Question

You work for Shrad Ltd (a small Canadian importing firm). Shrad Ltd is interested in having your help to manage the exchange rate exposure on its foreign currency transactions. In your first month the firm agrees to buy goods from a US supplier. Payment of US$10,000,000 is to be made in 90 days. To help with your decisions, you obtain the following information from the international money markets.

Exchange Market

Spot (C$/US$1) 1.5870/1.5886

Forward (C$/US$1) 90 days 1.5898/1.5908

Money Market Rates (annual)

90 day C$ interest rates 1.575 / 1.545%

90 day US$ interest rate 1.200 / 1.000%

Over the counter options

90 day options on C$ with strike price of C$1.60/US$1:

Premium C$50,000 for a US$10million contract.

Use 90 and 360 days in your calculations.

i. Determine the C$ value of the US$ payable if you lock in this amount using a forward contract.

ii. Describe how Shrad Ltd could construct a money market hedge for this situation. Present and explain your calculations in detail.

iii. Draw a diagram that illustrates the risk profile of the underlying risk facing Shrad Ltd, the forward contract and the option contract (y axis effective revenue, x axis C$/US$). Determine the exchange rate, C$/$, at which the option hedge would produce a better outcome for the firm than the forward hedge and also the exchange rate at which the option hedge would produce a better outcome than being unhedged.

Answer 1

i.

Since the firm has payable of 10000000, we have to take long position in the forward contract.

That means 90-day forward rate is 1.5908.

 

Therefore, 

C $ value = Forward rate*Payable 

                 = 1.5908*10000000 

                 = 15908000.00

 

ii.

The firm has payable in foreign currency. So for money market hedge we have to borrow at domestic currency (C$) and lend at foreign currency (US$).

Payable (US$), P = 10000000

Lending rate, rL = Lending rate of 90 days US$ interest rate = 1.000%

 

Therefore, present value of lending amount, L = P/(1+rL*90/360)

                                                                                    = 10000000/(1+1.000%*90/360) 

                                                                                   = 9975062.34

 

Current spot rate, S = Buy (Ask) spot rate 

                                    = 1.5886

 

Therefore, present value of borrowing amount, B = L*S 

                                                                                         = 9975062.34*1.5886 

                                                                                         = 15846384.04

 

Borrowing rate, rB = Borrowing rate of 90 days C$ interest rate 

                                  = 1.575%

 

Therefore, C$ value of amount payable in 90 days = B*(1+rB*90/360) 

                                                                                          = 15846384.04*(1+1.575%*90/360) 

                                                                                         = 15908779.18

 

iii.

90-day forward rate, F = Buy rate of forward (C$/US$) 90 days 

                                         = 1.5908

 

Effective revenue of the forward contract hedge = Payable*(Spot rate-Forward rate) 

                                                                                       = 10000000*(1.5908-Spot rate)

 

For the option contract,

Upfront premium = 50000

 

Therefore, payoff of the option contract = Max[Spot rate-Strike price,0]*Payable-Upfront premium 

                                                                        = Max[Spot rate-1.60,0]*10000000-50000

 

The payoff diagram of the forward contract and option contract are shown below:

 

The point of intersection of the two graphs happens at spot rate lower than strike price of the option contract.

 

The point of intersection of the two graphs is calculated below:

Payoff of forward contract = Payoff of option contract

10000000*(1.5908-Spot rate) = Max[Spot rate-1.60,0]*10000000-50000

or, 10000000*(1.5908-Spot rate) = 0*10000000-50000

or, Spot rate = 1.5958

 

So, when spot rate is higher than 1.5958, option contract hedge is better than forward hedge.

 

The exchange rate at which the option hedge would produce a better result than being unhedged is calculated below:

Payoff of option contract = 0

or, Max[Spot rate-1.60,0]*10000000-50000 = 0

or, Spot rate-1.60 = 50000/10000000

or, Spot rate = 1.6050.

a. C $ value = 15908000.00