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:
$$\begin{array} { c c c c }
\text { State } & \text { Recession } & \text { Average } & \text { Boom } \
\text { Probability of state } & 0.25 & 0.55 & 0.20 \
\text { Expected EBIT in state } & \$ 5 \text { million } & \$ 10 \text { million } & \$ 17 \text { million }
\end{array}$$
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 level of expected 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:
$$\begin{array} { c c c c } 
\text { State } & \text { Recession } & \text { Average } & \text { Boom } \
\text { Probability of state } & 0.25 & 0.55 & 0.20 \
\text { Expected EBIT in state } & \$ 5 \text { million } & \$ 10 \text { million } & \$ 17 \text { million }
\end{array}$$
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 level of expected EPS if they switch to the proposed capital structure?

Quizplus · Accepted Answer

First, calculate the firm's total market value under the all-equity scenario, which is $250 million. With a 25% debt capital structure, the firm would have $62.5 million in debt (25% of $250 million) and $187.5 million in equity. The interest expense on the debt would be 10% of $62.5 million, which is $6.25 million annually.Next, calculate the expected EBIT:$$ \text{Expected EBIT} = 0.25 \times \$5\text{m} + 0.55 \times \$10\text{m} + 0.20 \times \$17\text{m} = \$10.15\text{m} $$Subtract the interest expense from the expected EBIT to get expected net income:$$ \text{Expected Net Income} = \$10.15\text{m} - \$6.25\text{m} = \$3.9\text{m} $$Given that the market value of equity is $187.5 million and each share is worth $13, the number of shares is:$$ \text{Number of shares} = \frac{\$187.5\text{m}}{\$13\text{per share}} = 14.423\text{m shares} $$Finally, calculate the expected EPS:$$ \text{Expected EPS} = \frac{\$3.9\text{m}}{14.423\text{m shares}} = \$0.27 $$Therefore, the level of expected EPS with the proposed capital structure is $0.27.

Daddi Mac, Inc The Firm Is Considering Switching to a 25 Percent Debt