Question

Suppose that you (i.e., company XYZ) are a US-based importer of goods from Canada. You expect the value of the Canada to increase against the US dollar over the next 6 months. You will be making payment on a shipment of imported goods (CAD100,000) in 6 months and want to hedge your currency exposure. The US risk-free rate is 5% and the Canada risk-free rate is 4% per year. The current spot rate is $1.25/CAD, and the 6-month forward rate is $1.3/CAD. You can also buy a 6-month option on Canadian dollars at the strike price of $1.4 /CAD for a premium of $0.10/CAD.

1) If XYZ enters a forward contract today, the guaranteed dollar cost for this CAD obligation today (not in six months) should be $______

2) In six months, if the spot exchange rate turns to be $1.4/CAD. XYZ will be _______ using forward hedge compared with unhedged position. a) better off b) worse off c) indifferent

3) If XYZ wants to hedge the transaction exposure using money market hedge, XYZ should ______________. a) borrow PV of CAD and buy USD today, and deposit USD in the bank and sit on it. b) buy PV of CAD today using USD, and deposit CAD in the bank and sit on it.

4) If XYZ uses MMH, the guaranteed dollar cost today should be $_____

5) At what 6-month forward rate: $ /CAD will XYZ be indifferent between the forward hedge and MMH? Please leave 4 decimal points for your answer.

6) If XYZ wants to hedge the transaction exposure using option hedge, XYZ should ______. a) buy a put option b) sell a put option c) buy a call option d) sell a call option

7) If XYZ hedges the exposure using an option hedge, total option premium: $____ will be paid today. The option premium will grow to $_____ in six months at the US interest rate. In six months, if the spot price is $1.3 per CAD, the option is (in or out) of the money. So, XYZ will buy 100,000 CAD at the price of $ per CAD, which equals to a total cost of $____ After the option premium, the total (net) dollar costs in six month is $____

8) At what future spot exchange rate do you think XYZ will be indifferent between the option and forward hedge?

9) The range that you will prefer option hedge to forward hedge is ________.

a) when the future spot rate is higher than the indifference price that you solved in the above question.

b) when the future spot rate is lower than the indifference price that you solved in the above question. 10) Suppose Canada company gave XYZ a choice of paying either CAD100,000 or $125,000 in six months. If the spot exchange rate in six months turns out to be $1.3/CAD, which currency (USD or CAD) do you think XYZ will choose to use for payment? The value of this free option for XYZ is $________ .

Answer 1

1) If XYZ enters a forward contract today, the guaranteed dollar cost for this CAD obligation today (not in six months) should be $_1.3/CAD. Since it is given that 6 month forward rate is $1.3/CAD.

2) In six months, if the spot exchange rate turns to be $1.4/CAD. XYZ will be better off using forward hedge compared with unhedged position. Because the forward rate is $1.3/CAD which is lower than the spot exchange rate after 3 months which means payment for imports will have less outflow than if it was not hedged.

3) If XYZ wants to hedge the transaction exposure using money market hedge, XYZ should buy PV of CAD today using USD, and deposit CAD in the bank and sit on it. In case of payables, we borrow PV of domestic currency, convert it into foreign currrency at the spot rate and then deposit it at prevailing rate.

4) If XYZ uses MMH, the guaranteed dollar cost today should be $1,25,612.75

By use of money market hedge, the dollar cost is obtained as follows:

Borrow PV of CAD1,00,000 at 4/2=2% for 6 months. Amount borrowed=CAD1,00,000/1.02=CAD98039.22

Convert CAD to USD using spot rate of $1.25/CAD. Dollars received=$(98039.22*1.25)=$1,22,549.02

Borrow dollars received at 5/2=2/5% for 6 months. Amount payable=$(1,22,549.02*1.025)=$1,25,612.75

5) Effective dollar cost of MMH=$1,25,612.75

Payment under MMH = $1,25,612.75

Foreign currency exposure = CAD1,00,000

Exchange rate for indifference=$1,25,612.75/CAD1,00,000=$1.2561/CAD

6) If XYZ wants to hedge the transaction exposure using option hedge, XYZ should buy a call option. Because XYZ is afraid of dollar rising so it should hedge via call.

7) If XYZ hedges the exposure using an option hedge, total option premium: $10000 will be paid today. The option premium will grow to $0.1025  in six months at the US interest rate. In six months, if the spot price is $1.3 per CAD, the option is out of the money. So, XYZ will buy 100,000 CAD at the price of $1.3 per CAD, which equals to a total cost of $130000 After the option premium, the total (net) dollar costs in six month is $140000.

Total option premium paid=$(1,00,000*0.1)=$10,000

Option premium will grow to $(0.1*1.025)=$0.1025 in 6 months.

The option is out of the money because on maturity price is less than strike price and so call will lapse.

Total payment= option premium + cost of making payment for the imports at spot rate after 6 months

= $(1,30,000+10,000)

= $1,40,000

8) Payment under option hedge for call premium=$10,000

Payment under forward hedge=$1,30,000.

Thus, indifference point=$(1,30,000-10,000)/CAD1,00,000=$1.20/CAD

9) The range that you will prefer option hedge to forward hedge is when the future spot rate is lower than the indifference price that you solved in the above question.

Unless the spot rate is lower than $1.20/CAD, option hedge will not be cheaper than forward hedge.

10) For payment of CAD1,00,000 if exchange rate is $1.30/CAD, then outflow=$1,30,000 which is more than payment of $1,25,000 after six months. So XYZ will choose USD for payment.

Value of this option = $(1,30,000-1,25,000)/CAD1,00,000=$0.05/CAD.