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Blenman Corporation, based in the United States, arranged a 2-year , $1,000,000 loan to fund a project in Mexico. The loan is denominated in Mexican pesos, carries a 6.50% nominal rate, and requires equal semi-annual payments. The exchange rate at the time of the loan was 5.75 pesos per dollar, but it dropped to 5.10 pesos per dollar before the first payment came due. The loan was not hedged in the foreign exchange market. Thus, Blenman must convert U.S. funds to Mexican pesos to make its payments. If the exchange rate remains at 5.10 pesos per dollar through the end of the loan period, what effective annual interest rate will Blenman end up paying on the loan

Respuesta :

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Answer:

17.67%

Explanation:

Solution

Given that:

The Loan amount in USD = $1,000,000

The Loan is denominated in Mexican pesos.

The rate of exchange at the time of loan = 5.75 pesos per USD

Thus,

The Loan amount in Mexican pesos = 1000000 * 5.75 = 5,750,000 Mexican pesos

The Loan carries interest rate = 6.5%

Now,

The Loan duration = 2 years = 4 semiannual periods

The Loan to be repaid in Mexican pesos in 4 equal semiannual installments

So,

To get semiannual installments we will apply PMT function of excel:

Which is,

PMT (rate, nper, pv, fv, type)  = PMT(6.5%/2, 4, -5750000, 0, 0)

= 1556164.09 Mexican pesos

Thus,

The exchange rate dropped to 5.10 pesos per USD before  the first semiannual payment is due and  stays so till the end of loan period.

Then,

The Semiannual installment in USD = 1556164.09 / 5.10 = $305,130.2137

To get nominal semiannual rate (for USD amounts) we will use RATE function of excel:

The RATE(nper, pmt, pv, fv, type)

= RATE (4, 305130.2137, -1000000, 0,0)

= 8.477%

Effective annual rate = (1 + 8.477%) 2 - 1 = 17.67%

Therefore, the effective annual interest rate will Blenman end up paying on the loan is  17.67%

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