is $0.92 ($33.88 x 0.0258). The best choice is therefore B.