Question

Standard Olive Company of California has a $1,000 par value convertible bond outstanding with a coupon rate of 6 percent and a maturity date of 5 years. It is rated Aa, and competitive, nonconvertible bonds of the same risk class carry a 10 percent yield. The conversion ratio is 25. Currently the common stock is selling for $20 per share on the New York Stock Exchange. a. What is the conversion price? (Round your answer to 2 decimal places.) b. What is the conversion value? (Round your answer to 2 decimal places.) c. Compute the pure bond value. (Use semiannual analysis.) Use Appendix B and Appendix D as an approximate answer, but calculate your final answer using the formula and financial calculator methods. (Do not round intermediate calculations. Round your final answer to 2 decimal places.) d. Calculate the crossover point at which the pure bond value equals conversion value. (Do not round intermediate calculations. Round your answer to 2 decimal places.) Explanation a. Conversion price = Par value / Conversion ratio = $1,000 / 25 = $40.00 b. Conversion value = Conversion ratio × Stock price = 25 × $20 = $500.00 c. Pure bond value = PV of interest payments + PV of par value = [(0.06 × $1,000) / 2] × {[1 − (1 / 1.0510)] / 0.05} + $1,000 / 1.0510 = $845.57 With semiannual analysis, the interest payment, interest rate, and number of periods must be expressed in semiannual terms. The interest rate for 6 months is 5 percent and there are 10 six-month periods in 5 years. d. Crossover point = Pure bond value / Conversion ratio = $845.57 / 25 = $33.82 At a stock price of $20 per share, the price of the bond will be influenced more by the pure bond value (floor price) of $845.57. If interest rates move up, the pure bond value will fall, and if they move down, the pure bond value will rise. As the stock rises from $20 per share to the crossover point of $33.82 ($845.57 / 25) the market price of the bond will react directly to stock price changes and the market price of the bond will rise with the stock price. Calculator Solution: N I/Y PV PMT FV 10 5 CPT PV –845.57 30 1,000 Answer: $845.57 Appendix Solution: Appendix D Present value of interest payments: PVA = FV × PVIFA (n = 10, i = 5%) = $30.00 × 7.722 = $231.66 Appendix B Present value of par value: PV = FV × PVIF (n = 10, i = 5%) = $1,000 × 0.614 = $614.00 Bond price = $231.66 + 614.00 = $845.66

Answer #1

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