Managing Multinational Cash Flows Evaluating Interest Rates in Foreign Currency Fernando Arellano, Ph.D. Graduate School of Management University of Dallas.

Managing Multinational Cash Flows

Evaluating Interest Rates in Foreign Currency

Fernando Arellano, Ph.D.

Graduate School of Management

University of Dallas

2

• Your firm has operations abroad. The subsidiary borrows money from local and US banks in foreign currency and in US$.

• The local treasurer is analyzing two loans. In one, the currency is local and the interest rate is 17.5%. In the other, the currency is US dollars and the interest rate is 9%.

• The term is one year.

• What should the decision be?


3

• Before doing the analysis we need to understand devaluation and how changes in exchange rates cause depreciation and appreciation of one currency with respect to to another currency.


4

• Devaluation is the official act of reducing the rate at which one currency is exchanged for another in international currency markets. Devaluations are sometimes dramatic.

• When the exchange rate is allowed to change due to market forces, changes are usually gradual, and the decline in value is called depreciation instead of devaluation.

Understanding Devaluation

5

• Many times these terms devaluation and depreciation are used interchangeably.

• When one currency gains value with respect to the other, then this currency has appreciated or revaluated with respect to the other.

• When one currency loses value with respect to the other, then this currency has depreciated or devaluated with respect to the other.


6

• Let’s assume that the exchange rate between a foreign currency (FC) and the US$ is 3 units of the FC for each each unit of US$.

• We express this as: FC$3.00 / US$

• Let’s assume further that after one year, the exchange rate is FC$3.30/US$

• You can see that the US$ costs more now. It has appreciated with the respect to the FC.

• If the US$ costs more, the FC costs less.


7

• If the US$ costs more it has appreciated with repect to the FC.

• Consequently, the FC has depreciated with respect to the US$.

• What was the depreciation of the foreign currency with respect to the US dollar?

• You may be inclined to answer 10%.


8

• It is not 10%, but it is close to 10%.

• Let’s analize why it is not 10%.

• An exchange rate of FC$3/US$ means that each dollar has a value of FC$3.

• If the exchange rate changes to FC$3.30, what has changed in value?

• The dollar or the foreign currency?

• Answer: the dollar. Before, its price was FC$3, now it is FC$3.30.


9

• This change is positive. It means that the US$ has appreciated. By how much?

• From 3 to 3.30 the change is 10%.

• So the appreciation of the US$ is 10%.

• The foreign curreny has lost value, it has depreciated. By how much?

• We need to know the value or price of the foreign currency before the change.

• The value of the USD was FC$3.00.


10

• The value of the FC$ is then 1 / 3 = US$ 0.3333333.

• The value of currency A in terms of currency B is the reciprocal of the value of currency B with respect to currency A.

• After the depreciation, if the value of US$1.00 in terms of FC$ is FC$3.30, the value of FC$1.00 in terms of US$ is US$ 0.303030.


11

• The FC has lost value: it went from US$ 0.333 to US$ 0.303 .

• With these two exchange rates we can estimate the change in value of the foreign currency in percentage terms.


valueinitial

valueinitialvalueendingvalue

%

12

• The change in value of the foreign currency was –9.09%.

• It can be said that the depreciation of the foreign currency was 9.09%


%090909.9333333.0

333333.030303.0value%

13

• It would have been a devaluation if the change in value (or the new exchange rate) was decided by the foreign country’s government or central bank.


14

• In the case of the change in value of the US dollar, the operation is as follows:

%1000.3

00.330.3%

value

• The change in value has a positive sign implying that the USD has appreciated.


15

• In conclusion, when the exchange rate goes from FC$3 to FC$3.30, the US$ has appreciated (gained value) by 10% and the foreign currency has depreciated (lost value) by 9.09%.


16

• If there is no information about the exchange rates, the devaluation (depreciation) can be estimated from the revaluation (appreciation):

• d is devaluation, r is revaluation:r

rd

1

• Revaluation can also be estimated from devaluation:

rd

d

1


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• The previous formulas are derived from the equation that establishes the relationship between revaluation and devaluation:

( ) ( )1 1 1 r d


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• Calculate the revaluation of the US$ with respect to a foreign currency if the exchange rate went from FC$3/US$ to $6/US$.

Answer: 100%

• Calculate now the devaluation of the foreign currency.

Answer: 50%


19

• Calculate the revaluation of the USD with respect to a foreign currency if the exchange rate went from FC$3 to FC$3.10/US$

Answer: 3.33%

• Calculate now the devaluation of the foreign currency.

Answer: 3.23%


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• From the equations and from the last two results it can be concluded that:

• Devaluation is always less than revaluation.

• When the devaluation and revaluation rates are low, the difference between d and r is minimal.


21

• Accumulated devaluation can be estimated with the following equation:

1)1(....)1)(1)(1( 321 naccum ddddd

where:

daccum = accumulated devaluation rate

dn = devaluation rate for period nn = number of periods


22

• The accumulated devaluation can be estimated as an effective interest rate if the periodic devaluations are equal. Note the sign.

1)1( naccum dd

where:daccum = accumulated devaluation rated = devaluation rate for the periodn = number of periods


23

• Calculate the accumulated annual devaluation that corresponds to a monthly devaluation of 1%.

1)01.01( naccumd

%36.111136.0 accumd

• The accumulated devaluation has been 11.36%

• The change in value has been -11.36%


24

• Note the difference with an interest rate of 1% per month. The accumulated (effective) interest would have been:

1)01.01(i neffective

%68.121268.0ieffective


25

• Now that we have a clear concept of devaluation (depreciation) and how to estimate it, let’s go back to our original problem.

• Should the company borrow in USD paying 9% as interest rate or in the foreign currency paying 17.5%?

Borrow in Dollars or in a Foreign Currency?

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• Does it depend on the inflation rate of one or both currencies?

• On the devaluation (or depreciation) of one currency with respect to the other?

• On both?• Assume 8% depreciation of the FC with respect to

the USD.• Assume 10% inflation in the foreign country and

3% in the U.S.


27

• Let’s say that we have US$100 and that the exchange rate of the Peruvian sol (sun) with respect to the US$ is S/.3.00 / US$.

USD100

at 9% annual USD109

at FC$ 3.00/US

FC$ 300 at 17.5% anual

US$108.10

8% devaluation at FC$ 3.26087/USD

FC$ 352.50

vs

And now what?

Soles are converted back to dollars and compared to USD109


After one year

After one year

After one year

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• According to the previous analysis the interest rate is higher when you borrow in USD.

• Conclusion: an interest rate of 17.5% in Peruvian soles is better than an interest rate of 9% in USD.

• . . . . . when the annual devaluation is 8%• . . . . . and when the exchange rate to purchase the

currency is the same exchange rate to sell it. No transaction costs.

• Transactions costs are about 1% of the transaction amount.


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• So, do we need information on inflation and devaluation?


30

• In the previous problem, the loan (principal plus interest) in US$ became US$109.

• The loan in soles became the equivalent of US$108.10.

• In US$ the interest rate is 9%.

• In soles, we can say that the equivalent interest rate in US$ is 8.1%.

• 8.1% is the equivalent interest rate in US$ of a loan in Peruvian soles


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• The equivalent rate in USD allows us to make direct comparisons between rates in US$ and in other currencies.

• I.e.,the loan in Peruvian soles was cheaper than the loan in USD (8.1% vs 9%)

• To estimate an equivalent interest rate we need information (actual or expected) on depreciation or apreciation of one of the currencies with respect to the other.


32

• The equivalent interest rate can be computed using the following formula:

1)%1()1(/

FCUSDFCeUSD

valueii

where:

ieUS$ = equivalent interest rate in USD

iFC = interest rate in the foreign currency

% value = change in value in % of the foreign currency w/respect to the USD


33

• With the previous formula you don’t need information on amounts, just the interest rate in the foreign currency and the expected devaluation.

• When the foreign currency loses value with respect to the USD, the change in value carries a negative sign.


34

• Solve the previous problem using the formula:

1)08.01()175.01( eUSDi

• Have in mind that the change in value (depreciation) has a negative sign.

• One important conclusion: the higher the depreciation, the lower the interest rate (in terms of USD) in Peruvian soles becomes.

%10.8081.0 eUSDi


35

• If the depreciation were higher, which loan would be cheaper?

• As depreciation of the Peruvian sol increases, a loan in Peruvian soles becomes cheaper.

• When expectations of devaluation builds up it is not easy to get loans in Peruvian soles.

• In fact, because of the devaluation history of the Peruvian sol, nowadays, 80% of the loans are made in USD.


36

• At what devaluation rate would the two interest rates be the same?

• In other words, what annual depreciation makes the 17.5% in Peruvian soles the same as the 9% in USD?


37

US$100

FC$ 3.00/USD

FC$ 300

FC$ 3.233945/USD

USD109at 9% annual

at 17.5% annual FC$ 352.50


What exchange rate makes the two amounts equivalent?

What depreciation rate results in this exchange rate?

7.2340% deprec.

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• What would your decision be if you expect a devaluation of 7.2340%?

• Would you borrow in Peruvian soles or USD?

• In theory you should be indifferent.

• In practice, if the uncertainty is very high (low international reserves), you would prefer to borrow in Peruvian soles.


39

• The equation presented before can be used to estimate the annual depreciation rate that makes both interest rates equivalent.

1)1()1(

%/

FC

USD

FCUSD ii

valuechange

• FC/US$ refers to the change in value of the FC with respect to the USD.

• If the result is negative, it will mean depreciation.


40

• So now you know why an interest rate in a forreign currency may be higher than in US$.

• Because of depreciation of the foreign currency w/respect to the USD.

• Why is there depreciation?

• Because inflation in the foreign country is higher than in the U.S.

• However, after adjusting for depreciation, that interest rate may in fact be lower.


41

• In the long run interest rates in different currencies tend to be equivalent.

• In the short run there can be temporary disequilibriums that may cause loans in certain currency to be cheaper than in another currency.


42

• The equation presented before is derived from the equation proposed by the Interest Rate Parity Theory.

• “The interest rate parity holds that investors should earn the same return on security investments in all countries after adjusting for risk” Financial Management. Brigham and Daves.


43

• Another way to look at the interest rate parity equation:

• “In two different economies, the difference between interest rates for instruments of the same term and risk is related to the expected change between the values of both currencies (excluding transaction costs).”

• Source: Short-term Financial Management, Maness and Zietlow


44

• Should you try to obtain a loan in a hard currency (subject to continuous appreciation) or in a soft currency (subject to continuous depreciation)?

• If you receive hard currency as revenue, then it doesn’t matter. Do the analysis presented above and evaluate the certainty of the expected depreciation rate.

• If you receive soft currency as revenue and the future devaluation rate is uncertain, try to get a loan in soft currency. You avoid the risk of having to pay back the loan using more soft currency than anticipated because of a sudden devaluation.


45

• In the previous case, if you have to get a loan in hard currency, you can avoid the effect of a devaluation using forward contracts.

• Future contracts for exchange rates exist for few currencies, mainly hard currencies. Mexican pesos are an exception.


Managing Multinational Cash Flows Evaluating Interest Rates in Foreign Currency Fernando Arellano, Ph.D. Graduate School of Management University of Dallas.

Documents

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