bkmsol_ch20

# Position s t 50 50 s t 60 60 s t 110 s t 110 buy

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Position S T < 50 50 S T 60 60 < S T 110 S T > 110 Buy stock S T S T S T S T Write call, X = \$50 0 –(S T – 50) –(S T – 50) –(S T – 50) Write call, X = \$60 0 0 –(S T – 60) –(S T – 60) Buy call, X = \$110 0 0 0 S T – 110 Total S T 50 110 – S T 0 The investor is making a volatility bet. Profits will be highest when volatility is low and the stock price S T is between \$50 and \$60. 26. i. Conversion value of a convertible bond is the value of the security if it is converted immediately. That is: Conversion value = market price of the common stock × conversion ratio = \$40 × 22 = \$880 ii. Market conversion price is the price that an investor effectively pays for the common stock if the convertible bond is purchased: Market conversion price = market price of the convertible bond/conversion ratio = \$1,050/22 = \$47.73 27. a. i. The current market conversion price is computed as follows: Market conversion price = market price of the convertible bond/conversion ratio = \$980/25 = \$39.20 ii. The expected one-year return for the Ytel convertible bond is: Expected return = [(end of year price + coupon)/current price] – 1 = [(\$1,125 + \$40)/\$980] – 1 = 0.1888 = 18.88% iii. The expected one-year return for the Ytel common equity is: Expected return = [(end of year price + dividend)/current price] – 1 = (\$45/\$35) – 1 = 0.2857 = 28.57% 20-17

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b. The two components of a convertible bond’s value are: the straight bond value, which is the convertible bond’s value as a bond, and; the option value, which is the value associated with the potential conversion into equity. (i.) In response to the increase in Ytel’s common equity price, the straight bond value should stay the same and the option value should increase. The increase in equity price does not affect the straight bond value component of the Ytel convertible. The increase in equity price increases the option value component significantly, because the call option becomes deep “in the money” when the \$51 per share equity price is compared to the convertible’s conversion price of: \$1,000/25 = \$40 per share. (ii.) In response to the increase in interest rates, the straight bond value should decrease and the option value should increase. The increase in interest rates decreases the straight bond value component (bond values decline as interest rates increase) of the convertible bond and increases the value of the equity call option component (call option values increase as interest rates increase). This increase may be small or even unnoticeable when compared to the change in the option value resulting from the increase in the equity price. 28. a. (ii) [Profit = \$40 – \$25 + \$2.50 – \$4.00] b. (i) 20-18
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