BFB Bank believes the New Zealand dollar will appreciate over the next five days

Question

BFB 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 .071 0.0739

New Zealand dollar (NZ$) 0.0508 .0725

BFB Bank has the capacity to borrow either NZ$10,000,000 or $4,700,000. If BFB Bank’s forecast if 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)?

Explanation / Answer

Solution:

BFB Borrow fund in US $ 4,700,000 at the rate of 7.39% and convert it into NZ$ at spot rate of $0.48

Therefore Total NZ$ acquired = $4,700,000 / $0.48 = 9,791,666.67 NZ $

Now bank will lend 9,791,666.67 NZ $ at 5.08% for 5 days

Then NZ$ bank will get after 5 days = 9,791,666.67 NZ $ + 9,791,666.67 NZ $ * 5.08%*5/365 = 9,798,480.59 NZ$

Now convert 9,798,480.59 NZ$ in US $ at $0.50 and he will receive amount in US $ = 9,798,480.59 NZ$ * 0.50 = $4,899,240.29

Now bank will repay loan with interest = $4,700,000 + $4,700,000 * 7.39%* 5/365 = $4,704,757.94

Dollar profit from speculation over 5 days = $4,899,240.29 - $4,704,757.94 = $194,482.35

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