Question

A convertible bond has a coupon of 7 percent, paid semiannually, and will mature in 20 years. If the bond were not convertible, it would be priced to yield 6 percent. The conversion ratio on the bond is 15 and the stock is currently selling for $54 per share. What is the minimum value of this bond? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Minimum value:

Answer 1

Assumptions made:

7% is the annual coupons, i.e., 3.5% is paid every 6 months

Face value of bond if it were not convertible= $1000 (to calculate coupons)

First step is to calculate present value of future payments of coupons of the bond, which will essentially give us the bond value pertaining to coupon payments

PV=

Since there are 20 semi-annual payments, we have a total of 40 periods.

C1 = C2 =C3 = ......= C40 = coupon payments in each of the 40 periods = 3.5% x 1000 = $35

r= half yearly yield = 6%/2 = 3%

Substituting the values (or using NPV function in Excel), PV = $809.02

Proceeds realized when bond is converted to stocks = 54 x 15 = $810 (at present value of stock)

Therefore, minimum value of bond = 809.02+810 = $1619.02