Question

Sun Bank USA has purchased a 16 million one-year Australian
dollar loan that pays 12 percent interest annually. The spot rate
of U.S. dollars for Australian dollars (AUD/USD) is $0.757/A$1. It
has funded this loan by accepting a British pound (BP)–denominated
deposit for the equivalent amount and maturity at an annual rate of
10 percent. The current spot rate of U.S. dollars for British
pounds (GBP/USD) is $1.320/£1. (LG 9-5)

What is the net interest income earned in dollars on this
one-year transaction if the spot rate of U.S. dollars for
Australian dollars and U.S. dollars for BPs at the end of the year
are $0.715/A$1 and $1.520/£1, respectively?

What should the spot rate of U.S. dollars for BPs be at the
end of the year in order for the bank to earn a net interest income
of $200,000 (disregarding any change in principal values)?

Answer #1

a)

Loan amount = $16,000,000 * 0.757 = $12,112,000

Deposit amount = $12,112,000/ 1.320 = $9,175,757.58

Interest Income at end of year (EOY) = ($16,000,000 * 0.12 ) * 0.757 = 1,920,000 * 0.757 = $1,453,440

Interest expense at EOY =( $9,175,757.58 * 0.10) * 1.520 = $917,575.76 * 1.520 = $1,394,715.15

Net interest income = $1,454,440 - $1,394,715.15 = $59,724.85

b)

Cost of deposits should be = ($1,453,440 - $200,000)/ $917,575.76 = $1,253,440 / $917,575.76 = 1.366.

So the bank earns $200,000 they need to have a BPs of $1.366

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