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7.3: Exchange Rates and Currency Exchange

  • Page ID
    22105
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    You have set aside $6,000 in Canadian funds toward hostel costs during a long backpacking trip through the United States, Mexico, and Europe. After searching on the Internet, you decide to use Hotwire.com to reserve your hostel rooms. The website quotes you the following amounts for each country: 1,980 US dollars, 21,675 Mexican pesos, and 1,400 euros. Have you allocated enough money to cover these costs?

    Whether you are a consumer backpacking around the world on distant vacations, investing in international securities, or shopping online at global Internet sites, you must pay for your purchases in local currencies out of your Canadian currency accounts. Businesses are no different as they export and import products to and from other countries. With outsourcing on the rise, it is also common for business services such as call centers and advertising agencies to be located abroad along with manufacturing facilities. Large-scale companies may have operations in several countries throughout the world.

    All of these transactions and operations require the conversion of Canadian currency to a foreign currency or vice versa. This section shows you the basics of currency conversion rates and then explores finer details such as charges for currency conversion and what happens when one currency gets stronger or weaker relative to another.

    Exchange Rates

    An exchange rate between two currencies is defined as the number of units of a foreign currency that are bought with one unit of the domestic currency, or vice versa. Since two currencies are involved in every transaction, two published exchange rates are available. Let's use Canada and the United States to illustrate this concept.

    • The first exchange rate indicates what one dollar of Canada's currency becomes in US currency.
    • The second exchange rate indicates what one dollar of US currency becomes in Canadian currency.

    These two exchange rates allow Canadians to determine how many US dollars their money can buy and vice versa. These currency rates have an inverse relationship to one another: if 1 Canadian dollar equals 0.80 US dollars, then 1 US dollar equals \(\dfrac{1}{\$ 0.80}=1.25\) Canadian dollars.

    Most Canadian daily and business newspapers publish exchange rates in their financial sections. Although exchange rates are published in a variety of ways, a currency cross-rate table, like the table below, is most common. Note that exchange rates fluctuate all of the time as currencies are actively traded in exchange markets. Therefore, any published table needs to indicate the date and time at which the rates were determined. Also note that the cells where the same currency appears show no published rate as you never need to convert from Canadian dollars to Canadian dollars!

    Per C$ Per US$ Per € Per ¥ Per MXN$ Per AU$
    Canadian Dollar (C$) \(\diagdown\) 0.9787 1.4012 0.0122 0.0823 1.0360
    US Dollar (US$) 1.0218 \(\diagdown\) 1.4317 0.0125 0.0841 1.0585
    Euro (€) 0.7137 0.6985 \(\diagdown\) 0.0087 0.0588 0.7394
    Japanese Yen (¥) 82.0233 80.2765 114.9287 \(\diagdown\) 6.7540 84.9747
    Mexican Peso (MXN$) 12.1445 11.8859 17.0165 0.1481 \(\diagdown\) 12.5814
    Australian Dollar (AU$) 0.9652 0.9447 1.3525 0.0118 0.0795 \(\diagdown\)

    In the table, all exchange rates have been rounded to four decimals. In true exchange markets, most exchange rates are expressed in 10 decimals or more such that currency exchanges in larger denominations are precisely performed. For the purposes of this textbook, we will use a four decimal standard to simplify the calculations while still illustrating the principles of currency exchange.

    Technically, only half of the table is needed, since one side of the diagonal line is nothing more than the inverse of the other. For example, the euro is \(0.7137\) per \(C\$\) on the bottom of the diagonal. The inverse, or \(\dfrac{1}{0.7137}=1.4011\) per €, is what is listed on top of the diagonal (the difference of 0.0001 is due to rounding to four decimals).

    The Formula

    The formula is yet again another adaptation of Formula 2.2 on Rate, Portion, and Base. Formula 7.4 expresses this relationship in the language of currency exchange.

    clipboard_eaedb0b9a05c468fa318e79f329d1b94e.png

    Formula 7.4

    Important Notes

    Currencies, exchange rates, and currency cross-tables all raise issues regarding decimals and financial fees.

    1. Decimals in Currencies. Not all currencies in the world have decimals. Here in North America, MXN$, US$, and C$ have two decimals. Mexicans call those decimals centavos while Canadians and Americans call them cents. Australia and the European countries using the euro also have cents. However, the Japanese yen does not have any decimals in its currency. If you are unsure about the usage of decimals, perform a quick Internet search to clarify the issue.
    2. Financial Fees. Technically, the rates in a cross-rate table are known as mid-rates. A mid-rate is an exchange rate that does not involve or provide for any charges for currency conversion. When you convert currencies, you need to involve a financial organization, which will charge for its services.
      1. Sell Rates. When you go to a bank and convert your domestic money to a foreign currency, the bank charges you a sell rate, which is the rate at which a foreign currency is sold. When you exchange your money, think of this much like a purchase at a store—the bank's product is the foreign currency and the price it charges is marked up to its selling price. The sell rate is always higher than the mid-rate in terms of \(C\$\) per unit of foreign currency and thus is always lower than the mid-rate in terms of foreign currency per unit of \(C\$\). For example, the exchange rate of \(C\$\) per US$ is 0.9787 (you always look up the “per currency” column that you are purchasing). This means it will cost you \(C\$\)0.9787 to purchase US\(\$\)1.00. The bank, though, will sell you this money for a sell rate that is higher, say $0.9987. This means it will cost you an extra \(C\$\)0.02 per US\(\$\) to exchange the money. That $0.02 difference is the fee from the bank for its services, and it is how the bank makes a profit on the transaction.
      2. Buy Rates. When you go to a bank and convert your foreign currency back into your domestic money, the bank charges you a buy rate, which is the rate at which a foreign currency is purchased. The buy rate is always lower than the mid-rate in terms of \(C\$\) per unit of foreign currency and thus is always higher than the mid-rate in terms of foreign currency per unit of C$. Using the same example as above, if you want to take your US$1.00 to the bank and convert it back to Canadian funds, the bank charges you a buy rate that is lower, say $0.9587. In other words, you receive \(C\$\)0.02 less per US\(\$\). Again, the $0.02 difference is the bank's fee for making the currency exchange on your behalf.

    How It Works

    Follow these steps when performing a currency exchange:

    Step 1: Identify all known variables. Specifically, identify the currency associated with any amounts. You also require the mid-rate. If buy rates and sell rates are involved, identify how these rates are calculated.

    Step 2: If there are no buy or sell rates, skip this step. If buy and sell rates are involved, calculate these rates in the manner specified by the financial institution.

    Step 3: Apply Formula 7.4 using the appropriate mid-rate, buy rate, or sell rate to convert currencies.

    This section opened with your backpacking vacation to the United States, Mexico, and Europe, for which you were quoted prices of US$1,980, MXN$21,675, and €1,400 for hostels. Assume all purchases are made with your credit card and that your credit card company charges 2.5% on all currency exchanges. Can your C$6,000 budget cover these costs?

    Step 1: There are three currency amounts: US$1,980, MXN$21,675, and €1,400. Using the cross-rate table, the Canadian exchange mid-rate per unit of each of these currencies is 0.9787 US$, 0.0823 MXN$, and 1.4012 €.

    Step 2: Calculate the buy rates (since you are converting foreign currency into domestic currency) for each currency:

    \[\mathrm{US} \$=0.9787(1.025)=1.0032\nonumber \]

    \[\mathrm{MXN} \$=0.0823(1.025)=0.0844\nonumber \]

    \[€=1.4012(1.025)=1.4362\nonumber \]

    Step 3: Apply Formula 7.4 to each of these currencies:

    \[ \text { US}\$ \text{: Desired Currency }=\mathrm{US} \$ 1,980 \times 1.0032=\mathrm{C} \$ 1,986.34.\nonumber \]

    \[ \text { MXN}\$ \text{: Desired Currency }=\mathrm{MXN} \$ 21,675 \times 0.0844=\mathrm{C} \$ 1,829.37.\nonumber \]

    \[€ \text {: Desired Currency }=€ 1,400 \times 1.4362=\mathrm{C} \$ 2,010.68.\nonumber \]

    Putting the three amounts together, your total hostel bill is:

    \[\$ 1,986.34+\$ 1,829.37+\$ 2,010.68=\$ 5,826.39\nonumber \]

    Because this is under budget by $173.61, all is well with your vacation plans.

    Things To Watch Out For

    When working with currency exchange, probably the trickiest element is that you have to choose one of two inverse exchange rates depending on which way the money conversion is taking place. In any currency situation, it is important that you take the time to understand the basis on which the currency rate is being expressed. Typically, exchange rates are expressed on a per-unit basis in the country's domestic currency. For example, Canadians express the US dollar exchange rate on a per \(C\$\) basis. From the cross-rate table, that exchange rate is 1.0218. In contrast, Americans express the Canadian dollar exchange rate on a per US$ basis, or 0.9787.

    Paths To Success

    Let the buyer beware when it comes to international transactions. If you have ever purchased and returned an item to an international seller, you may have noticed that you did not receive all of your money back. For most consumers, international purchases are made via credit cards. What most consumers do not know is that the credit card companies do in fact use buy and sell rates that typically charge 2.5% of the exchange rate when both buying and selling.

    For example, if you purchase a US$2,000 item at the rates listed in the cross-rate table, your credit card is charged \(\$ 2,000 \times 0.9787(1.025)=\$ 2,006.40\). If you return an item you do not want, your credit card is refunded \(\$ 2,000 \times 0.9787(0.975)=\$ 1,908.40\). In other words, you are out \(\$ 2,006.40-\$ 1,908.40=\$ 98 !\) This amount represents your credit card company's charge for the currency conversion—a whopping 4.9% of your purchase price!

    Exercise \(\PageIndex{1}\): Give It Some Thought

    In each of the following situations and using the cross-rate table, determine on a strictly numerical basis whether you would have more or fewer units of the target currency than of the original currency. You want to convert:

    1. C$ into US$
    2. AU$ into MXN$
    3. MXN$ into ¥
    4. C$ into €
    Answer
    1. More, since C$1 becomes US$1.0218
    2. More, since AU$1 becomes MXN$12.5814
    3. More, since MXN$1 becomes ¥6.7540
    4. Less, since C$1 becomes €0.7137
    Example \(\PageIndex{1}\): A Straight Currency Conversion

    Strictly using the mid-rates from the cross-rate table presented earlier, if you wanted to convert C$1,500 into MXN$ for your spring break vacation in Cancun, Mexico, how many Mexican pesos would you have?

    Solution

    Take Canadian currency and convert it into the desired Mexican currency.

    What You Already Know

    Step 1:

    The amount and the exchange rate are known:

    Current Currency = $1,500

    Exchange Rate = 12.1445

    How You Will Get There

    Step 2:

    No buy or sell rates are involved. Skip this step.

    Step 3:

    Apply Formula 7.4.

    Perform

    Step 3:

    Desired Currency = 12.1445 × $1,500 = $18,216.75

    You have $18,216.75 Mexican pesos available for your spring break vacation.

    Example \(\PageIndex{2}\): Calculating Profit Using Buy and Sell Rates

    A Mexican manufacturer imports its parts from Canada and assembles its product in Mexico, then exports some of the finished product back to Canada to sell at retail. Suppose the total cost of the imported parts, purchased and paid for in Canadian funds, is C$5.50 per unit, assembly costs are MXN$24.54 per unit, and expenses are MXN$4.38 per unit. If the product is exported back to Canada at a selling price of C$9.95 (for which its Canadian customers pay in Canadian funds), what is the total profit in Mexican pesos on 10,000 units? The manufacturer's financial institution charges a sell rate 2% higher than the mid-rate and has a buy rate that is 3% lower than the mid-rate. Use the mid-rates from the cross-rate table.

    Solution

    Calculate the total profit (\(P\)) in MXN$ for the Mexican manufacturer. However, since money is being expressed in different currencies, you must first convert all amounts into Mexican pesos.

    What You Already Know

    Step 1:

    You know the costs, expenses, price, and mid-rate:

    \[C_{parts}=10,000 \times C \$ 5.50=C \$ 55,000 \nonumber \]

    \[C_ {assembly}=10,000 \times \text{MXN} \$ 24.54=\text{MXN} \$ 245,400 \nonumber \]

    \[E=10,000 \times \text{MXN}\$ 4.38=\text{MXN}\$ 43,800 \nonumber \]

    \[S=10,000 \times C\$ 9.95=C\$ 99,500 \nonumber \]

    Mid-Rate = 12.1445 per \(C\$\)

    Sell Rate = 2% higher

    Buy Rate = 3% lower

    Note the mid-rate used is “per \(C\$\)” since the manufacturer needs to purchase Canadian funds to pay its suppliers and also needs to sell its Canadian revenues to the bank.

    How You Will Get There

    Step 2:

    Calculate the buy and sell rates.

    Step 3 (Parts):

    Convert the purchase of the parts in \(C\$\) into \(\text{MXN} \$\) using the sell rate. Apply and adapt Formula 7.4.

    Step 3 (Sale):

    Convert the sale of the product in \(C\$\) into \(\text{MXN} \$\) using the buy rate. Apply and adapt Formula 7.4.

    Step 4:

    All amounts are in \(\text{MXN} \$\). Apply Formula 6.5: \(S=C_{parts}+C_{assembly}+E+P\)

    Perform

    Step 2:

    Sell Rate = 2% higher than mid-rate = 12.1445 (1 + 0.02) = 12.3874

    Buy Rate = 3% lower than mid-rate = 12.1445 (1 − 0.03) = 11.7802

    Step 3 (Parts):

    \[C_{parts} \text { in } \text{MXN}\$=12.3874 \times \$ 55,000=\$ 681,307 \nonumber \]

    Step 3 (Sale):

    \[S \text{ in MXN}\$=11.7802 \times \$ 99,500= \$ 1,172,129.90 \nonumber \]

    \[\begin{aligned}
    \$ 1,172,129.90 &=\$ 681,307+\$ 245,400+\$ 43,800+P \\
    \$ 1,172,129.90 &=\$ 970,507+P \\
    \$ 201,622.90 &=P
    \end{aligned} \nonumber \]

    After converting all Canadian currency into Mexican pesos and factoring in the financial institution's buy and sell rates, the manufacturer realizes a profit of $201,622.90 in Mexican pesos.

    clipboard_ebbc0b041fe0fbb8b52d348c78793b0a9.png

    Currency Appreciation and Depreciation

    An analyst on Global News is discussing how the Canadian dollar has strengthened against the US dollar. Your first reaction is that a strong Canadian dollar ought to be good thing, so hearing that this change might hurt Canada's exports, you wonder how that could be.

    Currencies are actively traded in the international marketplace, which means that exchange rates are changing all the time. As such, exchange rates rise and decline. A currency appreciates (or strengthens) relative to another currency when it is able to purchase more of that other currency than it could previously. A currency depreciates (or weakens) relative to another currency when it is able to purchase less of that other currency than it could previously. Take a look at two examples illustrating these concepts:

    • EXAMPLE 1: If \(C\$\)1 buys US$1.02 and the exchange rate rises to US$1.03, then your \(C\$\)1 purchases an additional penny of the US dollars. Therefore, the Canadian currency appreciates, or strengthens, relative to the US dollar.
    • EXAMPLE 2: Similarly, if the exchange rate drops to US$1.01, then your \(C\$\)1 purchases one less penny of the US dollars. Therefore, the Canadian currency depreciates, or weakens, relative to the US dollar.

    These concepts are particularly important to international business and global economies. Generally speaking, when a currency appreciates it has a positive effect on imports from the other country because it costs less money than it used to for domestic companies to purchase the same amount of products from the other country. However, the currency appreciation tends to also have a negative effect on exports to other countries because it costs the foreign companies more money to purchase the same amount of products from the domestic companies.

    Important Notes

    clipboard_e6ea93fadbd807bd45e9c4e6fa23b8414.png

    It is critical to observe that if currency A appreciates relative to currency B, then the opposite is true for currency B relative to currency A (currency B depreciates relative to currency A). The figure to the right illustrates this concept. Recalling Example 1 above, the Canadian currency appreciated, so the US currency depreciated. In Example 2, the Canadian currency depreciated, so the US currency appreciated.

    How It Works

    When you work with currency appreciation or depreciation, you still use the same basic steps as before. The additional skill you require in the first step is to adjust an exchange rate appropriately based on how it has appreciated or depreciated.

    Things To Watch Out For

    clipboard_ef10d505f31c575387ce027af9bed74b2.png

    It is very easy to confuse the two relative currencies, their values, and the concepts of appreciation and depreciation. For example, if the exchange rate increases between currency A relative to a unit of currency B, which exchange rate appreciated? If currency A has increased per unit of currency B, then it takes more money of currency A to buy one unit of currency B. As a result, currency B appreciates because a single unit of currency B can now buy more of currency A. For example, if the exchange rate is US$1.0218 relative to C$1 and it increases to US$1.0318 relative to C$1, then the Canadian dollar purchases one penny more. The figure helps you understand the relationships involved and provides a visual reminder of which direction everything is moving.

    Exercise \(\PageIndex{2}\): Give It Some Thought
    1. If the exchange rate in terms of US dollars per unit of euros increases, which currency weakened?
    2. If the Australian dollar weakens against the Canadian dollar, did the exchange rate increase or decrease in terms of Australian dollars per unit of Canadian dollars?
    3. If the exchange rate in terms of yen per unit of the Mexican pesos decreases, which currency weakened?
    4. If the British pound (£) appreciates against the US dollar, did the exchange rate increase or decrease in terms of pounds per unit of US dollars?
    Answer
    1. US dollars
    2. Increase
    3. Mexican pesos
    4. Decrease
    Example \(\PageIndex{3}\): Effects of Currency Appreciation

    A Canadian manufacturer requires parts from the United States. It purchases from its supplier in lots of 100,000 units at a price of US$7.25 per unit. Since the last time the manufacturer made a purchase, the Canadian dollar has appreciated 0.0178 from the previous mid-rate of US$1.0218 per C$. If the sell rate is 1.5% above the mid-rate, how have the manufacturer's costs changed?

    Solution

    Calculate the cost of the product both before and after the currency appreciation. The difference between the two numbers is the change in the manufacturer's costs.

    What You Already Know

    Step 1:

    The following purchase and exchange rates are known:

    Current Currency = Total Purchase = 100,000 × $7.25 = US$725,000

    Mid-Rate = 1.0218

    Sell Rate = 1.5% higher

    Canadian appreciation = 0.0178

    How You Will Get There

    Step 2:

    Calculate the old and new sell rates, factoring in the currency appreciation. Notice that the Current Currency is in US dollars but the sell rates are per Canadian dollar. You will need to invert the rates so that the exchange rate is expressed per US dollar to match the Current Currency.

    Step 3:

    Apply Formula 7.4 for each transaction.

    Step 4:

    Calculate the difference between the two numbers to determine the change in cost.

    Perform

    Step 2:

    Previous Sell Rate = 1.0218 × (1 + 0.015) = 1.0371 per \(C\$\)

    Previous Sell Rate \(=\dfrac{1}{1.0371}=0.9642\) per US$

    If the Canadian dollar has appreciated, it buys more US dollars per \(C\$\). Therefore,

    New Sell Rate = (1.0218 + 0.0178) × (1 + 0.015) = 1.0552 per C$

    New Sell Rate \(=\dfrac{1}{1.0552}=0.9477\) per US$

    Step 3:

    Previous \(C\$\) = 0.9642 × $725,000 = $699,045

    New \(C\$\) = 0.9477 × $725,000 = $687,082.50

    Step 4:

    Change in Cost = New \(C\$\) − Previous \(C\$\) = $687,082.50 − $699,045 = −$11,962.50

    The manufacturer has its input costs decrease by $11,962.50 since \(C\$\)1 now purchases more US$.

    Contributors and Attributions


    This page titled 7.3: Exchange Rates and Currency Exchange is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Jean-Paul Olivier via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.