Appreciation, Depreciation, and Calculating the Rate of Change

Students often struggle with calculating Foreign Currency depreciation and appreciation rates. The concept itself is not particularly difficult, but many textbooks gloss over explaining why formulas work the way they do.

Understanding Appreciation and Depreciation

$1.00 = 7.07RMB

Depreciation occurs where the domestic currency begins to purchase less foreign currency in an exchange – you (an American) are able to buy fewer British Pounds with your $1 dollar bill than before.
Appreciation occurs where the domestic currency begins to purchase more foreign currency in an exchange – you (an American) are able to buy more British Pounds with your $1 dollar bill than before.

In the example above, $1.00 is able to purchase 7.07RMB. Reversing this to find what 1.00RMB can buy is a simple matter of reciprocals.

Reciprocal Exchange Rate Formula

In this example, where $1.00 is able to buy 7.07RMB . . . 1RMB will purchase $0.14.


Now consider a new situation: China and a neighboring country sign an agreement where the two countries will both use Chinese RMB for all business transactions between the two of them. The businesses who trade between China and this country suddenly find that they need more Chinese RMB to finish their transactions and the demand for RMB increases. As demand increases, RMB became slightly harder to get and each RMB increases in value. The American tourist unfortunately finds that he has to pay a little bit more $USD to the currency trader if he wants to get RMB for his next trip to Beijing.

January 1 → $1 will buy 7.08RMB
February 1 → $1 will buy 7.07RMB
March 1 → $1 will buy 7.06RMB

You will notice that $1 is purchasing decreasing amounts of RMB (7.08 → 7.07 →7.06) = depreciation.

The reverse can also be observed if you look at it from the perspective of a Chinese tourist buying dollars for a trip to New York:

  1. January 1 → 1RMB will buy $0.1412
  2. February 2 → 1RMB will buy $0.1414
  3. March 1 → 1RMB will buy $0.1416

One RMB is purchasing increasing amounts of USD (0.1412 → 0.1414 →0.1416) = appreciation.


If we were to reverse this, the opposite would be true.

  1. 7.06RMB per $1 → $0.1416 per 1RMB
  2. 7.07RMB per $1 → $0.1414 per 1RMB
  3. 7.08RMB per $1 → $0.1412 per 1RMB

Here the USD is appreciating and the RMB is depreciating.


Effects on the Economy

Changes in foreign exchange rates have substantial impact on the economy at all levels — corporate, investment, and national.

Translation Concerns

Companies buying or selling abroad can see an effect on their costs, revenue, and the value of their assets.

Consider an American company that has assets valued at 1millionRMB in China with an exchange rate of 7.07RMB/$. If they were to translate that money into USD immediately, they will find that they have $141,442.72 on their Balance Sheet. If they wait a few days and find the rate has changed to 7.08RMB/$ (RMB depreciated | USD appreciated), they will only have $141,242.94 on their Balance Sheet. That is a translation loss of $199.78 despite the fact that the company didn’t actually spend anything and the nature of their assets remains the same as before.

American companies who operate abroad but maintain financial records in USD or exchange money back into USD will benefit more from a depreciation of the USD.

Pricing and Costs

The pricing of exports and imports is also directly affected, significant for both final consumers and corporate purchasing departments.

Consider a Chinese store exporting Xiaomi phones at 3,999RMB each. Under the 7.07RMB/$ rate, American buyers would pay $565.63 each. If the RMB depreciates to a rate of 7.08RMB/$, American importer would pay $564.83 each. It’s small but the discount is there and sales are likely to increase.

Conversely, Apple is exporting iPhones at $3,999. At 7.07RMB/$, Chinese consumers would pay 28,272.93RMB. At 7.08RMB/$, they pay 28,312.92RMB. Apple will find that with the increase in prices at the Chinese stores, sales may begin to decline.

Depreciation generally benefits domestic exporters and foreign importers; while appreciation tends to benefit domestic importers and foreign exporters.

From a Chinese Perspective:

  • USD (Appreciate) / RMB (Depreciate) → Chinese Exports (Cheaper) / Chinese Imports (Expensive).
  • USD (Depreciate) / RMB (Appreciate) → Chinese Exports (Expensive) / Chinese Imports (Cheaper)

From an American Perspective:

  • USD (Appreciate) / RMB (Depreciate) → American Exports (Expensive) / American Imports (Cheaper).
  • USD (Depreciate) / RMB (Appreciate) → American Exports (Cheaper) / American Imports (Expensive)

For a standard international finance example, consider the following:

Nissan (Japanese) has purchased raw materials from a Mexican supplier for 1,000,000Pesos. Nissan now has account payables at 1,000,000Pesos. The Spot Exchange Rate (current) is 1JPY = 0.21MXN. The Forward Exchange Rate (in 90 days) is 1JPY = 0.32MXN. Is it more profitable for Nissan to exchange and pay the debt to Mexico now or to wait 90 days?

Investments

Dongfeng (China) currently has 1,000,000RMB they invested in a US bank 90 days ago. When they invested the money, the exchange rate was $1.00 = 7.06RMB. The rate of return is 4%. Today the exchange rate is $1.00 = 7.08RMB. What did Dongfeng expect to see in profits? What are their actual profits?

Step 1) Convert the original principal into USD to calculate what was invested. This requires a basic exchange formula.

Simple Exchange Rate Formula

Step 2) At 4% interest, what was the expected return at the original exchange rate?

Return on Investment at 7.06RMB / $1 rate

Step 3) At 4% interest, what is the actual return at the forward exchange rate?

Return on Investment at 7.08RMB/$1 rate

Step 4) Assess

The Chinese company was originally anticipating that it would receive 1,040,000.00RMB from its investment for a profit of 40,000RMB at the original exchange rate. After the USD appreciated and the RMB depreciated, the Chinese company actually received 1,042,946.16RMB. This is an increase in profits of 2,946.16RMB compared to the original expectations.

Those investing abroad tend to benefit more when the domestic currency depreciates and foreign currency appreciates.


Calculating the Rate of Change

The Facts:

  • CNY (China) | KRW (S. Korea)
  • March 1 → 1CNY = 1200KRW
  • March 5 → 1CNY = 1800KRW

Did the Korean Won appreciate or depreciate? By how much?

Go ahead. . . I’ll wait. . . .

Solution

Many students falsely assume the Korean Won appreciated by 50% since March 5 shows 600KRW more which is a 50% increase from March 1.

However, if you paid attention to the discussion above, you should know that this answer is wrong.

First, the KRW has depreciated. Although it seems there is more KRW, this actually means one Chinese RMB is buying more KRW. The RMB has increased in value (appreciated) and can buy more. When one currency appreciates, the other will depreciate; they are inversely related.

You can test your theory the same way we did before if you aren’t convinced.

  1. 1200KRW / 1 RMB → 0.0008RMB / 1 KRW
  2. 1800KRW / 1 RMB → 0.0006RMB / 1 KRW

Second, the rate of change isn’t 50%. You are probably familiar with the traditional percentage rate of change formula (%Δ).

Rate of Change for Currency A (where 1 A = ? Currency B)

If you go from 10Q to 11Q, the %Δ would be (11 – 10)/10 = 0.10 or 10%. Naturally:

So the KRW has changed by 50%. Right? What’s wrong with our answer?

What happened is the same issue that tricked us up before . . . just because we see 1200KRW and 1800KRW, we think this exchange rate is telling us about the Korea Won. It isn’t!

1200KRW is not now equal to 1800KRW . . . rather the RMB has changed. Before it could buy 1200KRW and now it can buy 1800KRW. This means that the RMB has changed 50%!

The simple way to find the rate of appreciation or depreciation is as follows:

1 Currency A = 1500 Currency B

1CNY = 1200KRW
1CNY = 1800KRW

RMB has increased (appreciated) by 50% . . . it can buy 50% more than before.

1KRW = 0.00083CNY
1KRW = 0.00056CNY

KRW has decreased (depreciated) by 32.5% – It would buy 32.5% less if you used it for RMB.

When the rate of change is positive = appreciation. When the rate of change is negative = depreciation.

It’s only when you translate the Korean Won into what RMB it can BUY that you will find the change in value. In this case. . . -32.5%.

Simplified Version

To find the exact rate of change, you must use the long versions and identify the reciprocal exchange rate to find the changing value of the KRW as shown above.

But most textbooks offer a shortcut that your professor may expect you to use.

See below:

1CNY = 1200KRW
1CNY = 1800KRW

RMB has increased (appreciated) by 50%.

1CNY = 1200KRW
1CNY = 1800KRW

KRW has decreased (depreciated) by 33%. This isn’t precisely correct (solution is -32.5%), but it’s close enough for many courses.

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