Question

# Problem 18-6 Convertible Bonds (LO3, CFA5) A convertible bond has a coupon of 6 percent, paid...

Problem 18-6 Convertible Bonds (LO3, CFA5) A convertible bond has a coupon of 6 percent, paid semiannually, and will mature in 18 years. If the bond were not convertible, it would be priced to yield 5 percent. The conversion ratio on the bond is 30 and the stock is currently selling for \$39 per share. What is the minimum value of this bond? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Bond Coupon = 6% per annum or 3% per half year, Yield = 5 % per annum or 2.5% per half year and maturity = 18 years or 36 half years.

Let the par value be \$1000

Let the market price be P(m)

Therefore, P(m) = 30 x (1/0.025) x [1-{1/(1.025)^(36)}] + 1000 / (1.025)^(36) = \$ 1117.78

Conversion Price = Conversion Ratio x Price per share = 30 x 39 = \$ 1170

The convertible bond's minimum value should be the higher of the two values between the straight bond price (without conversion option) and the conversion price.

Hence, bond's minimum value = MAX (1117.78, 1170) = \$ 1178.78

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