Appreciation, Depreciation, and Calculating the Rate of Change

Students often struggle with the calculation of Foreign Currency depreciation and appreciation rates. Not because the concept is difficult, but because many textbooks gloss over the discussion of why formulas are what they are.

Understanding Appreciation and Depreciation

$1.00 = 7.07RMB

Depreciation occurs where the domestic currency purchases less foreign currency in an exchange.
Appreciation occurs where the domestic currency purchases more foreign currency in an exchange.

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

One USD is purchasing decreasing amounts of RMB (7.08 → 7.07 →7.06) = depreciation. 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/$ → $0.1416/RMB
  2. 7.07RMB/$ → $0.1414/RMB
  3. 7.08RMB/$ → $0.1412/RMB

Here the USD is appreciating and the RMB is depreciating.

Affects 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/$. When translated into domestic US dollars, that is a value of $141,442.72 in assets for their Balance Sheet. On Day 2, the rate changes to 7.08RMB/$ → now asset value has dropped to $141,242.94. That is a translation loss of $199.78 although the company did nothing and the nature of their assets remains the same as before.

Foreign companies in China benefit more from an appreciation of the RMB than a depreciation when translating their assets or profits into their domestic currencies.

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 importers 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.

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 is 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?

Return on Investment at 7.06RMB / $1 rate

Step 3) At 4% interest, what is the actual return

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 if 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 increate in profits of 2,946.16 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). 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%.

1KRW = 0.00083CNY
1KRW = 0.00056CNY

KRW has decreased (depreciated) by 32.5%

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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