A 15-year maturity convertible bond with a face value of $1,000 and a 5% coupon

Question

A 15-year maturity convertible bond with a face value of $1,000 and a 5% coupon on a company with a bond rating of Aaa is selling for $1,170. The bond pays interest annually. Each bond can be exchanged for 20 shares, and the stock price currently is $50 per share. Other Aaa-rated bonds with the same maturity would sell at a yield to maturity of 7%. What is the value of the bondholders’ call option?

A 15-year maturity convertible bond with a face value of $1,000 and a 5% coupon on a company with a bond rating of Aaa is selling for $1,170. The bond pays interest annually. Each bond can be exchanged for 20 shares, and the stock price currently is $50 per share. Other Aaa-rated bonds with the same maturity would sell at a yield to maturity of 7%. What is the value of the bondholders’ call option?

Explanation / Answer

solution :

Value of bond = Present value of interest + maturity amount Present value of interest = (1000x5%x9.107914)                 455.40 Present value of maturity = (1000x0.362446)                 362.45 Value of bond                   817.84 converion value ( 20 shares x 50)             1,000.00 value of the bondholders’ call option                 182.16

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