Question

Vital Silence Corporation has just issued a 25-year callable, convertible bond with a coupon rate of 5.6 percent and annual coupon payments. The bond has a conversion price of $96.00. The company's stock is selling for $29.70 per share. The owner of the bond will be forced to convert if the bond's conversion value is ever greater than or equal to $1,160. The required return on an otherwise identical nonconvertible bond is 6.6 percent. Assume a par value of $1,000.

a. What is the minimum value of the bond? (Do not round Intermedlate calculations and round your answer to 2 declmal places, e.g., 32.16.)
b. If the stock price were to grow by 10.6 percent per year forever, how long would it take for the bond's conversion value to exceed $1,160 ? (Do not round Intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

The minimum value of the bond is calculated by considering it as a straight bond and discounting its future cash flows at the required rate of return. The time it takes for the bond's conversion value to exceed $1,160 can be found using compound growth formulas, considering a perpetual stock price growth rate of 10.6% per year.

Step-by-step explanation:

The question revolves around calculating the minimum value of a callable, convertible bond issued by Vital Silence Corporation and determining the time it would take for the bond's conversion value to exceed a certain amount if the stock price grows perpetually at a given rate.

The minimum value of this convertible bond will be the greater of its value as a straight bond or its conversion value. As a straight bond, its value can be determined by discounting the future cash flows (the annual coupon payments and principal at maturity) at the required rate of return for an otherwise identical nonconvertible bond, which is 6.6% in this case. As a convertible bond, its initial conversion value is less than its conversion price; therefore, its value as a convertible bond is not immediately relevant.

To find out how long it would take for the bond's conversion value to exceed $1,160 given the stock price grows by 10.6 percent per year, we would use the formula of compound growth to solve for the time period. The bond's conversion value will exceed $1,160 when the company's stock price, assuming consistent growth at the stated rate, leads to a scenario where the product of the conversion ratio and stock price is greater than $1,160.