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Unformatted text preview: on is essentially worthless, increasing the time to expiration would obviously increase its value. 12. An increase in volatility acts to increase both call and put values because the greater volatility increases the possibility of favorable inthemoney payoffs. 13. A put option is insurance since it guarantees the policyholder will be able to sell the asset for a specific price. Consider homeowners insurance. If a house burns down, it is essentially worthless. In essence, the homeowner is selling the worthless house to the insurance company for the amount of insurance. 14. The equityholders of a firm financed partially with debt can be thought as holding a call option on the assets of the firm with a strike price equal to the debt’s face value and a time to expiration equal to the debt’s time to maturity. If the value of the firm exceeds the face value of the debt when it matures, the firm will pay off the debtholders in full, leaving the equityholders with the firm’s remaining assets. However, if the value of the firm is less than the face value of debt when it matures, the firm must liquidate all of its assets in order to pay off the debtholders, and the equityholders receive nothing. Consider the following: Let VL = the value of a firm financed with both debt and equity FV(debt) = the face value of the firm’s outstanding debt at maturity If VL < FV(debt) VL 0 VL If VL > FV(debt) FV(debt) VL – FV(debt) VL Payoff to debtholders Payoff to equityholders Notice that the payoff to equityholders is identical to a call option of the form Max(0, S T – K), where the stock price at expiration (ST) is equal to the value of the firm at the time of the debt’s maturity and the strike price (K) is equal to the face value of outstanding debt. 15. Since you have a large number of stock options in the company, you have an incentive to accept the second project, which will increase the overall risk of the company and reduce the value of the firm’s debt. However, accepting the risky project will increase your wealth, as the options are more valuable when the risk of the firm increases. 16. Rearranging the putcall parity formula, we get: S – PV(E) = C – P. Since we know that the stock price and exercise price are the same, assuming a positive interest rate, the left hand side of the equation must be greater than zero. This implies the price of the call must be higher than the price of the put in this situation. 438 17. Rearranging the putcall parity formula, we get: S – PV(E) = C – P. If the call and the put have the same price, we know C – P = 0. This must mean the stock price is equal to the present value of the exercise price, so the put is inthemoney. 18. A stock can be replicated using a long call (to capture the upside gains), a short put (to reflect the downside losses) and a Tbill (to reflect the time value component – the “wait” factor). Solutions to Questions and Problems NOTE: All endofchapter problems were solved using a spreadsheet. Many problems require multiple steps. Due to space and readability constraints, when these intermediate steps are included in this solutions manual, rounding may appear to have occurred. However, the final answer for each problem is found without rounding during any step in the problem. Basic 1. a. The value of the call is the stock price minus the present value of the exercise price, so: C0 = $70 – [$60/1.055] = $13.13 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: C0 = $70 – [$50/1.055] = $22.61 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. 2. a. b. 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. The calls are in the money. The intrinsic value of the calls is $3. The puts are out of the money. The intrinsic value of the puts is $0. 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 $2.80, exercise it and pay $80 for a share of stock, and sell the stock for $83. A riskless profit of $0.20 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. Each contract is for 100 shares, so the total cost is: Cost = 10(100 shares/contract)($7.60) Cost = $7,600 3. a. 439 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,...
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This note was uploaded on 07/10/2010 for the course FIN 6301 taught by Professor Eshmalwi during the Spring '10 term at University of TexasTyler.
 Spring '10
 eshmalwi
 Finance, Corporate Finance

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