Business Assignment 3 Suggested Answers

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1 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, = $2, 584, 500 in May, and 3, 000, = $2, 589, 600 in June. 1

2 Month Type Strike Premium ($/Sfr) ($/Sfr) May put May put June put June put May call May call June call June call Table 1: Available options. At the firm s WACC, the present value of each payment is: WACC: 2, 584, 500 e.12/6 = 2, 533, 324 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 r f : 2, 584, 500 e.026/6 = 2, 573, 325 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/ = $2, 558, 089 for the May payment 3, 000, 000 e.04/ = $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

3 prices are in $/Sfr so we do not use the spot rate to calculate the premium): May : 3, 000, = $32, 000 May : 3, 000, = $53, 700 June : 3, 000, = $39, 000 June : 3, 000, = $61, 500 The present value of the minimum payoff guaranteed by each option, using the WACC as the discount rate, is then: May : 3, 000, e.12/6 32, 000 = $2, 467, 407 May : 3, 000, e.12/6 53, 700 = $2, 489, 916 June : 3, 000, e.12/4 39, 000 = $2, 435, 636 June : 3, 000, e.12/4 61, 500 = $2, 456, 806 Using the risk-free rate, these present values are: May (r f ): 3, 000, e.026/6 32, 000 = $2, 506, 874 May (r f ): 3, 000, e.026/6 53, 700 = $2, 530, 079 June (r f ): 3, 000, e.026/4 39, 000 = $2, 494, 479 June (r f ): 3, 000, 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 is sold when a May put is purchased. Then the cash flow in 3

4 May is 3, 000, = $2, 550, 000 regardless of the spot rate but cash flow in March is now 3, 000, , 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 : 3, 000, e.12/6 + 32, 200 = $2, 531, 607 May Synthetic : 3, 000, e.12/6 9, 600 = $2, 534, 016 June Synthetic : 3, 000, e.12/4 + 42, 300 = $2, 516, 936 June Synthetic : 3, 000, e.12/4 300 = $2, 518, 006 Note that the May synthetic 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 (r f ): 3, 000, e.026/6 + 32, 200 = $2, 571, 074 May Synthetic (r f ): 3, 000, e.026/6 9, 600 = $2, 574, 179 June Synthetic (r f ): 3, 000, e.026/4 + 42, 300 = $2, 575, 779 June Synthetic (r f ): 3, 000, 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

5 Figure 1: Present value of each strategy using Redwall s WACC (12%) as the discount rate. 5

6 Figure 2: Present value of each strategy using the risk-free rate (2.6%) as the discount rate. 6