Business Assignment 3 Suggested Answers

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1 Business 4079 Assignment 3 Suggested Answers On March 1, Redwall Pump Company sold a shipment of pumps to Vollendam Dike Company of the Netherlands for 4,000,000, payable 2,000,000 on June 1 and 2,000,000 on September 1. Redwall derived its price quote of 4,000,000 on February 1 by dividing its normal U.S. dollar sales price of $5,120,00 by the then-current spot rate of $1.2800/. By the time the order was received and booked on March 1, the euro had strenghtened to $1.3000/, so the sale was in fact worth 4, 000, 000 $1.3000/ = $5, 200, 000. Redwall had already gained an extra $80,000 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. There are four possibilities: (i) Hedge in the forward market. The 3-month forward exchange rate quote was $1.3030/ and the 6-month forward quote was $1.3070/. (ii) Hedge in the money market. Redwall could borrow euros from the Frankfurt branch of its U.S. bank at 8% per annum. (iii) Hedge with foreign currency options. June put options were available at a strike price of $1.3000/ for a premium of 2% per contract, and September put options were available at $1.3000/ for a premium of 1.2%. June call options at $1.3000/ could be purchased for a premium of 3%, and September call options at $1.3000/ were available at a 2.6% premium. (iv) Do nothing. 1

2 Redwall estimates its cost of equity 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: If Redwall enters into forward contracts for both dates, it would get 2, 000, 000 $1.3030/ = $2, 606, 000 in June and 2, 000, 000 $1.3030/ = $2, 614, 000 in September. At the firm s WACC, the present value of each payment is PV J WACC = 2, 606, 000 e.12/4 = 2, 528, 981 PV S WACC = 2, 614, 000 e.12/2 = 2, 461, 772 Total $4, 990, 754 where the superscripts J and S stand for June and September, respectively. Future values as of September would be FV J WACC = 2, 606, 000 e.12/4 = 2, 685, 365 FV S WACC = 2, 614, 000 e.12 0 = 2, 614, 000 Total $5, 299, 365 If instead we use the risk-free rate r f = 3.6% as the discount rate, we obtain PV J r f = 2, 606, 000 e.036/4 = 2, 582, 651 PV S r f = 2, 614, 000 e.036/2 = 2, 567, 369 Total $5, 150, 020 FV J r f = 2, 606, 000 e.036/4 = 2, 629, 560 FV S r f = 2, 614, 000 e = 2, 614, 000 Total $5, 243, 560 (b) (5 points) Money market hedge. Answer: For each payment Redwall expects to receive, it can borrow euros at an annual rate of 8%, which gives 2, 000, 000 e.08/4 = 1, 960, 397 = $2, 548, 517 for the June payment 2, 000, 000 e.08/2 = 1, 921, 579 = $2, 498, 053 for the September payment. 2

3 These are the present values of money market hedges on each of these payments. Future values are June Payment: September Payment: FV J WACC = 2, 548, 517 e.12/2 = $2, 706, 108 FV J r f = 2, 548, 517 e.036/2 = $2, 594, 805 FV S WACC = 2, 498, 053 e.12/2 = $2, 652, 523 FV S r f = 2, 498, 053 e.036/2 = $2, 543, 425 (c) (5 points) Options market hedge. Answer: Hedging is about limiting losses due to exchange rate changes. One way to hedge the above exposure is to buy put options, then fixing the minimum dollar value of the euros to be received in the future. Similarly, one could write call options on the euro, these calls being covered by the euros to be received in the future. When writing call options, Redwall gains the option premium when the value of the euro ends up being less than the strike price and gets the strike price if the euro value increases above it. Note that these options must European options otherwise the September options would always be worth more than the June options. Note also that the price of the call options are a bit weird given that the euro is expected to appreciate over time. That is, the premium on the September call should be greater than the premium on the call since the September spot rate is expected to be greater than the June spot rate. This is my fault, I should have been more careful when writing the problem. Let s start with the put options. (i) Hedging with Put Options Let P J and P S denote the prices of the June and the September put options, respectively. Then P J = 2, 000, 000 Premium Spot Rate = 2, 000, = $52, 000 P S = 2, 000, = $31, 200 3

4 Each option has a strike price of $1.3000/ and thus the minimum payment in dollars is 2, 000, = $2, 600, 000 both in June and September. The net present values of insuring Redwall s payments with put options are then June: PV J WACC = max { 2, 000, 000S J, 2, 600, 000 } e.12/4 52, 000 PV J r f = max { 2, 000, 000S S, 2, 600, 000 } e.036/4 52, 000 September: PV S WACC = max { 2, 000, 000S S, 2, 600, 000 } e.12/2 31, 200 PV S r f = max { 2, 000, 000S S, 2, 600, 000 } e.036/2 31, 200 where S J This gives and S S denote exchange rates in June and September, respectively. June Payment: September Payment: PV J WACC $2, 471, 158 PV J r f $2, 524, 705 PV S WACC $2, 417, 388 PV S r f $2, 522, 419 Future values, on the other hand, are FV J WACC $2, 623, 966 June Payment: FV J r f $2, 570, 561 FV S WACC $2, 566, 871 September Payment: FV S r f $2, 568, 233 (ii) Hedging with Call Options Let C J and C S denote the prices of the June and the September call options, respectively. Then C J = 2, 000, 000 Premium Spot Rate = 2, 000, = $78, 000 C S = 2, 000, = $67, 600 If Redwall writes call options, these will be covered with the payments it expects to receive in June and September. The money received from the sale of the option 4

5 can then be seen as a compensation were the euro to depreciate, in which case the options would not be exercised. This, however, limits the dollar value of the payments Redwall will receive to $2,600,000 each. The present values of writing call options are June: PV J WACC = min { 2, 000, 000S J, 2, 600, 000 } e.12/4 + 78, 000 PV J r f = min { 2, 000, 000S S, 2, 600, 000 } e.036/4 + 78, 000 September: PV S WACC = min { 2, 000, 000S S, 2, 600, 000 } e.12/2 + 67, 600 PV S r f = min { 2, 000, 000S S, 2, 600, 000 } e.036/2 + 67, 600 which gives June Payment: September Payment: PV J WACC $2, 601, 158 PV J r f $2, 654, 705 PV S WACC $2, 516, 188 PV S r f $2, 621, 219 I won t calculate future values. Note that if the euro is not expected to depreciate, writing covered calls is better than the forward and money market hedges for both payments regardless of the discount rate used. (d) (5 points) No hedging. Answer: This gives the payment times the expected spot rate discounted at either the firm s WACC or the risk-free rate. (e) (10 points) Which alternative is the best? (You may want to draw a graph here representing the payoff from each alternative with respect to the September exchange rate.) Answer: It is easier to look at the problem payment by payment, that is to draw a graph of the payoff of each alternative for each payment. The payoff to each strategy with respect to the first and second payments when the discount rate used is Redwall s WACC is depicted in Figure 1, while Figure 2 shows the payoffs when the discount rate is the risk-free rate. 5

6 We can see from these figures that the money market hedge always outperforms the forward hedge when the WACC is used as the discount rate. If, on the other hand, the risk-free rate is the relevant discount rate, then not only is the forward hedge better than the money market hedge regardless of the discount rate, but the put option hedge also outperforms the money market hedge for the September payment. Note also that the call option hedge is always the best alternative when the exchange rate is not expected to move too far away from $1.3000/. 6

7 Figure 1: Present value of each strategy using Redwall s WACC (12%) as the discount rate. 7

8 Figure 2: Present value of each strategy using the risk-free rate (3.6%). 8