Final answer:
Bondholders would consider converting their $1,000 bond into common stock if the stock trades above $50 per share, because at that price, the value of the converted stocks would be greater than the bond itself.
Step-by-step explanation:
To determine the minimum price at which the stock must be trading for bondholders to consider converting their bonds to common stock, we need to calculate the conversion price of the bond. We know that a $1,000 corporate bond is convertible to 20 shares of the corporation's common stock. Therefore, the minimum price per share that would make the conversion attractive is calculated by dividing the bond value by the number of shares it can be converted into.
The calculation is as follows: $1,000 / 20 shares = $50 per share. Bondholders would consider converting their bonds to common stock if the stock's trading price is above this minimum price because the market value of the shares they would receive would exceed the value of the bond.
Considering the changes in interest rates, and knowing that bond prices are inversely related to interest rates, if interest rates rise, the market value of existing bonds tends to decrease.
Therefore, you would expect to pay less than $10,000 for the bond, assuming the bond in question has a greater face value or a principal amount reflecting the described scenario. If the bond was initially valued at $1,000, rises in interest rates will cause it to sell for less than its face value to provide a yield that is competitive with the new interest rates