Question 24.S-TP.2: Convertible Bonds Old Cycle Corporation (OCC), publisher of ...
Convertible Bonds Old Cycle Corporation (OCC), publisher of Ancient Iron magazine, has a $1,000 par value convertible bond issue that is currently selling in the market for $950. Each bond can be exchanged for 100 shares of stock at the holder’s option.
The bond has a 7 percent coupon, payable annually, and it will mature in 10 years. OCC’s debt is BBB-rated. Debt with this rating is priced to yield 12 percent. Stock in OCC is trading at $7 per share.
What is the conversion ratio on this bond? The conversion price? The conversion premium? What is the floor value of the bond? What is its option value?
Because each bond can be exchanged for 100 shares, the conversion ratio is 100.
The conversion price is the face value of the bond ($1,000) divided by the conversion ratio, or $1,000/100 = $10. The conversion premium is the percentage difference between the current price and the conversion price, or ($10 − 7)/$7 = .43, or 43%.
The floor value of the bond is the greater of its straight bond value or its conversion value. Its conversion value is what the bond is worth if it is immediately converted: 100 × $7 = $700. The straight bond value is what the bond would be worth if it were not convertible. The annual coupon is $70, and the bond matures in 10 years. At a 12 percent required return, the straight bond value is:
Straight bond value = $70 × (1 − 1/1.12^{10})/.12 + $1,000/1.12^{10}
= $395.52 + 321.97
= $717.49
This exceeds the conversion value, so the floor value of the bond is $717.49. Finally, the option value is the value of the convertible in excess of its floor value. Because the bond is selling for $950, the option value is:
Option value = $950 − 717.49
= $232.51