Question

Baylor Bank believes the New Zealand dollar will appreciate over the next five days from $.48 to $.50. The following annual interest rates apply:
Currency Lending Rate Borrowing Rate
Dollars 7.00% 7.50%
New Zealand dollar (NZ$) 6.75% 7.25%
Baylor Bank has the capacity to borrow either NZ$10 million or $5 million.
If Baylor Bank's forecast is correct, what will its dollar profit be from speculation over the five-day period (assuming it does not use any of its existing consumer deposits to capitalize on its expectations)?

Answer 1

Answer:

Its dollar profit from speculation over the five-day period will be $208,035.93.

Explanation:

This can be determined as follows:

Assuming Baylor Bank borrow $5,000,000

The borrowing will be converted to New Zealand dollar at the current exchange rate and we will have:

Conversion = $5,000,000 / 0.48 = NZ$10,416,667

The NZ$10,416,667 shall be invested at an annualized based on  New Zealand lending rate of 6.75% over five days. This will produce future value (FV) as follows:

FV of investment = Amount invested * (1 + NZ lending rate)^(5 years / 360 days) = NZ$10,416,667 * (1 + 6.75%)^(5 / 360) = NZ$10,426,121.44

Converting the NZ$10,426,121.44 to dollar at the new rate of $.50 as follows:

New conversion = NZ$10,426,121.44 * $.05 = $5,213,060.72

Amount to repay based on the US borrowing rate = Amount borrowed in USD * (1 + US borrowing rate)^(5 years / 360 days) = $5,000,000 * (1 + 7.5%)^(5 / 360) = $5,000,000 * 1.00100495826555 = $5,005,024.79

Profit = New conversion - Amount to repay = $5,213,060.72 - $5,005,024.79 = $208,035.93

Therefore, its dollar profit from speculation over the five-day period will be $208,035.93.