Question

You believe that IRP presently exists. The nominal annual interest rate in Mexico is 14%. The nominal annual interest rate in the U.S. is 3%. You expect that annual inflation will be about 4% in Mexico and 5% in the U.S. The spot rate of the Mexican peso is $.10. Put options on pesos are available with a one-year expiration date, an exercise price of $.108, and a premium of $0.01 per unit. You will receive 12 million pesos in one year.

a). Determine the amount of dollars that you will receive if you use a forward hedge.

b). Determine the expected amount of dollars that you will receive if you do not hedge and believe in purchasing power parity (PPP).

c). Determine the amount of dollars that you will expect to receive if you use a currency put option hedge. Account for the premium you would pay on the put option.

Answer 1

Mexico interest rate = 14%

U.S. interest rate = 3%

Mexico inflation rate = 4%

U.S. inflation rate = 5%

Mexico spot rate = $0.10

Expiration = 1 year

Exercise price = $0.108

Premium = $.01 per unit

Amount receive = 12,000,000 peso

Calculation:

a.

Forward rate (1 year) = Mexico spot rate × (1 + U.S. interest rate / 1 + Mexico interest rate)

Forward rate (1 year) = 0.10 × (1 + 3% / 1 + 14%)

Forward rate (1 year) = 0.10 × (1 + 0.03 / 1 + 0.14)

Forward rate (1 year) = 0.10 × 1.03 / 1.14

Forward rate (1 year) = 0.0904 $/Mexican peso

Expected amount received in dollar = Amount receive * Forward rate (1 year)

Expected amount received in dollar = 12,000,000 * 0.0904

Expected amount received in dollar = $10,84,800

b.

Expected spot rate after 1 year = Mexico spot rate × (1 + U.S. inflation rate / 1 + Mexico inflation rate)

Expected spot rate after 1 year = 0.10 × (1 + 5% / 1 + 4%)

Expected spot rate after 1 year = 0.10 × (1 + 0.05 / 1 + 0.04)

Expected spot rate after 1 year = 0.10 × 1.05 /1.04

Expected spot rate after 1 year = 0.1009 $/Mexican peso

Expected amount received in dollar = Amount receive * Expected spot rate after 1 year

Expected amount received in dollar = 12,000,000 * 0.1009

Expected amount received in dollar = $12,10,800

c.

Proceeds received per peso net of premium = Expected spot rate after 1 year - Exercise price

Proceeds received per peso net of premium = 0.1009 - 0.01

Proceeds received per peso net of premium = $0.0909

Total cash received = Amount receive * Proceeds received per peso net of premium

Total cash received = 12,000,000 * 0.0909

Total cash received = $1090800