Question

Gotohell buys and sells regularly with customers worldwide. Its home currency is the dollar. The firm expects to receive €1.2 million in 6 months’ time from a customer abroad.

Current exchange rates in the home country of Gotohell are:

Exchange rate : Euros Per dollar

Spot : 4.1780-4.2080

6-month forward : 4.2302- 4.2606

12-month forward : 4.2825-4.3132

Required: a) Calculate the rate of forward discount of the euro on the 6-month forward exchange rate both for buying and selling rate.

b) Assuming that forward contract is the only hedging tool available in the home country of Gotohell, calculate, when compared to its current dollar value, the gain or loss which Gotohell will incur by taking out a forward exchange contract on the future receipt of euros.

c) On the basis of your answer in (b), advise Gotohell on the desirability of this hedge.

d) If the interest rate in the home country of Gotohell is 4% per year, calculate the implied annual interest rate in the foreign customer’s country, using the mid-spot and the mid-twelve-month forward exchange rate.

Answer 1

The exchange rates given are : (Euro per Dollar )

Spot : $1 = Euro 4.1780-4.2080  

6-month forward : $1 = Euro 4.2302- 4.2606

12-month forward : $1 = Euro 4.2825-4.3132

a) Calculate the rate of forward discount of the euro on the 6-month forward exchange rate both for buying and selling rate :

Rate of Forward discount = [(Spot rate - Forward rate) / Forward rate] x 100

i) For Buying rate = [(4.1780 - 4.2302) / 4.2302] x 100

= [-0.0522 / 4.2302] x 100

= -1.2339% or -1.23% (rounded off)

This rate of forward discount is for 6 months. In order to calculate the annualized rate, we have to multiply this by 12/6

Annualized rate = Forward discount rate x 12 / n (where n is the number of months for which the forward exchange rate is given)

Hence, Annualized Rate of Forward discount of Euro (buying rate) = -1.23% x 12/6 = -2.46%

ii) For Selling rate = [(4.2080 - 4.2606) / 4.2606] x 100

= [-0.0526 / 4.2606] x 100

= -1.2345% or -1.23% (rounded off)

Annualized Rate of Forward discount of Euro (selling rate) = -1.23% x 12/6 = -2.46%

b) The firm expects to receive €1.2 million in 6 months’ time from a customer abroad. The firm's home currency is dollar so it will sell Euros received from the customer to the bank, and purchase Dollars from it.

The gain or loss on a forward contract hedge is calculated by comparing the Amount receivable based on the expected spot rate with the Amount receivable based on the forward contract rate.

However, We don't have the information in the question about the expected spot rate in 6 months time from now.

Hence, the current dollar value of this receivable based on the current spot rate given, is as follows:

Spot : $1 = Euro 4.1780-4.2080

=> Euro 1 = $1 / 4.2080 - 1 / 4.1780

The firm will sell Euro to the bank and purchase Dollar from it, so we need to use the buying rate.

Hence, Dollar receivable = Euro receivable x Buying rate = € 1,200,000 x 1 / 4.2080 = $ 285,171.10 (rounded off)

Now by taking out a forward exchange contract, the dollar value of this receivable on receipt of euros after 6 months is as follows :

6-month forward : $1 = Euro 4.2302 - 4.2606

=> Euro 1 = $1 / 4.2606 - 1 / 4.2302

Dollar receivable after 6 months under forward contract = Euro receivable x Buying rate = € 1,200,000 x 1 / 4.2606 = $ 281,650.47 (rounded off)

Gain or Loss on the Forward hedge = Dollar receivable with Forward Hedge - Dollar receivable without Forward Hedge = $ 281,650.47 - $ 285,171.10 = $ -3,520.63 (Loss)

c) Based on the above answer, since there is a loss incurred on taking out a forward contract hedge, the hedge is not desirable.

d) As per the Interest Rate Parity equation :

1 + Foreign currency Interest rate / 1 + Home currency Interest rate = Forward Exchange Rate / Spot Exchange Rate

The interest rate in the home country of Gotohell is 4% per year or 0.04

We need to use the mid-spot and the mid-twelve-month forward exchange rates.

Mid rate = (Buying rate + Selling rate) / 2

Hence, Mid Spot rate (euro per dollar) = 4.1780 + 4.2080 / 2 = 8.3860 / 2 = 4.1930

12-month forward rate given is : 4.2825-4.3132

Mid 12-month forward rate (euro per dollar) = 4.2825 + 4.3132 / 2 = 8.5957 / 2 = 4.29785

1 + Foreign currency Interest rate / 1 + 0.04 = 4.29785 / 4.1930

=> 1 + Foreign currency Interest rate = 4.29785 x 1.04 / 4.1930 = 1.066

  Foreign currency Interest rate = 1.066 - 1 = 0.066 or 6.60% per year