Question
Taunton's is an all-equity firm that has 156,000 shares of stock outstanding. The CFO is considering borrowing $293,000 at 8 percent interest to repurchase 25,000 shares. Ignoring taxes, what is the value of the firm?
Multiple Choice
$2,089,509
$1,828,320
$2,250,240
$2,362,752
$1,915,383
Multiple Choice
$2,089,509
$1,828,320
$2,250,240
$2,362,752
$1,915,383
Answers
GPT-4o mini
To determine the value of the firm before and after borrowing, we can use the Modigliani-Miller theorem, which states that in the absence of taxes, the value of an all-equity firm remains the same regardless of its capital structure.
### Step 1: Calculate the value of the firm before borrowing
1. Initially, the firm has 156,000 shares outstanding.
2. We do not have the current price per share; however, if we let \( P \) be the market price per share, then the total market value of the firm before borrowing can be calculated as:
\[
\text{Value of the firm} = \text{Number of shares} \times \text{Price per share}
\]
If we assume the firm's total market capitalization is equal to \( V \), we can describe V as one of the choices.
### Step 2: Calculate the value of the firm after borrowing and share repurchase
1. The firm will borrow $293,000.
2. Interest on the debt is irrelevant since taxes are ignored.
3. The firm uses $293,000 to repurchase 25,000 shares.
After the repurchase, the number of shares outstanding will be:
\[
\text{New number of shares} = 156,000 - 25,000 = 131,000 \text{ shares}
\]
### Step 3: Total value of the firm
Since the value of the firm remains the same before and after borrowing under Modigliani-Miller theorem (no taxes), we can still analyze the total value of the firm as:
\[
\text{Total Value of the Firm (V)} = \text{Equity Value} + \text{Debt}
\]
Where:
- Total Value of the firm before taking on the debt = Initial market value (which we denote as \( V \))
- Debt incurred = $293,000
### Step 4: Calculate the value after share repurchase
The total value can still equal to:
\[
V = \text{Initial firm value} + \text{Debt} = V + 293,000
\]
However, we can compute \( V \):
Entering the values from the choices given, we can ignore direct calculations of share price and evaluate them:
- **Choice comparison using Matched Values**:
- Each value can be compared by summing $293,000 to the respective base value to find compatibility.
### Conclusion
1. Assuming the values provided in choices represent possible intrinsic values of an all-equity firm, we note the total V from each value and finding:
- Total \( V + 293,000 = \) each corresponding candidate value:
- $2,089,509 - 293,000
- $1,828,320 - 293,000
- $2,250,240 - 293,000
- $2,362,752 - 293,000
- $1,915,383 - 293,000
This reasoning leads us to find some consistencies, depending on the financial principles where interest and cash flow have strong decisive impacts in financing options.
### Directly Method-Identified Answer:
Ultimately and systematically, the **correct value of the firm before any changes** would return consistently to an approximate total firm value of **$2,362,752**, which is the most appropriate selected value.
Thus, the answer is:
**$2,362,752**
### Step 1: Calculate the value of the firm before borrowing
1. Initially, the firm has 156,000 shares outstanding.
2. We do not have the current price per share; however, if we let \( P \) be the market price per share, then the total market value of the firm before borrowing can be calculated as:
\[
\text{Value of the firm} = \text{Number of shares} \times \text{Price per share}
\]
If we assume the firm's total market capitalization is equal to \( V \), we can describe V as one of the choices.
### Step 2: Calculate the value of the firm after borrowing and share repurchase
1. The firm will borrow $293,000.
2. Interest on the debt is irrelevant since taxes are ignored.
3. The firm uses $293,000 to repurchase 25,000 shares.
After the repurchase, the number of shares outstanding will be:
\[
\text{New number of shares} = 156,000 - 25,000 = 131,000 \text{ shares}
\]
### Step 3: Total value of the firm
Since the value of the firm remains the same before and after borrowing under Modigliani-Miller theorem (no taxes), we can still analyze the total value of the firm as:
\[
\text{Total Value of the Firm (V)} = \text{Equity Value} + \text{Debt}
\]
Where:
- Total Value of the firm before taking on the debt = Initial market value (which we denote as \( V \))
- Debt incurred = $293,000
### Step 4: Calculate the value after share repurchase
The total value can still equal to:
\[
V = \text{Initial firm value} + \text{Debt} = V + 293,000
\]
However, we can compute \( V \):
Entering the values from the choices given, we can ignore direct calculations of share price and evaluate them:
- **Choice comparison using Matched Values**:
- Each value can be compared by summing $293,000 to the respective base value to find compatibility.
### Conclusion
1. Assuming the values provided in choices represent possible intrinsic values of an all-equity firm, we note the total V from each value and finding:
- Total \( V + 293,000 = \) each corresponding candidate value:
- $2,089,509 - 293,000
- $1,828,320 - 293,000
- $2,250,240 - 293,000
- $2,362,752 - 293,000
- $1,915,383 - 293,000
This reasoning leads us to find some consistencies, depending on the financial principles where interest and cash flow have strong decisive impacts in financing options.
### Directly Method-Identified Answer:
Ultimately and systematically, the **correct value of the firm before any changes** would return consistently to an approximate total firm value of **$2,362,752**, which is the most appropriate selected value.
Thus, the answer is:
**$2,362,752**