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Part 1

A 

​$1 comma 000.001,000.00 

face value bond has a conversion ratio of 

3232. 

You estimate the transaction costs of conversion to be 

3.5 %3.5% 

of the face value of the bond. What price must the stock reach in order for you to​ convert?

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Part 1

The required price per share will be 

​$enter your response here. 

 ​(Round to the nearest​ cent.)

To find the stock price at which it would be beneficial to convert the bond, we need to determine the **conversion price** considering the transaction costs. 

### Step-by-Step Process:

1. **Identify the given values**:
   - Face value of the bond: $1,000.00
   - Conversion ratio: 32 shares (you receive 32 shares for each bond you convert)
   - Transaction cost: 3.5% of the face value

2. **Calculate the transaction cost**:
   The transaction cost is 3.5% of the bond's face value:
   \[
   \text{Transaction Cost} = 3.5\% \times 1,000 = 0.035 \times 1,000 = 35.00
   \]

3. **Net proceeds after conversion**:
   After accounting for transaction costs, the proceeds from converting the bond would be:
   \[
   \text{Net Proceeds} = 1,000 - 35 = 965.00
   \]

4. **Find the required stock price**:
   To determine the required price per share, divide the net proceeds by the conversion ratio:
   \[
   \text{Required Price Per Share} = \frac{965}{32} = 30.16
   \]

Thus, the stock price must reach **$30.16** in order for you to convert the bond.

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Would you like any further details or explanations?

Here are 5 related questions to expand on this topic:
1. What is a conversion ratio in convertible bonds, and how does it affect investors?
2. How would changes in transaction costs impact the required stock price for conversion?
3. What is the difference between face value and market value of a bond?
4. How do convertible bonds benefit investors compared to traditional bonds?
5. What are the tax implications of converting a bond into stock?

**Tip**: Always consider transaction costs when calculating the profitability of converting a bond.

$1,000.00 face value bond has a conversion ratio of 32. You estimate the transaction costs of conversion to be 3.5% of the face value of the bond. What price must the stock reach in order for you to convert? (Round to the nearest cent.)

Learn how to calculate the required stock price for converting a $1,000 bond with a 3.5% transaction cost and a conversion ratio of 32. This problem covers key concepts in algebra and percentage calculation, suitable for high school students in Grades 9-12.

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