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

a. The amount of dollars that you will receive if you use a forward hedge is $1,084,000

b. The expected amount of dollars that you will receive if you do not hedge and believe in purchasing power parity is $1,211,520

c. The amount of dollars that you will expect to receive if you use a currency put option hedge is $1,091,520

Step-by-step explanation:

a. In According to IRP, the forward premium on the peso should be (1.03)/(1.14) – 1 = –0.0965 or –9.65%

Therefore, the forward rate is: $0.10 × [1 + (–.0965)] = $0.09035.

To hedge 12 million pesos, we will receive $1,084,000

Therefore, the amount of dollars that you will receive if you use a forward hedge is $1,084,000

b. The expected percentage change in the Mexican peso according to PPP is: (1 + .05)/(1 + .04) – 1 = 0.96%. Thus, the peso’s spot rate is expected to be: $.10 × (1.0096) = $0.10096

We will receive 12 million × $0.10096 = $1,211,520

The expected amount of dollars that you will receive if you do not hedge and believe in purchasing power parity is $1,211,520

c. Since the expected spot rate is $0.10096 based on PPP, you could receive $0.10096 per unit when we receive the pesos.

This amount is higher than the exercise price, so we will sell the pesos at this rate rather than exercise the option. We will have paid a premium of $0.01 per unit, so we will receive $0.09096 per unit ($0.10096 – $0.01).

The receivables would convert to 12 million × $0.09096 = $1,091,520

The amount of dollars that you will expect to receive if you use a currency put option hedge is $1,091,520