The Mathematics of Money

474 Chapter 11 International Business

exchange rate, suppose that on Thursday August 24, 2006, the company made a deal

to convert this sum into U.S. dollars 3 months later, on November 24, 2006. When the

exchange was made, how much did they receive in dollars?

Using the 3-month forward rate gives:

¥1 
 $0.008691

¥13,500,000 
 US$117,328.50

Whatever the exchange rate may actually have been on November 24, 2006, Rylad received

$117,328.50. In reality, it may be that had the company not made this forward rate deal, it

would have received more, or fewer, dollars. There was no way to know in advance whether

the company would do better or worse by making the forward deal. The point, though, of

this deal was to avoid the uncertainty, giving up the possibility of gain in exchange for

avoiding the risk of loss.

Forward rates are an example of a futures contract. For more discussion and other

examples of these sorts of deals, see Section 6.3.

Converting between Currencies—Cross Rates

Of course, plenty of international trade does not involve U.S. dollars at all. What if we want

to convert, say, £180.00 (British pounds) into Canadian dollars?

A cross rate is an exchange rate between two currencies, neither of which is the U.S.

dollar. Tables of cross rates for many major currencies are published in major financial

newspapers (though less commonly in other newspapers). Table 11.2 shows an example.

The table can be tricky to read, since it does not explain whether the “1.4171” in the

Canada row and Euro column means 1 Canadian dollar is worth 1.4171 euros, or vice

versa. As it happens, this particular table gives the value of the column currency in terms of

the row currency, so that entry actually means that 1 euro is worth 1.4171 Canadian dollars.

The easiest way to figure out which is which is to look at the rate between two currencies

where the rate is obvious. The Japanese yen is a good choice for this. Since the value of

1 yen is so small relative to most other currencies, if you look in the yen column the small

numbers in it tell you that the table must be giving the value of the column currency in

terms of the rows.

Example 11.1.5 Convert C$8,000 Canadian dollars into Mexican pesos.

From the table:

C$1 
 Mex$9.83930

And so:

C$8,000 
 Mex$78,714

US Dollar Euro Pound SFranc Peso Yen Cdn Dollar

Canada 1.11070 1.41710 2.09590 0.89600 0.10163 0.00953 1.00000

Japan 116.52000 148.66000 219.87000 93.99900 10.66200 1.00000 104.90600

Mexico 10.92900 13.94320 20.62200 8.81640 1.00000 0.09379 9.83930

Switzerland 1.23960 1.58150 2.33900 1.00000 0.11343 0.01064 1.11600

U.K. 0.53000 0.67610 1.00000 0.42750 0.04849 0.00455 0.47713

Euro 0.78380 1.00000 1.47900 0.63231 0.07172 0.00673 0.70567

U.S. 1.00000 1.27580 1.88690 0.80670 0.09150 0.00858 0.90030

TABLE 11.2

Currency Cross Rates as of 4 P.M. August 24, 2006