The Mathematics of Money

(Darren Dugan) #1

Copyright © 2008, The McGraw-Hill Companies, Inc.


Depending on the value of the currency, though, carrying values out to two decimal
places may not make much sense. The main unit of Japanese currency, the yen, is worth a
bit less than one U.S. penny. Given that, it doesn’t make much sense to worry about deci-
mal places for amounts in yen. Normally an amount expressed in Japanese currency would
be rounded to whole numbers. It takes about 100 Indonesian rupiah to equal one U.S. cent,
and so not only does it make no sense to express amounts in Indonesian currency to two
decimal places, in most cases it would be logical to round to the nearest hundred rupiah
(for example, rounding 187,584 rupiah to 187,600). There are no hard and fast rules that
we can set forth here about when to use how many decimal places, but as with anything
else you should use judgment and common sense about how far to round answers when
converting currencies.

Example 11.1.3 Convert $87.59 into South Korean won.

From Table 11.1:

US$1  W959.23

Multiplying both sides by 87.59 gives:

US$87.59  W84,018.96

Here we followed the usual two decimal places rule for currency. However, since it takes
nearly 1,000 won to equal US$1, it is highly unlikely that these decimal places would actually
be used. A more reasonable answer would be 84,018 won—or possibly even 84,000 won.

Forward Rates


You may notice that in the exchange rate table, beneath the listing for Japan there follow
listings for “1 month forward,” “3 months forward,” and “6 months forward.” The fact that
exchange rates change over time can pose a real risk and challenge to businesses and fi nan-
cial institutions. Forward rates present an opportunity to lock in an exchange rate today for
a currency exchange that will take place in the future.
Suppose that you work for an American company that does business in Japan. To some
extent at least, you will have to deal with the exchange rate between dollars (the currency
your business works in) and yen (the currency used in Japan). You of course can find out
what the exchange rate is today, but you don’t have a crystal ball to see what the exchange
rate will be in the future. Yet you might be signing contracts to buy or sell products over the
next several months. The deals you are making might look profitable at today’s rates, but
you could find that your profits disappear because of changes in the exchange rate between
now and when payment is made.
Businesses and financial institutions sometimes try to protect themselves from this risk
by making an agreement with another business or financial institution to exchange cur-
rencies at a future date at a rate agreed on today. These are the “forward rates” shown
in the currency table. (The rates that are in effect at present are sometimes called “spot”
rates.) If, for example, you made an agreement to exchange Japanese yen for U.S. dollars
3 months from now, right now the rate being offered in the market to do this is the 3-month
forward rate shown in the table. This sort of deal allows you to protect yourself against an
unforeseen change in the exchange rate, because 3 months from now you will be changing
currency at the rate you’ve locked in today, regardless of what the actual exchange rate is
then. Of course, if the exchange rate changes in your favor, you will miss out because you
will be obligated to make the exchange at the agreed rate.

Example 11.1.4 In August 2006 Rylad Drugs, an American company, sold a large
order of pharmaceuticals to a Japanese wholesaler. The price was set at ¥13,500,000,
and it was agreed that payment would be made when the order was delivered in mid-
November. At the current exchange rate Rylad is comfortable with the price, but it is
worried that changes in the yen-dollar exchange rate over the next 3 months might
make this deal less attractive. Rather than run the risk of being hurt by changes in the

11.1 Currency Conversion 473
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