Denim Industries can borrow its needed financing for expansion using one of two

Question

Denim Industries can borrow its needed financing for expansion using one of two foreign lending facilities. It can borrow at a nominal annual interest rate of

88%

in Mexican pesos or it can borrow at

55%

in Canadian dollars. If the peso is expected to depreciate by

11.9511.95%

and the Canadian dollar is expected to appreciate by

66%,

which loan has the lower effective annual interest rate?

The effective annual interest rate of the loan in Mexican pesos is

nothing%.

(Round to two decimal places.)

Explanation / Answer

One can borrow at Nominal annual interest rate of 88% in Mexican Pesos or it can borrow at 55% in Canadian dollars

if the peso is expected to depreciate by 11.95% and the Canadian dollar is expected to appreciate by 66%

Suppose one borrows 1000 Mexican pesos at 88% annual interest rate, then at t=0 , one will have 1000 Mexican pesos for which one would need to pay interest and principal combined at the end of one year of 880+1000=1880

now if peso is expected to depreciate by 11.95%, then the value of liability of 1880 committed today will get reduced to 1880*(1-11.95%)= 1,655.34 Pesos, so effective cost = (1655.34-1000)/1000=0.6553=65.53%

Suppose one borrows 1000 Canadian dollars at 55% annual interest rate, then at t=0 , one will have 1000 Canadian dollars for which one would need to pay interest and principal combined at the end of one year of 550+1000=1550

now if canadian dollar is expected to appreciate by 66%, then the value of liability of 1550 committed today will get increased to 1550*(1+66%)=2573 Canadian Dollars , so effective cost = (2573- 1000)/1000=1.573=157.3%

Therefore,Mexican pesos has the lower effective annual interest rate of 65.53%

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