Consider the following questions on the pricing of options on the stock of ARB Inc.: a. A share of ARB stock sells for $75 and has a standard deviation of returns equal to 20 percent per year. The current risk-free rate is 9 percent and the stock pays two dividends: (1) a $2 dividend just prior to the option's expiration day, which is 91 days from now (ie, exactly one-quarter of a year), and (2) a $2 dividend 182 days from now (ie., exactly one-half year). Calculate the Black-Shoules value for a European -style call option with an exercise price of $70. b. What would be the price of a 91-day European-style put option on ARB stock having the same exercise price? c. Calculate the change in a call option's value that would occur if ARB's management suddenly decided to suspend dividend payments and this action had no effect on the price of the company's stock. d. Briefly describe (without calculations) how your answer in Part a would differ under the following separate circumstances: (1) volitility of ARB stock increases to 30 percent, (2) the risk-free rate decreases to 8 percent.

GMBA 767-Security Analysis and Portfolio Management Textbook: Investment Analysis & Portfolio Management 10th edition by Frank K. Reilly and Keith C. Brown Consider the following questions on the pricing of options on the stock of ARB Inc.: a. A share of ARB stock sells for $75 and has a standard deviation of returns equal to 20 percent per year. The current risk-free rate is 9 percent and the stock pays two dividends: (1) a $2 dividend just prior to the option's expiration day, which is 91 days from now (ie, exactly one-quarter of a year), and (2) a $2 dividend 182 days from now (ie., exactly one-half year). Calculate the Black-Shoules value for a European -style call option with an exercise price of $70. b. What would be the price of a 91-day European-style put option on ARB stock having the same exercise price? c. Calculate the change in a call option's value that would occur if ARB's management suddenly decided to suspend dividend payments and this action had no effect on the price of the company's stock. d. Briefly describe (without calculations) how your answer in Part a would differ under the following separate circumstances: (1) volitility of ARB stock increases to 30 percent, (2) the risk-free rate decreases to 8 percent. GMBA 767-Security Analysis and Portfolio Management ARB Inc. Consider the following questions on the pricing of options on the stock of ARB Inc.: a. A share of ARB stock sells for $75 and has a standard deviation of returns equal to 20 percent per year. The current risk-free rate is 9 percent and the stock pays two dividends: (1) a $2 dividend just prior to the option's expiration day, which is 91 days from now (ie, exactly one-quarter of a year), and (2) a $2 dividend 182 days from now (ie., exactly one-half year). Calculate the Black-Shoules value for a European -style call option with an exercise price of $70. Current Security price = S1 = $75.00 Share value = S2 = $73.04 $70.00 Exercise price = X = Time to expiration 1 = T1 S2 = Cum dividend value - present value of dividend 91 Risk-free rate = RFR Security price volitility = = 0.25 0.50 182 9% 0.20 Time to expiration 2 = T2 0.5 S2 = 75 - 2/en = 75 - 2/e 0.09*3/12 =75 - 1.96 = 73.04 0.71 Black-Shoules value for a European call option 1) d1 = ln(S2/D) + (r + 2/2)T T ln(73.04/70) + (0.09 + 0.22/2)0.25 d1 = ln(1.0434) + (0.09 + 0.22/2)0.25 0.20.25 0.20.25 d1 = .0424 + 0.0275 0.10 N(d) = 0.5 + (d)(4.4-d)/10 V0 = SN(d1)-Ke-rT N(d2) N(d1) = 0.5 + (d1)(4.4-d1)/10 d1 = V0 = 73.04*0.7587 - 70*0.98*0.7277 N(d1) = N(d1) = V0 = 5.495 0.5 + (.699)(4.4 - 0.699)/10 0.7587 N(d2) = 0.5 + (d2)(4.4-d2)/10 d1 = 0.3174 N(d2) = N(d2) = 0.5 + (.599)(4.4 - 0.599)/10 0.7277 d1 - T d2 = d2 = 0.699 - 0.2*0.25 d2 = 0.2174 b. What would be the price of a 91-day European-style put option on ARB stock having the same exercise price? S + P - C = PV of E 73.04 + P - 5.495 = PV of 70 P = 68.51 + 5.495 - 73.04 P= 0.965 c. Calculate the change in a call option's value that would occur if ARB's management suddenly decided to suspend dividend payments and this action had no effect on the price of the company's stock. d1 = ln(S1/D) + (r + 2/2)T V0 = SN(d1)-Ke-rT N(d2) N(d) = 0.5 + (d)(4.4-d)/10 N(d1) = 0.5 + (d1)(4.4-d1)/10 ln(75/70) + (.09 + .022/2)0.25 0.20.25 V0 = 75.00*0.8314 - 70*0.98*0.8057 N(d1) = N(d1) = T d1 = V0 = 7.084 0.5 + (.9647)(4.4 - 0.9647)/10 0.8314 d1 = ln(1.0714) + (0.09 + 0.22/2)0.25 d1 = d1 = Vo without dividends = 7.084 N(d2) = 0.5 + (d2)(4.4-d2)/10 0.6897 + 0.0275 0.10 Vo with dividends = 5.495 N(d2) = N(d2) = 0.20.25 Change in value of option = 1.589 0.5 + (.8647)(4.4 - 0.8647)/10 0.8057 0.9647 d2 = d1 - T d2 = 0.9647 - 0.2*0.25 d2 = 0.8647 d. Briefly describe (without calculations) how your answer in Part a would differ under the following separate circumstances: (1) volitility of ARB stock increases to 30 percent, (2) the risk-free rate decreases to 8 percent. 1) Security price volitility = = 0.30 N(d) = 0.5 + (d)(4.4-d)/10 ln(S2/D) + (r + 2/2)T d1 = ln(73.04/70) + (0.09 + 0.32/2)0.25 0.300.25 T d1 = V0 = S2N(d1)-Ke-rT N(d2) N(d1) = 0.5 + (d1)(4.4-d1)/10 d1 = V0 = 73.04*0.6976 - 70*0.98*0.6446 N(d1) = N(d1) = V0 = 6.7331 0.5 + (.5077)(4.4 - 0.5077)/10 0.6976 2 ln(1.0434) + (0.09 + 0.3 /2)0.25 0.300.25 d1 = ln(1.0434 )+ 0.3375 0.15 d1 = 0.0424 + 0.03375 0.15 d1 = 0.2674 d2 = N(d2) = 0.5 + (d2)(4.4-d2)/10 d1 - T N(d2) = N(d2) = 0.5 + (.3577)(4.4 - 0.3577)/10 0.6446 d2 = 0.5077 - 0.3*0.25 d2 = 0.1174 2) Change in RFR = 8% N(d) = 0.5 + (d)(4.4-d)/10 ln(S2/D) + (r + 2/2)T d1 = ln(73.04/70) + (0.08 + 0.32/2)0.25 0.200.25 T V0 = S2N(d1)-Ke-rT N(d2) N(d1) = 0.5 + (d1)(4.4-d1)/10 d1 = V0 = 73.04*0.7511 - 70*0.98*0.7196 N(d1) = N(d1) = V0 = 5.4958 0.5 + (.674)(4.4 - 0.674)/10 0.7511 d1 = ln(1.0434) + (0.08 + 0.3 /2)0.25 0.200.25 N(d2) = 0.5 + (d2)(4.4-d2)/10 d1 = ln(1.0434 )+ 0.025 0.1 N(d2) = N(d2) = d1 = 0.0424 + 0.025 0.1 2 d1 = 0.2924 d2 = d1 - T d2 = 0.5077 - 0.3*0.25 d2 = 0.2924 0.5 + (.574)(4.4 - 0.574)/10 0.7196