You believe that IRP presently exists. The nominal annual interest rate in Mexic

Question

You believe that IRP presently exists. The nominal annual interest rate in Mexico is 14 percent. The nominal annual interest rate in the United States is 3 percent. You expect that annual inflation will be about 4 percent in Mexico and 5 percent in the United States. The spot rate of the Mexican peso is $.10. Put options on pesos are available with a 1-year expiration date, an exercise price of $.1008, and a premium of $.014 per unit. YOU WILL RECEIVE 1 MILLION PESOS IN 1 YEAR.

a. Determine the expected 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 believe in PPP and use a currency put option hedge. Account for the premium you would pay on the put option.

Explanation / Answer

a. According to IRP, the forward premium on the peso should be (1.03)/(1.14) – 1 = –.0965 or –9.65%

Thus, the forward rate is: $.10 × [1 + (–.0965)] = $.09035.

To hedge 1 million pesos, we will receive $90,350

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) = $.10096

We will receive 1,000,000 × $.10096 = $100,960

c.  Since the expected spot rate is $.10096 based on PPP, you could receive $.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 $.0014 per unit, so we will receive $.09956 per unit ($.10096 – $.0014).

The receivables would convert to 1,000,000 × $.09956 = $99,560

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