Question

Fifteen years ago, Roop Industries sold $400 million of convertible bonds. The bonds had a 40-year maturity, a 5.75% coupon rate, and paid interest annually. They were sold at their $1,000 par value. The conversion price was set at $64.15, and the common stock price was $58 per share. The bonds were subordinated debentures and were given an A rating; straight nonconvertible debentures of the same quality yielded about 8.85% at the time Roop's bonds were issued.

Calculate the premium on the bonds — that is, the percentage excess of the conversion price over the stock price at the time of issue. Do not round intermediate calculations. Round your answer to two decimal places.

Answer 1

The premium on Roop Industries' convertible bonds is calculated as the percentage excess of the conversion price over the stock price at the time of issue, which in this case is 10.59%.

Step-by-step explanation:

The question asks us to calculate the premium on convertible bonds issued by Roop Industries. The premium is the percentage excess of the conversion price over the stock price at the time of issue. To find the premium, we take the conversion price and subtract the stock price, then divide by the stock price and multiply by 100 to get the percentage.

The conversion price was set at $64.15, and the common stock price was $58 at the time of the issue. Therefore, the premium can be calculated as follows:

Premium = ((Conversion Price - Stock Price) / Stock Price) * 100

Premium = (($64.15 - $58) / $58) * 100

Premium = ($6.15 / $58) * 100

Premium = 0.1059 * 100

Premium = 10.59%

This means that the convertible bonds were issued with a premium of 10.59% over the stock price. The concept here involves understanding how to assess the relative cost or benefit of a convertible bond over the direct investment in the underlying stock at the time of the bond's issue.