Question

Problem 18-6 Convertible Bonds (LO3, CFA5) A convertible bond has a coupon of 7.5 percent, paid semiannually, and will mature in 10 years. If the bond were not convertible, it would be priced to yield 6.5 percent. The conversion ratio on the bond is 30 and the stock is currently selling for $52 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

The minimum value of the bond is computed as shown below:

Coupon payment will be as follows:

= 7.5% / 2 x $ 1,000

= $ 37.5

N = 10 x 2

= 20

YTM = 6.5% / 2

= 3.25%

So the price of the bond will be:

= $ 37.5 / 1.0325¹ + $ 37.5 / 1.0325² + $ 37.5 / 1.0325³ + $ 37.5 / 1.0325⁴ + $ 37.5 / 1.0325⁵ + $ 37.5 / 1.0325⁶ + $ 37.5 / 1.0325⁷ + $ 37.5 / 1.0325⁸ + $ 37.5 / 1.0325⁹ + $ 37.5 / 1.0325¹⁰ + $ 37.5 / 1.0325¹¹ + $ 37.5 / 1.0325¹² + $ 37.5 / 1.0325¹³ + $ 37.5 / 1.0325¹⁴ + $ 37.5 / 1.0325¹⁵ + $ 37.5 / 1.0325¹⁶ + $ 37.5 / 1.0325¹⁷ + $ 37.5 / 1.0325¹⁸ + $ 37.5 / 1.0325¹⁹ + $ 37.5 / 1.0325²⁰ + $ 1,000 / 1.0325²⁰

= $ 1,072.70 Approximately

Conversion value of the bond will be as follows:

= 30 x $ 52

= $ 1,560

So the minimum value of the bond will be $ 1,072.70

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