PART 5: SPECIAL TOPICSAssume that the current spot rate equals $0.95/€. Multiplying the spot rate times the NPV yields a
dollar-based NPV of $116,000 (rounded to the nearest thousand dollars).
In this example, we did not make specific year-by-year forecasts of the future spot rates. Doing so
is unnecessary, because the company can choose to hedge its currency exposure through a forward
contract. Hedging the currency exposure allows the company to separate the decision to accept or reject
the project from projections of where the dollar-to-euro exchange rate might be headed. Of course, the
company may have a view on the exchange rate question, but even so, it is wise to first consider the
investment on its own merits. For instance, suppose that this project has a negative NPV, but managers
believe that the euro will appreciate over the life of the project, increasing the project’s appeal in dollar
terms. Given that belief, there is no need for the company to undertake the project. Instead, it could
purchase euros directly, invest them in safe financial assets in Europe, and convert back to dollars several
years later. That is, if the company wants to speculate on currency movements, it need not invest in
physical assets to accomplish that objective.
A second approach for evaluating the investment project is to calculate the NPV in dollar terms,
assuming that the company hedges the project’s cash flows using forward contracts. To begin this
calculation, we must know the risk-free rate in Australia. Suppose that this is 3%. Recognising that
interest rate parity must hold, we can use this to calculate the one-year forward rate.
Interest rate parity means that risk-free investments should offer the same return (after converting
currencies) everywhere. We can express interest rate parity in mathematical terms. Letting Rfor and Rdom
represent the risk-free rate on foreign and domestic government debt; (F)for/dom and (S)for/dom represent the
forward and spot rates quoted per unit of domestic currency; and n represent the number of forward
periods, we obtain the following equation:^3 ,^4Eq. 17.2F
SR
Rnfor/dom
for/domforndomn()
()(1 )
(1 )=
+
+Thus, using Equation 17.2, but assuming that the dollar is the foreign currency, since we want the
resultant forward quoted as dollars per euro:.
.
.$.
$/
$/$/
F $/
SR
RF
F()
()(1 )
(1 )()
095103
104() 0 9319/
euro
euroAustralia
euroeuro
1 euro1
11
= 1+
+⇒=⇒=
Similarly, we can calculate the two-year and three-year forward rates as follows:
.
.
.$.
$/
$/
€F
F()
095103
105() 0 9142/
euro
2 euro2
=⇒ 2 2 =.
.
.$.
$/
()F F$/ €
095103
105() 0 8967/
euro
3 euro3
=⇒ 3 3 =3 Be careful to match the term of the forward rate to the term of the interest rate in this expression. For example, if you are comparing interest
rates on 180-day government bills, you must use a 180-day forward rate.
4 What does this expression mean? Observe that if the left-hand side of the equation is greater than 1.0, the domestic currency trades at a
forward premium. If domestic investors send money abroad, when they convert back to domestic currency, they will realise an exchange
loss, because the foreign currency buys less domestic currency than it did at the spot rate. Domestic investors know this, so they require an
incentive in the form of a higher foreign interest rate before they will send money abroad. To maintain equilibrium, the right-hand side must
also be greater than 1.0, which means that the foreign interest rate must exceed the domestic rate. The bottom line is that when a nation’s
currency trades at a forward premium (discount), risk-free interest rates in that country should be lower (higher) than they are abroad.interest rate parity
An equilibrium relationship
that predicts that differences
in risk-free interest rates in
two countries must be tied to
differences in currency values
on the spot and forward
marketsDo companies use different
methods to evaluate foreign as
opposed to domestic investment
projects?
thinking cap
question