Kenneth R. Szulczyk
Investors can use the net present value formula in Equation 28 to calculate the return of a
foreign investment. We add a new variable, the exchange rate, Ei, to the formula. Exchange rate
converts the value of the foreign investment into the equivalent of our home currency.
Unfortunately, the exchange rates change continually, and we assume we know the exchange
rate at every point in time. Subscript indicates the specific exchange rate for that year.
ܸܲܰ=−ܸܲܧ+
ிభாభ
(ଵା)భ+
ிమாమ
(ଵା)మ+⋯+
ிா
(ଵା)^ (^28 )^
For example, you invested 20,000 euros into Greece, and you expect to earn $8,000 each
year for Year 1, Year 2, and Year 3. Nevertheless, you could invest your money into your
country’s financial markets that earn a 5% APR. Is your investment profitable? We forecasted
the exchange rates below, and your home country is the United States:
Time 0: Exchange rate equals $1.5 0 per 1 euro.
Time 1: Exchange rate equals $1.75 per 1 euro.
Time 2: Exchange rate equals $2.00 per 1 euro.
Time 3: Exchange rate equals $2.10 per 1 euro.We calculate the net present value of your investment of $12,358.27 in Equation 29. The
NPV is positive, and the investment increases your wealth. However, we must forecast the
exchange rates, except today’s exchange rate, E 0. Exchange rates could fluctuate in any
direction.
ܸܲܰ=− 20 ,000€∙ 1. 50 $ൗ€+
଼, €∙ଵ.ହ$ൗ€
(ଵା.ହ)భ +
଼, €∙ଶ.$ൗ€
(ଵା.ହ)మ +
଼, €∙ଶ.ଵ$ൗ€
(ଵା.ହ)య^ (^29 )^
ܸܲܰ=−$30, 000 +$13, 333. 33 +$14, 512. 47 +$14, 512. 47 =$12, 358. 27
We continue our example, and we see Europe experiences a financial crisis. Euro begins
plunging against the U.S. dollar causing the exchange rates to change to below:
Time 0: Exchange rate equals $1.50 per 1 euro.
Time 1: Exchange rate equals $1.25 per 1 euro.
Time 2: Exchange rate equals $1.00 per 1 euro.
Time 3: Exchange rate equals $0.50 per 1 euro.We calculate the net present value of - $9,764.60 in Equation 30. Our investment became a
disaster because we earned a negative return because the euro had depreciated.