# CHAPTER 8 SUGGESTED ANSWERS TO CHAPTER 8 QUESTIONS

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6 CHAPTER 8: CURRENCY FUTURES AND OPTIONS MARKETS = \$8,750. If the yen settles at its minimum value, Apex will not exercise the option and it loses the call premium. But if the yen settles at its maximum value of \$ , Apex will exercise at \$ and earn \$0.0004/ for a total gain of.0004 x 5,000,000 = \$50,000. Apex's net gain will be \$50,000 - \$8,750 = \$3,50. PROFIT (LOSS) ON APEX CORPORATION'S FUTURES AND OPTIONS POSITIONS \$60,000 \$57,500 \$40,000 \$0,000 \$3,5 0 Profit (loss) \$ Yen price (\$ omitted) (\$0,000) (\$8,750) Profit (loss) on call option position (\$40,000) Profit (loss) on futures (\$60,000) OPTION Inflow \$,08,750 \$,050,000 Outflow Call Premium -\$8,750 -\$8,750-8,750 -,000,000 Exercise Cost ,000,000-8,750 Profit -\$8,750 -\$8,750 \$0 \$3,50 FUTURES Inflow \$937,500 \$99,500 \$,000,000 \$,050,000 Outflow -99,500-99,500-99,500-99,500 Profit -\$55,000 \$0 \$7,500 \$57,500 As the diagram shows, Apex can use a futures contract to lock in a price of \$ / at a total cost of x 5,000,000 = \$99,500. If the yen settles at its minimum value, Apex will lose \$ \$ = \$ / (remember it is buying yen at , when the spot price is only ), for a total loss on the futures contract of x 5,000,000 = \$55,000. On the other hand, if the yen appreciates to \$ , Apex will earn \$ \$ = \$ / for a total gain on the futures contracts of x 5,000,000 = \$57,500. b. Calculate what Apex would gain or lose on the option and futures positions if the yen settled at its most likely value. ANSWER. If the yen settles at its most likely price of \$ , Apex will not exercise its call option and will lose the call premium of \$8,750. If Apex hedges with futures, it will have to buy yen at a price of \$ when the spot rate is \$ This will cost Apex \$ /, for a total futures contract cost of x 5,000,000 = \$5,000. c. What is Apex's break-even future spot price on the option contract? On the futures contract? 6

9 INSTRUCTOR S MANUAL: MULTINATIONAL FINANCIAL MANAGEMENT, 9 TH ED \$3,875 GAIN (LOSS) ON BIOGEN'S FUTURES AND OPTIONS POSITIONS 0000 Gain (loss) on futures position \$.6 \$.63 \$.64 \$.65 \$.66 \$.67 \$.68 \$.69 \$.70 \$ Gain (loss) on put option position (\$5,000) Pound price (\$6,5) OPTION Inflow Outflow Put premium Exercise cost Profit.650 \$,076,500-5,000 -,03,50 \$0, \$,076,500-5,000 -,050,000 \$, \$,076,500-5,000 -,064,5 -\$, ,000 -\$5, ,000 -\$5,000 FUTURES Inflow Outflow Profit \$,064,5 -,03,50 \$3,875 \$,064,5 -,050,000 \$4,5 \$,064,5 -,064,5 \$0 \$,064,5 \$7,500 \$,064,5 -,6,50 -\$6,5 c. Calculate what Biogen would gain or lose on the option and futures positions within the range of expected future exchange rates and if the pound settled at its most likely value. ANSWER. If Biogen buys the put options, it must pay a put premium of 0.0 x,50,000 = \$5,000. If the pound settles at its maximum value, Biogen will not exercise and it loses the put premium. But if the pound settles at its minimum of \$.650, Biogen will exercise at \$.66 and earn \$0.036/ or a total of x,50,000 = \$45,50. Biogen's net gain will be \$45,50 - \$5,000 = \$0,50. With regard to the futures position, Biogen will lock in a price of \$.653/ for total revenue of \$.653 x,50,000 = \$,064,5. If the pound settles at its minimum value, Biogen will have a gain per pound on the futures contracts of \$ \$.650 = \$0.063/ (remember it is selling pounds at a price of \$.653 when the spot price is only \$.650) for a total gain of x,50,000 = \$3,875. On the other hand, if the pound 9

10 0 INSTRUCTORS MANUAL: MULTINATIONAL FINANCIAL MANAGEMENT, 7TH ED. appreciates to \$.7000, Biogen lose \$ \$.653 = \$0.0497/ for a total loss on the futures contract of x,50,000 = \$6,5. If the pound settles at its most likely price of \$.6400, Biogen will exercise its put option and earn \$.66 - \$.6400 = \$0.0/, or \$6,500. Subtracting off the put premium of \$5,000 yields a net gain of \$,500. If Biogen hedges with futures contracts, it will sell pounds at \$.653 when the spot rate is \$ This will yield Biogen a gain of \$0.03/ for a total gain on the futures contract equal to 0.03 x,50,000 = \$4,5. d. What is Biogen's break-even future spot price on the option contract? On the futures contract? ANSWER. On the option contract, the spot rate will have to sink to the exercise price less the put premium for Biogen to break even on the contract, or \$.66 - \$0.0 = \$.64. In the case of the futures contract, breakeven occurs when the spot rate equals the futures rate, or \$.653. e. Calculate and diagram the corresponding profit and loss and break-even positions on the futures and options contracts for those who took the other side of these contracts. ANSWER. As in the case of Apex, the sellers' profit and loss and break-even positions on the futures and options contracts will be the mirror image of Biogen's position on these contracts. For example, the sellers of the futures and options contracts will break even at future spot prices of \$.653/ and \$.64/, respectively. Similarly, if the pound falls to its minimum value, the options sellers will lose \$0,50 and the futures sellers will lose \$3,875. But if the pound hits its maximum value of \$.700, the options sellers will earn \$5,000 and the futures sellers will earn \$6,5. SUGGESTED SOLUTIONS TO APPENDIX 8A PROBLEMS. Assume that the spot price of the British pound is \$.55, the annualized 30-day sterling interest rate is 0%, the annualized 30-day U.S. interest rate is 8.5%, and the annualized standard deviation of the dollar:pound exchange rate is 7%. Calculate the value of a 30-day PHLX call option on the pound at a strike price of \$.57. ANSWER. To apply Equation 8. to value this option, we must first estimate B(t,0.0833) and B*(t,0.0833), since T = (one month equal years). Given the annualized one-month interest rates of 8.5% and 0%, the one-month U.S. and U.K. interest rates are % (8.5/) and % (0/), respectively. The associated bond prices are B(t,0.0833)= = * B (t,0.0833)= = Substituting in the values for B and B* along with those for S (.55), X (.57), and σ (0.7) in Equation 7., we can calculate 0

11 INSTRUCTOR S MANUAL: MULTINATIONAL FINANCIAL MANAGEMENT, 9 TH ED. * ln( SB /XB)+ 0.5σ T ln(.55x0.9974/.57 x0.9997)+ 0.5(0.7 ) (0.0833) d = = = σ T d = d σ T = = Using NORMDIST in Excel yields computed values of N(-0.699) = and N(-0.306) = Applying Equation 7., we can now calculate the value of the one-month pound call option: * C(t) = N( d ) x S(t) x B (t,t) N( d ) x X x B(t,T) = x.55 x x.57 x = \$0.0066/ That is, the value of the one-month option to acquire pounds at an exercise price of \$.57 when the spot rate is \$.55 is.066 /. Given that the PHLX pound call option contract consists of 3,50, the value of the one-month pound call option is \$645.5 (3,50 x ). This figure is exact; the other figures are subject to rounding error.. Suppose the spot price of the yen is \$0.009, the three-month annualized yen interest rate is 3%, the threemonth annualized dollar rate is 6%, and the annualized standard deviation of the dollar:yen exchange rate is 3.5%. What is the value of a three-month PHLX call option on the Japanese yen at a strike price of \$0.0099/? ANSWER. To apply Equation 8. to value this option, we must first estimate B(t,0.5) and B*(t,0.5), since T = 0.5 (three months equal 0.5 years). Given the annualized three-month interest rates of 6% and 3%, the threemonth U.S. and Japanese interest rates are.5% (6/4) and 0.75% (3/4), respectively. The associated bond prices are B(t,0.5)= = * B (t,0.5)= = Substituting in the values for B and B* along with those for S (0.009), X (0.0099), and σ (0.35) in Equation 7., we can calculate

12 INSTRUCTORS MANUAL: MULTINATIONAL FINANCIAL MANAGEMENT, 7TH ED. * ln( SB /XB)+ 0.5σ T ln(0.009x0.9956/0.0099x0.985)+ 0.5(0.35 ) (0.5) d = = =.5693 σ T d = d σ T = =.5073 Using NORMDIST in Excel yields computed values of N(.5693) = and N(.5073) = Applying Equation 7., we can now calculate the value of the one-month pound call option: * C(t) = N( d ) x S(t) x B (t,t) N( d ) x X x B(t,T) = x x x x = \$ / That is, the value of the three-month option to acquire yen at an exercise price of \$ when the spot rate is \$0.009 is /. Given that the PHLX yen call option con tract consists of 6,50,000, the value of the 90- day yen call option is \$6,774.3 (6,50,000 x ). This figure is exact; the other figures are subject to rounding error. 3. Suppose that the premium on March 0 on a June 0 yen put option is cents per yen at a strike price of \$ The forward rate for June 0 is = \$ and the quarterly U.S. interest rate is %. If put-call parity holds, what is the current price of a June 0 PHLX yen call option with an exercise price of \$0.0077? ANSWER. We can apply the version of put-call option interest parity as expressed in Equation 6.5 to value this option. According to this formula, f X C = + P + r h Substituting in the numbers given in the question, we have f X C = + rh P= = / Given that the size of the PHLX yen option contract is 6,50,000, the value of this contract is \$4,54.7 (6,50,000 x ). This figure is exact; the other figures are subject to rounding error.

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