Question

While in Mexico, you buy a lottery ticket and win. The award is 5 annual payments of MXN 1,000,000 with the first payment made today.

The APR interest rate for 4 years of future MXN cash flows is 6% and for USD cash flows is 2%.

The exchange rate today is MXN19.6/USD. What is the value today of your winnings in terms of USD? Show the result taking the present value (PV) in both currencies (hint: determine expected exchange rates for next 5 years to convert MXN payments into USD).

Answer 1

Expected exchange rate after n years = exchange rate today * [(1 + MXN rate / 1 + USD rate)]ⁿ

Expected exchange rate after 1 year = 19.6 * [(1 + 0.06) / (1 + 0.02)]¹ = 20.37

Expected exchange rate after 2 years = 19.6 * [(1 + 0.06) / (1 + 0.02)]² = 21.17

Expected exchange rate after 3 years = 19.6 * [(1 + 0.06) / (1 + 0.02)]³ = 22.00

Expected exchange rate after 4 years = 19.6 * [(1 + 0.06) / (1 + 0.02)]⁴ = 22.86