Vital Silence Corp. has just issued a 30-year callable, convertible bond with a coupon rate of 5 percent and annual coupon payments. The bond has a conversion price of $78. The company’s stock is selling for $24 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 $1,100. The required return on an otherwise identical nonconvertible bond is 7 percent. Assume a par value of $1,000.

a. What is the minimum value of the bond?

b. If the stock price were to grow by 10 percent per year forever, how long would it take for the bond’s conversion value to exceed $1,100?