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 

​$22.8022.80. 

 ​(Round to the nearest​ cent.)

The problem deals with a bond conversion scenario where the bond has a **face value** of $1,000.00, a **conversion ratio** of 4545, and transaction costs of **2.6%** of the face value of the bond. The objective is to determine the stock price that makes conversion worthwhile.

### Explanation:

1. **Face Value of the Bond (F):** $1,000.00
2. **Conversion Ratio (CR):** 4545 shares per bond (this means, upon conversion, you will get 4545 shares of stock for every bond).
3. **Transaction Cost Percentage (T):** 2.6% of the face value.

To convert the bond profitably, the **value of the stock received** after conversion must equal or exceed the bond's face value plus the transaction costs.

The total value you must achieve is the face value plus the transaction cost:

\[
\text{Total Required Value} = F + (T \times F)
\]
\[
\text{Total Required Value} = 1000 + (0.026 \times 1000) = 1000 + 26 = 1026
\]

This is the total value you need to recover when you convert the bond.

To find the **stock price** required for this, divide the total required value by the number of shares you will receive upon conversion (i.e., the conversion ratio):

\[
\text{Required Stock Price} = \frac{\text{Total Required Value}}{\text{Conversion Ratio}}
\]
\[
\text{Required Stock Price} = \frac{1026}{4545} \approx 0.2257
\]

So, the stock price must be approximately **$0.23** per share for you to break even after accounting for the transaction cost. If the question specified a stock price of **$22.80** then this may be the result of another calculation or assumption not covered in the question.

Would you like more details on a specific part or further clarifications?

### Related Questions:
1. How does the conversion ratio affect the decision to convert bonds to stocks?
2. What are other common costs associated with bond conversions, besides transaction costs?
3. How is the stock price expected to behave in scenarios where many bonds are converted to shares?
4. Could the conversion decision be influenced by expected future stock price changes?
5. What impact does inflation have on bond conversion scenarios?

#### Tip:
When calculating conversion costs, always check if there are other hidden fees, like brokerage or taxes, which could influence the final decision.

$1 comma 000.00 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?

Learn how to calculate the required stock price for converting a bond with a face value of $1,000.00 and a conversion ratio of 4545. This problem includes percentage calculations and division to determine the stock price after accounting for a 2.6% transaction cost. Suitable for advanced high school or college-level finance students.

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