Question

The Greenbriar is an all-equity firm with a total market value of $590,000 and 23,000 shares of stock outstanding. Management is considering issuing $205,000 of debt at an interest rate of 7 percent and using the proceeds on a stock repurchase. Ignore taxes. How many shares will the firm repurchase if it issues the debt securities?


Multiple Choice

9,687 shares


41,300 shares


8,879 shares


7,992 shares


559 shares

Answer 1

To determine how many shares The Greenbriar will repurchase by issuing debt, we can follow these steps:

1. **Calculate the amount per share before the debt issue**:
\[
\text{Market Value of the Firm} = \$590,000
\]
\[
\text{Shares Outstanding} = 23,000
\]
\[
\text{Price per Share} = \frac{\text{Market Value of the Firm}}{\text{Shares Outstanding}} = \frac{590,000}{23,000} \approx 25.65
\]

2. **Determine how many shares can be repurchased with the debt proceeds**:
\[
\text{Debt to be Issued} = \$205,000
\]
The number of shares repurchased will be:
\[
\text{Shares Repurchased} = \frac{\text{Debt to be Issued}}{\text{Price per Share}} = \frac{205,000}{25.65} \approx 8,000
\]

3. **Choose the closest answer from the options**. Since the calculated number of shares (8,000) is not among the options, let's double-check our previous calculations.

Calculating with more precision:
- Price per share rounding:
\[
\text{Price per Share} \approx 590,000 / 23,000 \approx 25.65217
\]
- Shares repurchased will therefore be:
\[
\text{Shares Repurchased} = \frac{205,000}{25.65217} \approx 8,000
\]

However, rounding issues can lead to small variations. Let's recalculate:

Using \(25.65217\):
\[
\text{Shares Repurchased} = \frac{205,000}{25.65217} \approx 7,998
\]

This is very close to **7,992**, which matches one of the answer choices provided.

Thus, the firm will repurchase approximately **7,992 shares**.

### Final Answer:
**7,992 shares**