# Ch25+Answers+to+assigned+problems++v7 - CHAPTER 25 OPTIONS...

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CHAPTER 25 OPTIONS AND CORPORATE SECURITIES 2. (LO1) a. The calls are in the money. The intrinsic value of the calls is \$4 = \$94 - \$90. b. The puts are out of the money. The intrinsic value of the puts is \$0. c. The Mar call and the Oct put are mispriced. The call is mispriced because it is selling for less than its intrinsic value. If the option expired today, the arbitrage strategy would be to buy the call for \$3.20, exercise it and pay \$90 for a share of stock, and sell the stock for \$94. A riskless profit of \$0.80 results. The October put is mispriced because it sells for less than the July put. To take advantage of this, sell the July put for \$3.90 and buy the October put for \$3.65, for a cash inflow of \$0.25. The exposure of the short position is completely covered by the long position in the October put, with a positive cash inflow today. 3. (LO1) a. Each contract is for 100 shares, so the total cost is: Cost = 10(100 shares/contract)(\$7.90) Cost = \$7,900 b. If the stock price at expiration is \$140, the payoff is: Payoff = 10(100)(\$140 – 112) Payoff = \$28,000 If the stock price at expiration is \$125, the payoff is: Payoff = 10(100)(\$125 – 112) Payoff = \$13,000 c. Remembering that each contract is for 100 shares of stock, the cost is: Cost = 10(100)(\$4.70) Cost = \$4,700 The maximum gain on the put option would occur if the stock price goes to \$0. We also need to subtract the initial cost, so: Maximum gain = 10(100)(\$112) – \$4,700 Maximum gain = \$107,300 If the stock price at expiration is \$102, the position will have a profit of: Profit = 10(100)(\$112 – 102) – \$4,700 Profit = \$10,000 – \$4,700 = \$5,300 d. At a stock price of \$104 the put is in the money. As the writer you will make: Net loss = \$4,700 – 10(100)(\$112 – 104) Net loss = –\$3,300 25-1

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At a stock price of \$134 the put is out of the money, so the writer will make the initial cost: Net gain = \$4,700 At the breakeven, you would recover the initial cost of \$4,700, so: \$4,700 = 10(100)(\$112 – S T ) S T = \$107.30 For terminal stock prices above \$107.30, the writer of the put option makes a net profit (ignoring transaction costs and the effects of the time value of money). 4. (LO2) a. The value of the call is the stock price minus the present value of the exercise price, so: C 0 = \$85 – 75/1.06 C 0 = \$14.25 b. Using the equation presented in the text to prevent arbitrage, we find the value of the call is: \$85 = [(\$95 – 80)/(\$95 – 90)]C 0 + \$80/1.06 C 0 = \$3.17 5. (LO2) a. The value of the call is the stock price minus the present value of the exercise price, so: C 0 = \$70 – \$45/1.05 C 0 = \$27.14 b.
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