Question

Best China Corp. has just issued a 30-year callable, convertible bond with a coupon rate of 6 percent annual coupon payments. The bond has a conversion price of $93. The company's stock is selling for $28 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.

a. What is the minimum value of the bond?

b. If the stock price were to grow by 11 percent per year forever, how long would it take for the bond's conversion value to exceed $1,100?

Answer 1

a) The minimum value of convertible bond occurs when the conversion option is worthless and will never gets to be exercised

Price of the bond in that case is same as non-convertible bond with a yield of 7%

Annual Coupon Amount =$1000 *6% =$60

So, Minimum value of bond =60/1.07+60/1.07^2+...+60/1.07^30+1000/1.07^30

=60/0.07*(1-1/1.07^30)+ 1000/1.07^30

=$875.91

b) Conversion price would be above $1100 when

Price of the stock = $1100/$1000*Conversion price

=>Price of the stock = $1100/$1000* $93 =$102.3

Let the time taken for the bond to reach/cross $102.30 be n years

Then 28*1.11^n>102.30

=> 1.1^n>3.63571

Taking natural log of both sides

n> ln(3.63571)/ln(1.11) =12.415

So, it will take 13 years for the bond's conversion value to reach $1100