HiLo, Inc., doesn't face any taxes and has $100 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:
The firm is considering switching to a 40 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

HiLo, Inc., doesn't face any taxes and has $100 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: 
The firm is considering switching to a 40 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

First, we need to calculate the new EBIT values for each state of the economy in order to calculate the EPS values under the new capital structure.

Under the new capital structure, the firm has a 40% debt-to-total capital ratio, so 60% of the capital will be from equity. This means that the firm will have $60 million in equity and $40 million in perpetual debt.

To calculate the new EBIT values, we need to subtract interest expense from the old EBIT values:

- In a recession, EBIT is $5 million. With $40 million in debt at a 10% yield, interest expense is $4 million. Therefore, new EBIT is $1 million.
- In a normal economy, EBIT is $50 million. Interest expense is still $4 million. Therefore, new EBIT is $46 million.
- In a boom, EBIT is $95 million. Interest expense is still $4 million. Therefore, new EBIT is $91 million.

Next, we need to calculate the EPS values. To do this, we need to subtract the interest expense from the new EBIT values and divide by the number of shares outstanding:

- In a recession, EPS is ($1 million - $0) / 2 million shares = -$0.50.
- In a normal economy, EPS is ($46 million - $4 million) / 2 million shares = $21.
- In a boom, EPS is ($91 million - $4 million) / 2 million shares = $43.50.

Finally, we can calculate the standard deviation of EPS using the same formula we used in previous questions:

σEPS = √[(pi * (EPSi - E(EPS))^2)]

- For the recession state, σEPS = √[(0.1 * (-$0.50 - $8.33)^2 + 0.3 * (-$0.50 - $1.67)^2 + 0.6 * (-$0.50 - $3.33)^2)] = $7.18.
- For the normal state, σEPS = √[(0.1 * ($21 - $8.33)^2 + 0.3 * ($21 - $1.67)^2 + 0.6 * ($21 - $3.33)^2)] = $5.50.
- For the boom state, σEPS = √[(0.1 * ($43.50 - $8.33)^2 + 0.3 * ($43.50 - $1.67)^2 + 0.6 * ($43.50 - $3.33)^2)] = $8.07.

Therefore, the overall standard deviation of EPS under the new capital structure is:

σEPS = √[(0.1 * $7.18^2 + 0.3 * $5.50^2 + 0.6 * $8.07^2)] = $7.54.

So the answer is B.

HiLo, Inc, Doesn't Face Any Taxes and Has $100 Million in in Assets