Business Assignment 3 Suggested Answers. Forward Hedge: The dollar payment in three months is

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1 Business 4079 Assignment 3 Suggested Answers 1. (50 points) Do questions 5-9 at the end of Chapter 8 in Eiteman et al. s textbook (all the questions on Tektronics). For each question, consider all possible hedging strategies and determine the most advantageous one. Each question is worth 10 points. Answer: Q5. Tek has an account receivable of 4,000,000 due in three months. It says in the question that the money market hedge is not an option but I ll assume it is in my answer. The spot rate is $.9800/, the three-month forward rate is $.9850/, the three-month euro interest rate is 6.0% (annually), three-month put options on the euro with a strike price of $.9800/ have a premium of 3% and Tek s cost of capital is 12%. Forward Hedge: The dollar payment in three months is 4, 000, = $3, 940, 000 and thus the present value using the firm s cost of capital is PV of Payment under Forward Hedge = 3, 940, 000 e.12/4 = $3, 823, 555 Money Market Hedge: Let s assume 6% is the rate at which Tek can borrow 1

2 euros. Then the money market hedge gives the firm an instantaneous Spot Rate 4, 000, 000 e Borrowing Rate/4 = , 000, 000 e.06/4 = $3, 861, 639 Options Hedge: The company will have euros to sell in three months and put options provide insurance against a depreciation of the euro. The option is quoted as a percentage and thus its cost is Spot Rate 3% 4, 000, 000 = % 4, 000, 000 = $117, 600. The strike price being $.9800/, this options guarantees a minimum payment of 4.98 = $3.92 million in three months and thus the present value of the minimum payment is 3, 920, 000 e.12/4 = $3, 804, 146 for a minimum net present value of 3, 804, , 600 = $3, 686, 546. Q6. Tek has an account payable of 8,000,000 due in six months. The spot rate is 125/$, the six-month forward rate is 122/$, the six-month yen deposit rate is 1.5%, the six-month dollar interest rate is 4%, six-month call options with exercise price 125/$ on the yen have a premium of 4% and Tek s cost of capital is 12%. Forward Hedge: The dollar payment in six months is 8, 000, 000/122 = $65, 574 and thus the present value using the firm s cost of capital is PV of Payment under Forward Hedge = 65, 574 e.12/2 2 = $61, 755

3 Money Market Hedge: Tek can save in a yen-denominated account with interest rate of 1.5%. The money market would then induce the firm to pay an instantaneous 1 Spot Rate 8, 000, 000 e Lending Rate/2 = 1 8, 000, 000 e.015/2 125 = $63, 522 Options Hedge: The company will have to buy yens in six months and call options provide insurance against a appreciation of the yen. The option is quoted as a percentage and thus its cost is 1 1 4% 8, 000, 000 = 4% 8, 000, 000 = $2, 560. Spot Rate 125 The strike price being 125/$, this options guarantees a maximum payment of 8, 000/125 = $64 thousand in six months and thus the present value of the maximum payment is for a maximum net present value of 64, 000 e.12/2 = $60, , , 560 = $62, 833. Q7. Tek is bidding on a project that, if the bid is successful, which will be known in one month, will become an account receivable of 1,000,000 due in four months. Two things here: The amount should be partially hedged, as it may not be received at all. There are at least four other bidders and thus Tek has approximately 20% chance to win the bid. Maybe it should then hedge only 20% of the amount. The four-month instruments should be used to hedge, as there is no transfer of money taking place after one month. If the company hedges for a period of one month, then it will have to re-hedge for three month if its bid is successful and we do not have the three-month forward values. 3

4 A successful bid would create an account receivable of 1,000,000 due in four months. The spot rate is $1.5700/, the four-month forward rate is $1.5750/, the four-month pounds borrowing rate is 9.0%, four-month put options on the pound sterling with a strike price of $1.5800/ have a premium of $.012/ and Tek s cost of capital is 12%. Forward Hedge: This hedge implies a dollar payment in four months of 1, 000, = $1, 575, 000 and thus the present value using the firm s cost of capital is PV of Payment under Forward Hedge = 1, 575, 000 e.12/3 = $1, 559, 328 Money Market Hedge: Tek can borrow pounds at the rate of 9% and thus the money market hedge would provide an instantaneous payment of Spot Rate 1, 000, 000 e Borrowing Rate/3 = , 000, 000 e.09/3 = $1, 558, 269 Options Hedge: The company will have pounds to sell in four months if the bid is successful and put options provide insurance against a depreciation of the pound. The way the option is quoted, its cost is.012 1, 000, 000 = $12, 000. The strike price being $1.5800/, this options guarantees a minimum payment of $1.58 million in four months and thus the present value of the minimum payment is 1, 580, 000 e.12/3 = $1, 564, 279 for a minimum net present value of 1, 564, , 000 = $1, 576,

5 If the company hedges 20% of the amount, then the present values to be considered are 20% of the values calculated above. Q8. Same idea as question 7, an amount between SKr 5,000,000 and SKr 10,000,000 should be hedged as an account receivable. Q9. This is an account receivable. 2. On March 1, Redwall Pump Company sold a shipment of pumps to Vollendam Dike Company of the Netherlands for 5,000,000. Of this amount, 2,500,000 will be received on June 1 and 2,500,000 will be received on September 1. Redwall derived its price quote of 5,000,000 on February 1 by dividing its normal U.S. dollar sales price of $6,350,000 by the then-current spot rate of $1.2700/. By the time the order was received and booked on March 1, the euro had strenghtened to $1.2900/, so the sale was in fact worth 5, 000, 000 $1.2900/ = $6, 450, 000. That is, Redwall had already gained an extra $100,000 from favorable exchange rate movements. Nevertheless, Redwall s director of finance now wondered if the firm should hedge against a reversal of the recent trend of the euro. Use the following information to answer this question. (i) The 3-month forward exchange rate quote was $1.2930/ and the 6-month forward quote was $1.2960/. (ii) Redwall could borrow euros from the Frankfurt branch of its U.S. bank at 7.50% per annum. (iii) The available options are shown in Table 1. Redwall estimates its cost of capital to be 12% per annum. As a small firm, Redwall is unable to raise funds with long-term debt. U.S. T-bills yielded 3.6% per annum. Calculate Redwall s expected outcome under each scenario: (a) (5 points) Forward market hedge. Answer: The present values of the payments with forward contracts are (through- 5

6 Type Expiry month Strike Price ($/ ) Premium ($/unit) Put June Put June Put September Put September Call June Call June Call September Call September Table 1: Available options for Problem 2. out this exercise, I will be using the firm s cost of capital as the discount rate): June Payment: 2, 500, e.12/4 = $3, 136, 952 September Payment: 2, 500, e.12/2 = $3, 051, 317 (b) (5 points) Money market hedge. Answer: Hedging on the money market provides an immediate cash flow of , 500, 000 e.075/4 = $3, 165, 095 for the June payment , 500, 000 e.075/2 = $3, 106, 302 for the September payment (c) (5 points) Options market hedge. Answer: Using the put options with a strike price, we have (S 3 and S 6 represent the June and the September spot exchange rates, respectively): June Payment: max{s 3, 1.29} 2, 500, 000 e.12/4 57, 000 September Payment: max{s 6, 1.29} 2, 500, 000 e.12/2 86, 500 Using the put options with a strike price, we have (S 3 represents the June spot exchange rate): June Payment: max{s 3, 1.28} 2, 500, 000 e.12/4 45, 250 September Payment: max{s 6, 1.28} 2, 500, 000 e.12/2 60, 000 6

7 (d) (5 points) Synthetic forward hedge using options. Answer: If the firm simultaneously buys a 1.29 put option and writes a 1.29 call option, then its cash flow is: June Payment: , 500, 000 e.12/4 57, , 250 = $3, 158, 937 September Payment: , 500, 000 e.12/2 86, , 000 = $3, 050, 691 If the firm simultaneously buys a 1.28 put option and writes a 1.28 call option, then its cash flow is: June Payment: , 500, 000 e.12/4 45, , 750 = $3, 153, 926 September Payment: , 500, 000 e.12/2 60, , 000 = $3, 068, 647 (e) (10 points) Which alternative would you recommend and why? You may want to draw a graph here representing the payoff from each alternative with respect to the June and September exchange rates. Note that you do not have to use the same type of strategy for both payments. That is, you could use a money market hedge for the June payment and an options market hedge for the September payment. Answer: Figure 1 compares each alternative for both payments. 7

8 Figure 1: Present value of each strategy for varying spot rates at the time of the payment using Redwall s WACC (12%) as the discount rate. 8