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Ross5eChap23sm

# Ross5eChap23sm - Chapter 23 Options and Corporate Finance...

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Answers to End-of-Chapter Problems B- 336 Chapter 23: Options and Corporate Finance: Basic Concepts 23.2 An American option can be exercised on any date up to and including the expiration date. A European option can only be exercised on the expiration date. Since an American option gives its owner the right to exercise on any date up to and including the expiration date, it must be worth at least as much as a European option, if not more. 23.4 a. If the option is American, it can be exercised on any date up to and including its expiration on February 14. b. If the option is European, it can only be exercised on its expiration date, February 14. c. The option is not worthless. There is a chance that the stock price of Futura Corporation will remain above \$47 sometime before the option’s expiration on February 14. In this case, a call option with a strike price of \$47 would be valuable at expiration. The probability of such an event happening is built into the current price of the option. 23.6 a. The payoff to the owner of a put option at expiration is the maximum of zero and the strike price minus the current stock price. The payoff to the owner of a put option on Stock A on December 21 is: max[0, K– S T ] = max[0, \$50–\$55] = \$0 The payoff to the seller of a put option at expiration is the minimum of zero and the current stock price minus the strike price. The payoff to the seller of a call option on Stock A on December 21 is: min[0, S T – K] = min[0, \$55–\$50] = \$0 c. The payoff to the owner of a put option at expiration is the maximum of zero and the strike price minus the current stock price. The payoff to the owner of a put option on Stock A on December 21 is: max[0, K– S T ] = max[0, \$50–\$45] = \$5 d. The payoff to the seller of a put option at expiration is the minimum of zero and the current stock price minus the strike price. The payoff to the seller of a call option on Stock A on December 21 is: min[0, S T – K] = min[0, \$45–\$50] = –\$5 In other words, the seller must pay \$5. e.

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Answers to End-of-Chapter Problems B- 337 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 Stock Price at Expiration Payoff to Owner f. -25 -20 -15 -10 -5 0 30 35 40 45 50 55 60 65 70 Stock Price at Expiration Payoff to Seller 23.8 a. Using the equation for the PV of a continuously compounded lump sum, we get: PV = \$30,000 e –0.05(2) = \$27,145.12 b. Using Black–Scholes model to value the equity, we get: d 1 = [ln(\$13,000/\$30,000) + (0.05 + 0.60 2 /2) x 2] / (0.60 2 ) = –0.4434 d2 =–0.4434 – (0.60 2)= – 1.2919 N(d 1 ) = N(–0.4434) = 0.3287
Answers to End-of-Chapter Problems B- 338 N(d 2 ) = N(– 1.2919) = 0.0982 Putting these values into Black–Scholes: E = \$13,000(0.3287) – (\$30,000e –0.05(2) )(0.0982) = \$1,608.19 And using put–call parity, the price of the put option is: Put = \$30,000e –0.05(2) + \$1,608.19 – \$13,000 = \$15,753.31 c. The value of a risky bond is the value of a risk–free bond minus the value of a put option on the firm’s equity, so: Value of risky bond = \$27,145.12 – \$15,753.31 = \$11,391.81 Using the equation for the PV of a continuously compounded lump sum to find the return on debt, we get: \$11,391.81 = \$30,000e – r (2) 0.37973 = e –r 2 r B = –(1/2) ln(.37973) = 0.4842 or 48.42% d. The value of the debt with five years to maturity at the risk–free rate is: PV = \$30,000 e –0.05(5) = \$23,364.02 Using Black–Scholes model to value the equity, we get: d1= [ln(\$13,000/\$30,000) + (0.05 + 0.602/2) 5] / (0.60

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Ross5eChap23sm - Chapter 23 Options and Corporate Finance...

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