Business 4079 Assignment 3 Suggested Answers On March 1, Redwall Pump Company sells a shipment of pumps to Omega, a company based in Switzerland, for Sfr6,000,000, payable Sfr3,000,000 on May 1 and Sfr3,000,000 on June 1. The spot rate on March 1 is $0.8584/Sfr and Redwall s director of finance wonders whether the firm should hedge against a decrease in the value of the Swiss franc. Consider the following: (i) The 2-month forward exchange rate quote is $0.8615/Sfr and the 3-month forward quote is $0.8632/Sfr. (ii) Redwall can borrow Swiss francs from the Geneva branch of its U.S. bank at a rate of 4% per annum and it can borrow U.S. dollars at the rate of 8% per annum. (iii) The available options are shown in Table 1: Redwall estimates its cost of equity capital to be 12% per annum. The short-term money market rate in Switzerland is 0.75% and the short-term money market rate in the U.S. is 2.60%. Explain how Redwall can hedge and calculate the company s expected payoff under each of the following scenarios: (a) (5 points) Forward market hedge. Answer: With forward contracts, the present value of 3, 000, 000 0.8615 = $2, 584, 500 in May, and 3, 000, 000 0.8632 = $2, 589, 600 in June. 1
Month Type Strike Premium ($/Sfr) ($/Sfr) May put.8500.0107 May put.8650.0179 June put.8500.0130 June put.8650.0205 May call.8500.0214 May call.8650.0147 June call.8500.0271 June call.8650.0204 Table 1: Available options. At the firm s WACC, the present value of each payment is: May @ WACC: 2, 584, 500 e.12/6 = 2, 533, 324 June @ WACC: 2, 589, 600 e.12/4 = 2, 513, 066 If instead we use the risk-free rate r f = 2.6% as the discount rate, we obtain May @ r f : 2, 584, 500 e.026/6 = 2, 573, 325 June @ r f : 2, 589, 600 e.026/4 = 2, 572, 822 (b) (5 points) Money market hedge. Answer: For each payment Redwall expects to receive, it can borrow Swiss francs at an annual rate of 4% which gives, as of March 1, 3, 000, 000 e.04/6 0.8584 = $2, 558, 089 for the May payment 3, 000, 000 e.04/4 0.8584 = $2, 549, 576 for the June payment. (c) (5 points) Options market hedge. Answer: Hedging is about limiting losses or reducing the risk due to possible changes in exchange rate. Put options limit losses when the exchange rate falls, i.e. they provide insurance. The premium of each put option listed above is (note that option 2
prices are in $/Sfr so we do not use the spot rate to calculate the premium): May Put @ 0.8500: 3, 000, 000.0107 = $32, 000 May Put @ 0.8650: 3, 000, 000.0179 = $53, 700 June Put @ 0.8500: 3, 000, 000.0130 = $39, 000 June Put @ 0.8650: 3, 000, 000.0205 = $61, 500 The present value of the minimum payoff guaranteed by each option, using the WACC as the discount rate, is then: May Put @ 0.8500: 3, 000, 000.8500 e.12/6 32, 000 = $2, 467, 407 May Put @ 0.8650: 3, 000, 000.8650 e.12/6 53, 700 = $2, 489, 916 June Put @ 0.8500: 3, 000, 000.8500 e.12/4 39, 000 = $2, 435, 636 June Put @ 0.8650: 3, 000, 000.8650 e.12/4 61, 500 = $2, 456, 806 Using the risk-free rate, these present values are: May Put @ 0.8500 (r f ): 3, 000, 000.8500 e.026/6 32, 000 = $2, 506, 874 May Put @ 0.8650 (r f ): 3, 000, 000.8650 e.026/6 53, 700 = $2, 530, 079 June Put @ 0.8500 (r f ): 3, 000, 000.8500 e.026/4 39, 000 = $2, 494, 479 June Put @ 0.8650 (r f ): 3, 000, 000.8650 e.026/4 61, 500 = $2, 516, 687 These minimum payoffs are much smaller than the payoffs from forward hedges due to the premium that has to be paid on option contracts. A good way to reduce the effect of these premia is to sell call options at the same time. Writing call options in the present case corresponds to writing covered calls since Redwall will have the Swiss francs to meet its obligations if the calls are exercised. More specifically, calls and puts can be combined to create synthetic forward contracts. That is, simultaneously buying a put and selling a call with the same strike price guarantees an exchange rate equal to the strike price since one of the two options is always exercised and thus the Swiss francs are always exchanged at the options strike price. Suppose, for example, that a May call 0.8500 is sold when a May put 0.8500 is purchased. Then the cash flow in 3
May is 3, 000, 000 0.8500 = $2, 550, 000 regardless of the spot rate but cash flow in March is now 3, 000, 000 0.0214 32, 000 = $32, 200, i.e. Redwall makes money when the options are purchased. The present value of Redwall s May payoff under this strategy, using the WACC as the discount rate, is then 2, 550, 000 e.12/6 + 32, 200 = $2, 531, 607. If we do that for each strike prices, we obtain: May Synthetic Forward @ 0.8500: 3, 000, 000.8500 e.12/6 + 32, 200 = $2, 531, 607 May Synthetic Forward @ 0.8650: 3, 000, 000.8650 e.12/6 9, 600 = $2, 534, 016 June Synthetic Forward @ 0.8500: 3, 000, 000.8500 e.12/4 + 42, 300 = $2, 516, 936 June Synthetic Forward @ 0.8650: 3, 000, 000.8650 e.12/4 300 = $2, 518, 006 Note that the May synthetic forward @ 0.8500 is the only synthetic forward that does not provide a better payoff than the forward hedge. If the use the risk-free rate as the discount rate, we have May Synthetic Forward @ 0.8500 (r f ): 3, 000, 000.8500 e.026/6 + 32, 200 = $2, 571, 074 May Synthetic Forward @ 0.8650 (r f ): 3, 000, 000.8650 e.026/6 9, 600 = $2, 574, 179 June Synthetic Forward @ 0.8500 (r f ): 3, 000, 000.8500 e.026/4 + 42, 300 = $2, 575, 779 June Synthetic Forward @ 0.8650 (r f ): 3, 000, 000.8650 e.026/4 300 = $2, 577, 887 (d) (5 points) No hedging. (e) (10 points) Which alternative is the best? Draw a graph representing the payoff from each alternative with respect to the May and June exchange rates. Answer: Please see figures 1 and reffig:payoffrf. Using the WACC as the discount rate, the money market hedge is the best risk-free strategy. When the risk-free rate is used as the discount rate, then the best risk-free strategy is a synthetic forward. 4
Figure 1: Present value of each strategy using Redwall s WACC (12%) as the discount rate. 5
Figure 2: Present value of each strategy using the risk-free rate (2.6%) as the discount rate. 6