A firm has just issued a 30-year callable, convertible bond with a coupon rate of 5 percent. The bond makes semi-annual

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A firm has just issued a 30-year callable, convertible bond with
a coupon rate of 5 percent. The bond makes semi-annual coupon
payments. The par value of the bond is $1,000. The bond has a
conversion price of $50. The company’s stock is currently selling
for $30 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
$1,300. The required return on an otherwise identical
nonconvertible bond is 7 percent.
a) Find the current conversion value and the value of the
straight bond (i.e., value of the bond without the call options).
What is the value of the convertible bond?
b) If the stock price were to grow by 8 percent per year
forever, how long would it take for the bond’s conversion value to
exceed $1,300?
c) Assume that the stock price has grown at 8% a year as
expected and the bond is converted when the conversion value is
1,300. What value would you assign to this bond?