An Australian company exports products to New Zealand. Typically, it takes T days for an invoice to be paid in NZD. The invoice is worth F NZD, and the exchange rate at time t is X(t).

(a) How much will the company receive in AUD when the invoice is paid at time T?

(b) The company wishes to mediate risk by purchasing either a call or a put option on the exchange rate, at strike rate k (and face value F). How much will the company receive in AUD at time T if they purchase a call? Consider two cases, depending on the relative values of k and X(T) (i.e., X(T) > k and X(T) < k).

(c) How much will the company receive in AUD at time T if instead they purchase a put? Consider two cases, depending on the relative values of k and X(T) (i.e., X(T) > k and X(T) < k).

(d) Which option should the company purchase to mediate the risk of a strengthening Australian dollar?