# Example one

Forward period = 60 days

Spot rate = USD / LCC 7.50

irbc = 5.0%pa

irvc = 10.0% pa

Outright forward rate19

= SP x {[1 + (irvc x t)] / [1 + (irbc x t)]}

= 7.50 x {[1 + (0.10 x 60/365)] / [1 + (0.05 x 60/365)]}

= 7.50 x (1.01643836 / 1.00821918)

= 7.56114134

= USD / LCC 7.56114134.

Let us test the logic. An investor has the choice of investing in a LCC 60-day deposit at 10.0% pa or in a USD 60-day deposit at 5.0% pa. In the former case the investor will earn (assuming LCC 10 000 000 is available to invest):

Forward consideration = present consideration x [1 + (irvc x 60/365)] = LCC 10 000 000 x [1 + (0.10 x 60/365)] = LCC 10 000 000 x 1.01643836 = LCC 10 164 383.60

In the latter case the investor buys the USD equivalent of LCC 10 000 000 = USD 1 333 333.33 [LCC 10 000 000 x (1 / 7.5)]. The investor immediately deposits this amount for 60 days at 5.0% pa, and sells the USD forward consideration forward for LCC at the forward rate of USD / LCC 7.56114134:

Forward consideration = present consideration x [1 + (irbc x 60/365)] = USD 1 333 333.33 x [1 + (0.05 x 60/365)] = USD 1 333 333.33 x 1.00821918 = USD 1 344 292.23.

LCC equivalent at forward exchange rate:

= USD 1 344 292.23 x 7.56114134

= LCC 10 164 383.60.

It should be evident that the forward exchange rate may be calculated by dividing the LCC forward consideration by the USD forward consideration:

LCC 10 164 383.60 / USD 1 344 292.23 = 7.5611.

Conclusion: the investor earns the same return in both countries, and this is so because of the principle of **interest rate parity:**

**The net rate of return from an investment offshore should be equal to the interest earned minus or plus the forward discount or forward premium on the price of the foreign currency involved in the transaction.**

This says that the interest differential between two currencies is related to the forward discount or premium, and that * interest rate parity *is reached when the interest rate differential is equal to the discount or premium on one of the currencies. In this example USDs are selling at a premium in the forward market (think:

**more LCC per USD in the forward market).**This condition in the forward market is brought about by arbitrage. The many participants in the foreign exchange market seek out arbitrage opportunities in this regard (mispricing) and drive the forward exchange rate to reflect the condition of **interest rate parity.**

In the above example the spot exchange rate was USD / LCC 7.5 and the forward exchange rate USD / LCC 7.5611 (rounded). Thus the * forward points *(or forward

*points) are 611 (or LCC 0.0611). This is clarified in the following section on foreign exchange swaps.*

**swap**# Example two

It will be useful to provide another example in order to clarify the PV/FV concept:

A citizen of Local Country borrows funds for 6 months from a Local Country bank, buys USD at the spot rate, invests immediately in a 60-day USD deposit, and converts the USD forward consideration into LCC at the forward rate. The elements of the transactions are:

Amount borrowed = LCC 10 000 000 at 10% pa

LCC borrowing rate = 10.0%pa

Spot exchange rate = USD / LCC 7.5

USD 6-month deposit rate = 5% pa

Forward exchange rate = 7.56114134.

LCC 10 000 000 at spot rate = USD 1 333 333.33 (LCC 10 000 000 / 7.5)

USD 1 333 333.33 at 5% for 60 days

= USD 1 333 333.33 x (1 + 0.05 x 60 / 365) = USD 1 333 333.33 x 1.0082192 = USD 1 344 292.26

USD 1 344 292.26 sold for LCC at forward rate

= USD 1 344 292.26 x 7.56114134

= LCC 10 164 384

LCC owed to bank after 60 days

= LCC 10 000 000 x (1 + 0.10 x 60 / 365) = LCC 10 000 000 x 1.01643834

= LCC 10 164 384.

It will be clear that the Local Country LCC borrower / USD investor did not benefit from the deal; he is at break-even. Had he benefited the forward rate would have been out of line, allowing an arbitrage deal to be undertaken.

From this example it will have been established that if the cost of borrowing is higher than the gain from lending the forward rate will have to be at a premium to compensate for the interest rate differential. It may also be explained as follows:

**If LCC invested increases by more than USD invested (because of the higher LCC interest rate), the numerator (LCC) will increase by more than the denominator (USD) and thus result in a forward rate that is higher than the spot rate.**

The numerator and denominator referred to are of course from the formula presented above and repeated here: