Question

You are the manager of a U.S. company situated in Los Angeles and manages the import/export division of the company. The company distributes (resells) a variety of consumer products imported to the U.S.A from Europe and also exports goods manufactured in the U.S.A. to Canada.

The first transaction is for the import of good quality wines from France, since a retail liquor trading chain customer in the United States, for who you have been doing imports over the past five years has a very large order this time. The producer in France informed you that the current cost of the wine that you want to import is and €2,500,000. The producer in France will only ship goods in three months’ time due to seasonal differences but payment will have to be conducted six months from now.

The second transaction is for the export of 3d printers manufactured in the U.S.A. The country where it will be exported to is Canada. The payment of CAD 2,500,000 for the export to Canada will be received twelve months from now.

You consider different transaction hedges, namely forwards, options and money market hedges.

You are provided with the following quotes from your bank, which is an international bank with branches in all the countries:

Forward rates:

Currencies	Spot	3 month (90 days)	6 month (180 days)	9 month (270 days)	12 month (360 days)
$/€	1.14134	1.14743	1.15354	1.15969	1.16587
$/CAD	0.76465	0.76559	0.77475	0.76748	0.76843

Bank applies 360 day-count convention to all currencies (for this assignment apply 360 days in all calculations).

Annual borrowing and investment rates for your company:

Country	3 month rates		6 months rates		9 month rates		12 month rates
	Borrow	Invest	Borrow	Invest	Borrow	Invest	Borrow	Invest
United States	2.687%	2.554%	2.713%	2.580%	2.740%	2.607%	2.766%	2.633%
Europe	0.505%	0.480%	0.510%	0.485%	0.515%	0.490%	0.520%	0.495%
Canada	2.177%	2.069%	2.198%	2.090%	2.220%	2.112%	2.241%	2.133%

Bank applies 360 day-count convention to all currencies. Explanation – e.g. 3 month borrowing rate on $ = 2.687%. This is the annual borrowing rate for 3 months. If you only borrow for 3 months the interest rate is actually 2.687%/4 = 0.67175% (always round to 5 decimals when you do calculations). Furthermore, note that these are the rates at which your company borrows and invests. The rates are not borrowing and investment rates from a bank perspective.

Option prices:

Currencies	3 month options				6 month options
	Call option		Put option		Call option		Put option
	Strike	Premium in $	Strike	Premium in $	Strike	Premium in $	Strike	Premium in $
$/€	$1.14399	$0.00174	$1.15088	$0.00174	$1.15010	$0.00173	$1.15702	$0.00152
$/CAD	$0.76292	$0.00392	$0.76828	$0.00392	$0.77205	$0.00387	$0.77747	$0.00387

Bank applies 360 day-count convention to all currencies. (Students also have to apply 360 days in all calculations). Option premium calculations should include time value calculations based on US $ annual borrowing interest rates for applicable time periods e.g. 3 month $ option premium is subject to 2.687%/4 interest rate.)

1. Assume you entered into the forward hedge for the import from France. Three months have passed since you entered into the hedge. Interest rates are the same as before. The spot exchange rate of the $/€ is 15510. Calculate the value of your forward position. Please use a 360 day-count convention, since the bank also used a 360 day-count convention with the forward quotes provided to you. Also remember for interest rates use risk free rates provided under scenario Show your calculation in the table

Table 8: Value of the forward position

Show answer in this row: ($ loss or gain for long/short position in forward)
Show your workings in the columns below the answers

Answer 1

The trader has entered into 6months forward for €2,500,000 @ $/€ 1.15354.
After 3months the spot exchange rate of $/€ = 1.15510
Investment rate is assumed as risk free rate. US 3months risk free rate = 2.554%/4 = 0.6385%, France 3months risk free rate = 0.48%/4 = 0.12%
Expected forward rate after 3months from now = After 3months spot exchange rate*(1+US 3months risk free rate)/(1+France 3months risk free rate) = 1.15510*(1+0.006385)/(1+0.0012) = 1.15510*1.006385/1.0012 = $/€ 1.16108

Gain on long position in forward = 2,500,000*(1.16108-1.15354) = 2,500,000*$0.00754 = $18,850