Calculation of forward exchange rates explained with the illustrations

A currency forward contract is a customized, written contract between two parties that sets a fixed foreign currency exchange rate for a transaction, set for a specified future date. Currency forward contracts are used to hedge foreign currency exchange risk. They are most commonly made between importers and exporters headquartered in different countries.

A forward exchange rate is the price at which a bank agrees to exchange one currency for another at a future date. It’s a key part of foreign exchange markets, and is used by businesses and investors to hedge against currency fluctuations risks.

Calculations:

The forward exchange rate is calculated using the current spot rate, the interest rates of the currencies involved, and the time of the contract. The formula is:

Forward rate= [S x (1+r(d)x(t/360)]÷ [(1+r(f) x (t/360)

(Note: The base currency is the first currency in the pair, and the quote currency is the second).

Where,

S is the current spot rate of the currency pair

r(d) is the domestic currency (base currency) interest rate

r(f) is the foreign currency (quote currency) interest rate

t is the time of the contract in days

• As an example, assume the current U.S. dollar to Indian Rupee exchange rate is:

Spot rate 1USD    :  Rs.86.5008 and the domestic interest rate or the IRS is 6% and U.S. currency interest rate is 5%

Solution:

The forward exchange rate is calculated using the current spot rate, the interest rates of the currencies involved, and the time of the contract.

The formula is: Forward rate is = [S x (1+r(d) x (t/360)]÷ [(1+r(f) x (t/360)

Forward rate for one year = 86.5008 x [1+0.06) ÷ (1+0.05)] x 1        Here t/360=1

86.5008 x1.0095= 87.3225

So forward contract rate of 1USD for one year is at premium of Rs.87.3225

Similarly, let us calculate for forward rate for 90 days, with the above example

 t for base currency (domestic currency) for 90 days is (0.06) x 90/360= 0.015,  

 t for Quote currency (foreign currency) for 90 days is (0.05)x 90/360= 0.0125

Spot rate is; 86.5008, interest rates on domestic currency are 0.015 and foreign currency is 0.0125 respectively.

Now use the formula for forward rate for 90 days

Forward rate is = [S x (1+r(d) x (t/360)]÷ [(1+r(f) x (t/360)

Forward Rate= 86.5008 x (1+0.015/(1+0.0125)= 86.5008 x (1.015/1.0125)=86.7144

Therefore, the 90 days forward rate will be at premium of 1 USD=86.7144

In the cases where interest rate of quote currency is higher than the base currency than the forward rate will be less than the spot rate.

For an example, suppose domestic (Base currency) interest rate  is 5% and quote currency rate is 6% the forward rate for above illustration for 90 days is as under.

The forward exchange rate is calculated using the current spot rate, the interest rates of the currencies involved, and the time of the contract. The formula is:

Spot rate is; 86.5008, interest rates on domestic currency are 0.0125 and foreign currency is 0.015 respectively.

The forward currency rate for 1 USD= 86.5008 x (1.0125/1.015)= 86.2877

The 90 days forward rate will be at discount rate of 1 USD=Rs.86.2877 which is less than spot rate of Rs.86.5008

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