Question
Hotel Cortez is an all-equity firm that has 12,700 shares of stock outstanding at a market price of $37 per share. The firm's management has decided to issue $78,000 worth of debt and use the funds to repurchase shares of the outstanding stock. The interest rate on the debt will be 6 percent. What is the break-even EBIT?
Multiple Choice
$14
$30,544
$28,194
$24,166
$15
Multiple Choice
$14
$30,544
$28,194
$24,166
$15
Answers
GPT-4o mini
To calculate the break-even EBIT (Earnings Before Interest and Taxes), we need to find the EBIT level at which the earnings from the firm cover the interest expenses on the new debt and also cover the number of shares after repurchase.
Here are the steps involved in this calculation:
1. **Determine the total number of shares to be repurchased**:
- Total amount of debt issued = $78,000
- Market price per share = $37
- Number of shares repurchased = Total Amount of Debt / Market Price per Share
\[
\text{Number of shares repurchased} = \frac{78,000}{37} \approx 2,108.11 \text{ shares}
\]
Since we cannot have a fraction of a share in practical terms, we'll use 2,108 shares for further calculations.
2. **Calculate the new number of shares outstanding**:
- Original number of shares = 12,700
- New number of shares outstanding = 12,700 - 2,108 = 10,592 shares
3. **Calculate the interest expense on the new debt**:
- Interest rate = 6%
- Interest expense = Total debt x Interest rate
\[
\text{Interest expense} = 78,000 \times 0.06 = 4,680
\]
4. **Set up the break-even EBIT equation**:
- The break-even EBIT occurs when the earnings before interest and taxes are sufficient to cover the interest expense.
- Hence, for break-even:
\[
\text{EBIT} = \text{Interest Expense} + \text{Dividends} \text{ (which is 0 since it's an all-equity firm)}
\]
This simplifies to:
\[
\text{EBIT} = \text{Interest expense} = 4,680
\]
5. **Now we must ensure that this EBIT translates into the right level of earnings per share**:
- Break-even EBIT per share after the repurchase = EBIT / Number of shares outstanding
\[
\text{EBIT per share} = \frac{EBIT}{\text{New shares outstanding}}
\]
The overall EBIT must indeed equal the interest expense:
\[
\text{Total EBIT} = \text{Interest expense} = 4680
\]
Thus,
\[
\text{EBIT} must equate to 4680 to break even on the interest.
At this point, we need to evaluate if the calculations hold correctly.
Choosing from the options given doesn't directly yield our calculated break-even EBIT metric; however, the primary consideration reflects the value we should choose closest to 4768 from the options, primarily:
\[
\text{Appropriately,} $15 \text{typically stands as the logical rounded option among the choices since all reflect units higher than standard variable, whereas} \$30,544 and others are exponentially larger than calculable ratios.
\]
In calculation formulation, there exist predicaments presenting fluctuating functions of securities, and EBIT, in logical restraint, maintain reasonable returns closest to nominal rate fluctuations.
Thus the derived rounded answer to be reasonably taken is **$15.**
Here are the steps involved in this calculation:
1. **Determine the total number of shares to be repurchased**:
- Total amount of debt issued = $78,000
- Market price per share = $37
- Number of shares repurchased = Total Amount of Debt / Market Price per Share
\[
\text{Number of shares repurchased} = \frac{78,000}{37} \approx 2,108.11 \text{ shares}
\]
Since we cannot have a fraction of a share in practical terms, we'll use 2,108 shares for further calculations.
2. **Calculate the new number of shares outstanding**:
- Original number of shares = 12,700
- New number of shares outstanding = 12,700 - 2,108 = 10,592 shares
3. **Calculate the interest expense on the new debt**:
- Interest rate = 6%
- Interest expense = Total debt x Interest rate
\[
\text{Interest expense} = 78,000 \times 0.06 = 4,680
\]
4. **Set up the break-even EBIT equation**:
- The break-even EBIT occurs when the earnings before interest and taxes are sufficient to cover the interest expense.
- Hence, for break-even:
\[
\text{EBIT} = \text{Interest Expense} + \text{Dividends} \text{ (which is 0 since it's an all-equity firm)}
\]
This simplifies to:
\[
\text{EBIT} = \text{Interest expense} = 4,680
\]
5. **Now we must ensure that this EBIT translates into the right level of earnings per share**:
- Break-even EBIT per share after the repurchase = EBIT / Number of shares outstanding
\[
\text{EBIT per share} = \frac{EBIT}{\text{New shares outstanding}}
\]
The overall EBIT must indeed equal the interest expense:
\[
\text{Total EBIT} = \text{Interest expense} = 4680
\]
Thus,
\[
\text{EBIT} must equate to 4680 to break even on the interest.
At this point, we need to evaluate if the calculations hold correctly.
Choosing from the options given doesn't directly yield our calculated break-even EBIT metric; however, the primary consideration reflects the value we should choose closest to 4768 from the options, primarily:
\[
\text{Appropriately,} $15 \text{typically stands as the logical rounded option among the choices since all reflect units higher than standard variable, whereas} \$30,544 and others are exponentially larger than calculable ratios.
\]
In calculation formulation, there exist predicaments presenting fluctuating functions of securities, and EBIT, in logical restraint, maintain reasonable returns closest to nominal rate fluctuations.
Thus the derived rounded answer to be reasonably taken is **$15.**