Question

A company issues a 10-year convertible bond with a 6% coupon, paid annually. The bond is convertible into common shares at a conversion rate of 55. Straight bonds of similar risk currently yield 7.8%. The stock price is currently priced 25% less than the conversion price. The company's stock price is expected to grow by 8% per year, and the bond is callable at $1,100. The bonds will not be called until their price is 125% of the conversion value.

a.
How many years do you expect it will take for the bonds to be called? (Round your answer up to a full year.)

b.
What will be the overall return to the convertible bondholder?

Answer 1

a. The bond is convertible into common shares at a conversion rate of 55.

The stock price is currently priced 25% less than the conversion price

So the stock price right now is

55*100/125 = 44

The bonds will not be called until their price is 125% of the conversion value.

Conversion value = 55

125 % of the conversion value = 55*125/100 = 68.75

The company's stock price is expected to grow by 8% per year.

Stock price right now is at 44

44*8/100 = 3.52

The company's stock price is expected to grow by 3.52 per year

68.75 - 44 = 24.75

24.75/3.52 = 7.03

So the answer in the round figure is 7 years

b. Conversion ratio

= number shares for which one bond may be exchanged

= par/conversion price

= $1100/55 = 20 shares

Conversion value

= stock price * conversion ratio

= 68.75 * 20 = $1375

Overall return

=1375/1100*100

=125

=125-100 = 25% plus 6% coupen rate for 7 years so 6 * 7 = 42%

25 plus 42 = 67 % overall returns