Final answer:
The present value of a 1.5 million Euro payment in USD, factoring in the spot and forward exchange rates as well as the risk-free rate, is calculated by first converting the future payment into USD at the forward rate, then discounting this amount to the present value at the given risk-free interest rate.
Step-by-step explanation:
The question is about calculating the present value of a future payment in a different currency, considering the spot exchange rate and the forward exchange rate.
Given the spot exchange rate of 1.0752 USD/EUR, a payment of 1.5 million Euros would be equivalent to 1,612,800 USD today. However, the payment is in the future, so we need to use the six-month forward exchange rate of 1.0853 USD/EUR. Consequently, the future payment would amount to 1,627,950 USD. To find the present value, we need to discount this future amount by using the given risk-free rate in USD (rᵐᵣD), which is 5.0%.
To discount the future payment, we can use the following formula for present value (PV):
PV = FV / (1 + r/n)^(nt)
Where:
- FV is the future value of the payment in USD
- r is the annual interest rate (risk-free rate in USD)
- n is the number of times that interest is compounded per year
- t is the time in years
In this case, assuming that the interest is compounded semi-annually (n = 2), the present value of the payment would be calculated as:
PV = 1,627,950 / (1 + 0.05/2)^(2*(1/2))
This equation will give the present value in USD that represents the current worth of a future payment of 1.5 million Euros using a 5.0% risk-free rate.