B481/S98/NOTES/Grabbe-5 FORWARDS, SWAPS, AND INTEREST ...

Hedging Costs
The interest parity equation can be used to determine an optimal hedging
plan. The key point is that a corporation, if it faces interest rates, does
not face the interbank eurocurrency rates. Corporations rarely engage in
currency arbitrage, but they regularly engage in hedging.
Example 5.5 (Hedging Costs)
Suppose a US corp. must pay DM2million in 6 months (180 days). The corp.
can borrow US$ at 10% or DM at 5.5%. The relevant exchange rates are S(t)
= US$.3752/DM and F(t,180) = US$.3900/DM. The corp. wishes to lock in
the US$ cost of the DM2million now. How should it do so
The possibilities are to hedge via the forward market and to use a money
market equivalent. We need simply to compare the two. Of course, they
are the two sides to the interest parity equation.
The hedge requires the corp. to buy forward DM$2million, which costs
(DM2million)(US$.3900/DM) = $780,000 to be paid in 180 days.
The money market equivalent is to acquire and deposit sufficiently many
DM to generate DM2million, at 5.5%, in 180 days. Thus, we need to find X
where [1+.055(180/360)]X = 2million. Clearly, X = DM1,946,472. To
acquire DM1,946,472 today, the corp. must borrow US$ in the amount
(DM1,946,472)(US$.3752/DM) = $730,316.30. If the corp. borrows this
amount today, it will have to pay back ($730,316.30)[1+.10(180/360)] =
$766,832.12 in 180 days.
Thus, we have two comparable numbers:
the hedge costs $780,000 to be paid in 180 days;
the money market plan costs $766,832.12 to be paid in 180 days.
Clearly, the money market plan costs less and should be adopted.
The key point is this -- the corp. faces interest rates other than the
eurocurrency rates. Therefore, the interest parity equation does not hold
for the rates faced by the corp. Hence, the equation provides a means for
determining the superior plan. Note that we have ignored, for simplicity,
both the bid/asked form of exchange rates and transactions costs.
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