Question

The USD/MXN spot FX is 18.91. You can borrow or deposit USD for one year at 2.36%. You can borrow or deposit MXN for one year at 8.12%. You get a 1-year FX forward quote from a bank of 20.75 USD/MXN. What is your gain/loss position in millions of USD if you borrow USD 100 mil., convert USD/MXN spot, lend MXN, and lock in your FX rate using the 1-year forward contract? Take to 4 decimals.

Answer 1

It is given that

Spot rate of home country USA, = S(h)= $ 18.91

Rate of interest of borrow or lend in USA= R(h)= 2.36%

Rate of interest of borrow or lend in MXN= R(f)= 8.12%

Forward rate of USD/MXN= F(h)=$ 20.75

Now, if we borrow $100 mill now, we will have to pay an interest of 2.36% foe one year .

So interest we have to pay after 1 year = 100*2.36%= $2.36mil

So we have to return principal and interest amounting to = 100+2.36= $102.36 mil

The money borrowed from USA is lend in Mexico

So the amount lend will be:

1 MXN= 18.91 USD, So 100 USD will be, = 100/18.91 = 5.2882 MXN

So we will lend 5.288 MXN now.

After one year

we will receive an interest on that money lend, which will be equal to,

=5.288*8.12%= 0.4294 MXN

Now, this money is paid back in USA for the money. The money received is 5.2882+0.4294= 5.7176 MXN.

Now as the future exchange rate is fixed by the borrower, it was set at $20.75/MXN, which means that 1 MXN= $20.75, this means that ,

For 5.7176 MXN, the total amount in USD currency will be = 5.7176*20.75= $118.64.

So the amount received from investing = $118.64 mil

And the amount to be paid back that was borrowed = $102.36 mil

So the gain from this transaction = 118.64-102.36= 16.28

So the total gain is $16.28 mil.