A 

​$1 comma 000.001,000.00 

face value bond has a conversion ratio of 

4545. 

You estimate the transaction costs of conversion to be 

2.6 %2.6% 

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

Question content area bottom

Part 1

The required price per share will be 

​$enter your response here. 

 ​(Round to the nearest​ cent.)

To find the required stock price at which the bond should be converted, we need to first understand the components involved in the problem:

1. **Face value of the bond**: \$1,000.00.
2. **Conversion ratio**: 4545 (this is the number of shares obtained by converting the bond).
3. **Transaction cost**: 2.6% of the face value of the bond, which means there’s an additional cost associated with converting the bond.

### Step-by-step solution:

1. **Calculate the transaction cost**:  
   The transaction cost is 2.6% of the face value, so:
   \[
   \text{Transaction cost} = 0.026 \times 1000 = 26
   \]
   So, the total cost to convert the bond would be \$26.

2. **Calculate the net amount after conversion**:  
   After conversion, the amount you're aiming for is the face value of the bond plus the transaction cost:
   \[
   \text{Total amount to cover} = 1000 + 26 = 1026
   \]

3. **Determine the stock price for conversion**:  
   The conversion ratio is 4545, meaning for every bond converted, you receive 4545 shares of stock. Therefore, the price per share at which it becomes worthwhile to convert is:
   \[
   \text{Required stock price} = \frac{1026}{4545}
   \]
   Let's calculate that.

\[
\text{Required stock price} = \frac{1026}{4545} = 0.2257
\]

4. **Round to the nearest cent**:  
   The required stock price is \$0.23 per share (rounded to the nearest cent).

### Answer:
The required stock price for conversion is **\$0.23**.

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Would you like further details or have any questions? Here are 5 related questions to explore:

1. How does a conversion premium affect the decision to convert bonds?
2. What is the relationship between bond yield and conversion ratios?
3. How does market volatility impact the timing of bond conversion?
4. What are some risks associated with convertible bonds?
5. How is the conversion price affected by stock dividends?

**Tip**: Convertible bonds provide both fixed income and equity-like potential, so timing the conversion optimally is key to maximizing returns.

$1,000.00 face value bond has a conversion ratio of 4545. You estimate the transaction costs of conversion to be 2.6% of the face value of the bond. What price must the stock reach in order for you to convert? (Round to the nearest cent.)

Calculate the required stock price for bond conversion with a $1,000 face value, 4545 conversion ratio, and 2.6% transaction cost. This finance problem involves percentage and ratio calculations, ideal for college students studying bonds and investments.

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