Final answer:
The realized rate of return on a bond is calculated by summing up the total interest payments and capital gains from a call premium and then dividing this total by the original investment.
Step-by-step explanation:
The question is about computing the realized rate of return for investors who purchased 25-year bonds with a 12% annual coupon rate and a 7% call premium a decade ago, which were called today by Ginger Incorporated. The bonds were sold at their face value of $1,000.
To calculate the realized rate of return, we consider that investors received annual interest payments of 12% of the face value, which is $120 per year. After ten years, the total interest payments would be $1200. Since the bonds were called today, investors will also receive the face value plus a 7% call premium. Hence, the call price would be $1,000 + 7% of $1,000, which equals $1,070. Combining the interest payments with the call price gives us the total cash received by the investors. The yield, or total return, is the sum of the interest payments and the capital gains realized from the call premium.
The realized rate of return for the investors is therefore the ratio of the total benefits received (interest and call premium) minus the original investment, over the original investment. This would be the interest ($1,200) plus call premium ($70) minus the initial $1,000, divided by the original investment of $1,000. The formula simplifies to: (Total benefits received - $1,000) / $1,000.