Consider a 12% convertible bond that has $100 face value, 3 years to maturity, CR = 20, and pays interest annually. The market perceives that 3 years from now the shares of the firm are equally likely to be worth $4.50 and $7. The term structure is assumed to be flat at 10%. Assume that investors delay conversion until after they receive their last coupon. What is the fair price for this bond?
The following information is given
Face value of bond = $100
Coupon = 100 x 12% = 12
Coupon frequency = Yearly
Discount rate = 10%
Share price after 3 years = (4.5+7)/2 = 5.75
CR i.e conversion ratio = 20
Redemption value of bond = share price after 3 years x conversion ratio
=5.75 x 20 = 115
Fairvalue of bond = PV of coupons + PV of Redemption
Therefore,
| Year | Cash Flows | PV of Cash Flows |
| 1 | 12 | 10.91 |
| 2 | 12 | 9.92 |
| 3 | 12 | 9.02 |
| 3 | 115 | 86.40 |
| Fair Value of Bond | 116.24 |
Therefore fairvalue of bond is $116.24
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