# Exchange Rate Calculation

1. If the spot rate for the Won is 800 won equals 1 US $, and the annual interest rate on fixed rate one-year deposits of won is 9% and for US$ is 3%, what is the one-year forward rate for one won in terms of dollars? Assuming the same interest rates, what is the 8-month forward rate for one dollar in terms of won? Is this an indirect or a direct rate? If the forward rate is an accurate predictor of exchange rates, in this case will the won get stronger or weaker against the dollar? What does this indicate about inflation expectations in Korea compared to the US?

2. On January 3rd, 2007, Daimler-Chrysler expects to ship 10,000 cars from its Hyundai affiliated plant in Korea to the US, which it will sell through its US dealers on 240-day terms at $10,000 each. So Daimler-Chrysler will receive payment from its dealers on August 30, 2007. Assuming that Daimler-Chrysler group needs to cover its expenses in Korea and thus wants to hedge its won exposure using a forward contract with a US bank in Korea, what is the minimum amount of won they should receive on August 30th, 2007 given the eight month forward rate for one US dollar in terms of won that you calculated in problem one? What is one other way they might they hedge their won/dollar exposure?

HINT:

1.To calculate a forward rate for which one currency will be exchanged for another at a date in the future, one needs to know the spot rate and the interest rates for the two currencies involved. In this case a Canadian Dollar is being exchanged for US dollars or a US dollar is being quoted in terms of Canadian Dollars. In the first instance if the base or single unit of currency being measured is a foreign currency other than US dollars in terms of US dollars, then the quote is in direct or US terms where one Canadian dollar equals a certain amount of US currency. If the base or single unit being measured is a US dollar in terms of Canadian dollars then the rate is being quoted in indirect or European terms. The FX Crib Sheet gives you formulas for calculating indirect and direct quotes on a forward basis (4b and 4a respectively). In looking at these formulas note and be sure to use the indirect spot rate with the indirect forward formula (4b) and the direct spot rate(4a) with the direct forward formula. In addition the annual interest rate for each currency must correspond with its currency, e.g. US$ must be multiplied by 1 plus the US interest rate. Further, because the rates are annualized note that the formula adjusts the interest rate to account for different time periods. For example 4 months or a 120 day period would mean that an annual interest rate of 4.5% on US$ would be adjusted to an effective rate of 1.5% and the US$ would be multiplied by 1.015 in applying the formula. A currency is appreciating when it takes fewer of its units to buy one unit of the other currency in the future. It is depreciating in the reverse case.

2. Forward rate contracts can be used to hedge currency exposures. In this case Sony wishes to hedge the chance the yen might get stronger against the dollar between the time Sony ships the PlayStations in September and gets paid in dollars in January. This is because if the yen gets stronger Sony will receive fewer yen for its dollars. Yet, its expenses are in yen. To find out how much Sony will receive if it hedges you must determine whether the quote given is in direct or indirect terms and apply the proper formula (4a or b) as you did in problem 1. This will give you the forward rate. Then you must calculate the dollars Sony will receive and how much yen it can lock in when it exchanges these dollar receipts for yen under the terms of the forward exchange contract.

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#### Solution Preview

1. The rate is Won per dollar and so is an indirect rate. To calculate the foward rate we use the forward rate formula

FFC/$ = SFC/$ (1 + ARIFC x n/360)/(1 + ARIUS x n/360)

Where SFC/$ = 800

ARIFC = 9%

ARIUS = 3%

Forward rate for 1 year = 800 X ...

#### Solution Summary

Exchange rate calculations are examined. The annual interest rate on fixed rate one-year deposits are determined.

Calculate the 6-Month Forward Exchange Rate Based on the Nominal Interest Rates on Bonds

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