Question

The following spot and forward rates for the euro ($/euro) were reported:

Spot		1.6360
30-day forward		1.6359
90-day forward		1.6359
180-day forward		1.6366

a-1. Was the euro selling at a discount or premium in the forward market at 30 days.

• Premium

• Discount

a-2. Was the euro selling at a discount or premium in the forward market at 90 days.

• Discount

• Premium

a-3. Was the euro selling at a discount or premium in the forward market at 180 days.

• Discount

• Premium

b. What was the 30-day forward premium (or discount)? (Negative answer should be indicated by a minus sign. Do not round intermediate calculations. Round the final answer to 2 decimal places.)

30-day forward premium/discount            %

c. What was the 180-day forward premium (or discount)? (Do not round intermediate calculations. Round the final answer to 2 decimal places. Negative answer should be indicated by a minus sign.)

180-day forward premium/discount            %

d. Suppose you executed a 90-day forward contract to exchange 210,000 euros into Canadian dollars. How many dollars would you get 90 days hence?

Dollars for euros francs            $

e. Assume a French bank entered into a 180-day forward contract with TD Bank to buy $210,000. How many euros will the French bank deliver in six months to get the Canadian dollars? (Do not round intermediate calculations. Round the final answer to the nearest whole dollar.)

Euros francs for dollars          €

Answer 1

The interpretation of the $/Euro exchange rate is that for purchase of 1 EURO, at the spot rate 1.636 Dollars need to be provided. That's how the dollar Euro pair is interpreted. A currency is at a premium or a discount when the forward rate is more than or less than the spot rate respectively.

Answer to A-1, Since the forward rate at 30 days of 1.6359 is lesser than the spot rate of 1.636, it means that less of dollars is required to purchase 1 euro. Hence the Euro was selling at a discount at 30 days forward.

Answer to A-2, Since the forward rate at 90 days of 1.6359 is lesser than the spot rate of 1.636, it means that less of dollars is required to purchase 1 euro. Hence the Euro was selling at a discount at 90 days forward.

Answer to A-3, Since the forward rate at 180 days of 1.6366 is more than the spot rate of 1.636, it means that more of dollars is required to purchase 1 euro. Hence the Euro was selling at a premium at 180 days forward.

Answer to b, The formula for calculating Forward premium or discount in terms of percentage is as follows

Fwd Premium or discount = (Forward exchange rate - Spot rate)/Spot rate * 360/n *100

where n = the forward exchange rate period.

In our question, the 30 days Forward exchange rate is 1.6359, Spot rate is 1.6360, n = 30. Substituting the values in the formula, we get the following calculations

Forward premium or discount percentage = (1.6359-1.6360)/1.6360 *360/30*100

= -7.33%

Answer to c, The formula for calculating Forward premium or discount in terms of percentage is as follows

Fwd Premium or discount = (Forward exchange rate - Spot rate)/Spot rate * 360/n *100

where n = the forward exchange rate period.

In our question, the 180 days Forward exchange rate is 1.6366, Spot rate is 1.6360, n = 180. Substituting the values in the formula, we get the following calculations

Forward discount percentage = (1.6366-1.6360)/1.6360 *360/180*100

= 7.33%.

Answer to d, 90 days forward rate is 1.6359. Hence for 1 euro, you would get 1.6359 Dollars. So for 210,000 Euro, one would get 210000*1.6359 Dollars which is equal to $343,539.00.

Answer to e, to find out how much Euro is required to buy $210,000, we have to reverse the 180 day forward rate in terms of dollars. This can be done by identifying how much euro can be bought out of 1 dollar. i.e i/180 day forward rate.

One dollar shall be able to buy = 1/1.6366 which is equal to 0.611 Euro.

Accordingly, $210,000 shall be able to buy 0.611* 210,000 which is equal to EUR 128,314.8.