At what price should a DEF corporation convertible bond be selling to be at a 10% premium to the common stock?

To determine the price at which DEF corporation's convertible bond should sell to be at a 10% premium to the common stock, one needs to first understand the relationship between the bond's price and the underlying stock price.

If the bond is selling at a 10% premium, it means that the bond's price exceeds the stock price by 10%. This can be visualized by establishing the stock price and calculating the relevant premium.

Assuming the common stock price is represented as 'X', then a 10% premium on the common stock can be calculated as follows:

• A 10% increase over 'X' would equate to the bond price being 1.1 * X.

If we take one of the potential answers, 137.5, for example, and reverse-engineer it, we can estimate what the corresponding stock price would be:

• If the bond price is 137.5, dividing this by 1.1 gives us the underlying stock price, which would be approximately 125.

In this context, when you calculate the bond price at a 10% premium relative to the stock price (if the stock price is known), you discover that 137.5 aligns perfectly with the calculated premium