# Decrease in purchasing power due to FX currency depreciation and inflation

If the annual U.S. inflation rate is expected to be 3%, and the Indian rupee is expected to depreciate against the U.S. dollar by 12%, a Indian firm importing from its U.S. parent can expect the rupee
costs of imports denominated in dollars to increase by what percentage ?

The answer is increase by about 17%. Please explain in detail the calculation and the “why” behind the calculations.

While importing, the importer pays in usd. If the inr depreciates by 12 % , that would imply the usd appreciated by 100/88 = 13.46 %. Hence the importer will be paying (1.136 x 1.03) -1 = 17 % more

According to my calculations depreciation of INR by 12% would mean appreciation of USD by 10.71. Here is the calculation…

Direct quote in India

Let

OLD 1 USD = 100 INR

NEW 1 USD = 112 INR

INR depreciation % = (100-112) / 100= -12%

Above FX rate are converted to Direct quote in USA

1 INR = 1/100 USD = 0.01 USD

NEW 1 INR = 1/112 USD = 0.008928571 USD

USD appreciation % = (0.01 – 0.008928571)/ 0.01 = 10.71%

Request you to please revert on this. Thanks

That’s not what 12% depreciation means.

Twelve percent depreciation means that rupees now buy 12% less than they used to buy:

• Old: 1 USD = 100 INR
• New: 0.88 USD = 100 INR

Calculatorsuoup dot com

I had selected base currency as USD and quote currency as INR.
The exchange rate I had put was 100 and 88 as you mentioned.
After clicking calculate button I got below answer:

Relative to USD, INR Appreciated 13.636%

Relative to INR, USD Depreciated 12%

Other way round: INR depreciated 12% vis-à-vis USD; USD appreciated 13.6364% vis-à-vis INR.

Got it. It is clear now. Thanks to you both - S2000magician and HerbsDelite.

I just have one more query regarding my initial question posted.

The question tells us that there is appreciation / depreciation of exchange rates and then about the inflation rate in one country.

The exchange rate changes due to many factors including inflation. So, my question is why should we consider / factor in separately inflation again to answer the question. Cannot we just assume that the change in exchange rate has already considered inflation. I believe it is a reasonable assumption.

Thanks

Because US inflation affects two things:

• the USD/INR exchange rate
• the USD price of goods

If you look at this from the viewpoint of PPP its falrly clear:

USD/INR_{today}\frac{1 + inf_{USD}}{1 + inf_{INR}} = USD/INR_{future} = \left(0.88\right)USD/INR_{today}
\frac{1.03}{1 + inf_{INR}} = 0.88
1 + inf_{INR} = \frac{1.03}{0.88} = 1.1705
inf_{INR} = 1,1708 - 1 = 0.1708 = 17.08\%

Thanks again.

Can you tell me why depreciation of one currency in percentage terms will not be equal to appreciation of counter currency in percentage terms without discussing the formula. I am aware of formula for calculating appreciation / depreciation of currency but not able to comprehend why the percentages do not remain same.

\frac{1}{1 + x} ≠ 1 - x

For example, suppose the last year an exchange rate was A/B 2.00 (i.e., A 2.00 = B 1.00), but today the rate is A/B 4.00 (i.e., A 4.00 = B 1.00). Currency A has depreciated 50% vis-à-vis currency B (last year A 1.00 bought B 0.50, while this year it buys only B 0.25, while currency B has appreciated 100% vis-à-vis currency A (last year B 1.00 bought A 2.00, while this year it buys A 4.00),

Thanks for the explanation.

It is clear now.

My pleasure.

Good to hear.

When a currency appreciation percentage or depreciation percentage is known, can we easily calculate the appreciation percentage or depreciation percentage of counter currency using BA II Plus calculator? If so, how?

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Yes you can. For example if the question asks what the appreciation of the USD is versus the Euro given the old exchange rate of 1.1 EUR/USD and new exchange rate of 1.2 EUR/USD, you calculate it as:

(1.2/1.1) - 1 = 9.09%

If you want to calculate the depreciation of the Euro versus the dollar, just take the inverse:

(1/1.2)/(1/1.1) - 1 = negative 8.33% (8.33% depreciation)

to calculate 1/1.2 or 1/1.1 easily on the calculator just enter 1.2 or 1.1 then hit the [1/X] key

They will almost certainly give you the underlying exchange rate movement as part of the problem. If they don’t then you can insert simple proxy numbers to get the percentage appreciation/depreciation, and then run the formulas above using those proxy numbers. For example if they say currency X appreciated 10 percent versus currency Y, use (1.1/1) - 1 as the proxy numbers. To then calculate the depreciation of currency Y you’d use (1/1.1)/(1/1) -1 = 9.09% depreciation.

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Do it in steps. If A appreciates 10% vis-à-vis B, then:

1 + 10\% = 1.1
\frac{1}{1.1} = 0.909091
0.909091 - 1 = -0.090909 = -9.0909\%

So, B depreciates 9.0909% vis-à-vis A.

If A depreciates 10% vis-à-vis B, then:

1 - 10\% = 0.9
\frac{1}{0.9} = 1.111111
1.111111 - 1 = 0.111111 = 11.1111\%

So, B appreciates 11.1111% vis-à-vis A.

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Thank you very much

Thank you so much

The rate of increase in YTM will not be same as rate of decrease in bond value. Is logic for this somewhat similar to the explanation you have provided for statement - An appreciation rate of a currency will not be same as depreciation rate of counter currency?

If logic is slightly different , please let me know how it is different.

Thanks