Question

A U.S.-based company, Stewart, Inc., arranged a 2-year, $1,000,000 loan to fund a project in Mexico. The loan is denominated in Mexican pesos, carries a 10.0% nominal rate, and requires equal semiannual 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, Stewart 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 interest rate will Stewart end up paying on the loan? Select one: a. 10.36% b. 11.50% c. 17.44% d. 20.00% e. 21.79%

Answer 1

Answer:

$PMT = \frac{0.05*5750000}{1-(1+0.05)^{-2*2}}= 1621568.037 MP$

So then we need 1621568.037 Mexican pesos in order to pay each payment date.

Using the exchange rate of 5.75 pesos/ $US we can convert the amount to USD and we got:

$1621568.037 MP *\frac{1 USD}{5.75 MP}= 282011.83 USD$

But using the other exchange rate provided of 5.1 MP/ USD the cost would be:

$1621568.037 MP *\frac{1 USD}{5.1 MP}= 317954.52 USD$

We can calculate the annal nominal rate and we got using n =4 and PV =1000000, PMT = 317954.52 and we got

$In = 10.36*2 =20.72\%$

And then we can calculate the effective annual rate and we got:

$ER= (1+ \frac{in}{m})^m -1$

And replacing we got:

$ER= (1+ \frac{0.2072}{2})^2 -1 =0.2179 = 21.79\%$

So then the final answer for this case would be:

e. 21.79 %

Explanation:

For this case we can begin calculating the monthly payments in Mexican pesos with the following formula:

$PMT = \frac{i* PV}{1-(1+i)^{-nt}}$

For this case we have this:

$PV = 1000000*5.75 = 5750000$ represent the presnt value in Mexiacn pesos

$i = \frac{0.1}{2}=0.05$ since is semiannual

n= 2 number of times that the interest is compounded in a year

t =2 represent the number of years

And replacing we have this:

$PMT = \frac{0.05*5750000}{1-(1+0.05)^{-2*2}}= 1621568.037 MP$

So then we need 1621568.037 Mexican pesos in order to pay each payment date.

Using the exchange rate of 5.75 pesos/ $US we can convert the amount to USD and we got:

$1621568.037 MP *\frac{1 USD}{5.75 MP}= 282011.83 USD$

But using the other exchange rate provided of 5.1 MP/ USD the cost would be:

$1621568.037 MP *\frac{1 USD}{5.1 MP}= 317954.52 USD$

We can calculate the annal nominal rate and we got using n =4 and PV =1000000, PMT = 317954.52 and we got

$In = 10.36*2 =20.72\%$

And then we can calculate the effective annual rate and we got:

$ER= (1+ \frac{in}{m})^m -1$

And replacing we got:

$ER= (1+ \frac{0.2072}{2})^2 -1 =0.2179 = 21.79\%$

So then the final answer for this case would be:

e. 21.79 %