Question

# Sun Bank USA has purchased a 16 million one-year Australian dollar loan that pays 12 percent...

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)?

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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