ans-odd-problems-ch22

ans-odd-problems-ch22 - CHAPTER 22 OPTIONS AND CORPORATE...

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CHAPTER 22 OPTIONS AND CORPORATE FINANCE: BASIC CONCEPTS Answers to odd-numbered problems Basic 1. a. The value of the call is the stock price minus the present value of the exercise price, so: C 0 = $55 – [$45/1.055] = $12.35 The intrinsic value is the amount by which the stock price exceeds the exercise price of the call, so the intrinsic value is $10. b. The value of the call is the stock price minus the present value of the exercise price, so: C 0 = $55 – [$35/1.055] = $21.82 The intrinsic value is the amount by which the stock price exceeds the exercise price of the call, so the intrinsic value is $20. c. The value of the put option is $0 since there is no possibility that the put will finish in the money. The intrinsic value is also $0. 3. a. Each contract is for 100 shares, so the total cost is: Cost = 10(100 shares/contract)($7.60) Cost = $7,600 b. If the stock price at expiration is $140, the payoff is: Payoff = 10(100)($140 – 110) Payoff = $30,000 If the stock price at expiration is $125, the payoff is: Payoff = 10(100)($125 – 110) Payoff = $15,000 c. Remembering that each contract is for 100 shares of stock, the cost is: Cost = 10(100)($4.70) Cost = $4,700
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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)($110) – $4,700 Maximum gain = $105,300 If the stock price at expiration is $104, the position will have a profit of: Profit = 10(100)($110 – 104) – $4,700 Profit = $1,300 d. At a stock price of $103 the put is in the money. As the writer, you will make: Net loss = $4,700 – 10(100)($110 – 103) Net loss = –$2,300 At a stock price of $132 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)($110 – S T ) S T = $105.30 For terminal stock prices above $105.30, the writer of the put option makes a net profit (ignoring transaction costs and the effects of the time value of money). 5. 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. Using the equation presented in the text to prevent arbitrage, we find the value of the call is: $70 = 2C 0 + $60/1.05 C 0 = $6.43 7. Using put-call parity and solving for the call price we get: $53 + $4.89 = $50e –(.036)(.5) + C C = $8.78 9. Using put-call parity, we can solve for the risk-free rate as follows: $65.80 + $2.86 = $65e –R(2/12) + $4.08 $64.58 = $65e –R(2/12) 0.9935 = e –R(2/12) ln(0.9935) = ln(e –R(2/12) )
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–0.0065 = –R(2/12) R f = 3.89% 11. Using the Black-Scholes option pricing model to find the price of the call option, we find: d 1 = [ln($86/$90) + (.04 + .62 2 /2) × (8/12)] / (.62 × 12 / 8 ) = .2160 d 2 = .2160 – (.62 × 12 / 8 ) = –.2902 N(d 1 ) = .5855 N(d 2 ) = .3858 Putting these values into the Black-Scholes model, we find the call price is: C = $86(.5855) – ($90e
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ans-odd-problems-ch22 - CHAPTER 22 OPTIONS AND CORPORATE...

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