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Answer: $1.50
### Solution 1. **Convert the euro loan to U.S. dollars at inception** - €16.0 million × $1.10/€ = **$17.6 million** 2. **Determine the pound-denominated deposit amount** - The bank funds the loan with the equivalent amount in pounds: - £ amount = $17.6 million / $1.60 per £ = **£11.0 million** 3. **Compute end-of-year asset value in dollars** - Euro loan grows to €16.0 million × 1.07 = **€17.12 million** - Convert at end-of-year exchange rate $1.00/€: - Asset value = **$17.12 million** 4. **Compute end-of-year liability value in dollars** - Pound deposit grows to £11.0 million × 1.05 = **£11.55 million** - Let the end-of-year spot rate be **x** dollars per pound - Liability value = **11.55x million dollars** 5. **Set net interest margin equal to 2.0%** - Net interest income = Assets − Liabilities = 17.12 − 11.55x - NIM = Net interest income / earning assets - Use initial earning assets of $17.6 million: \[ \frac{17.12 - 11.55x}{17.6} = 0.02 \] \[ 17.12 - 11.55x = 0.352 \] \[ 11.55x = 16.768 \] \[ x \approx 1.45 \] 6. **Nearest answer** - **$1.50 per £1** ### Final Answer **B. $1.50**
Author: Manit Arora
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Q-502.1. Sun Bank USA purchased a 16.0 million one-year euro loan that pays 7.0% interest annually. The spot rate of U.S. dollars per euro is $1.10. Sun Bank has funded this loan by accepting a British pound-denominated deposit for the equivalent amount and maturity at an annual rate of 5.0%. The current spot rate of U.S. dollars per British pound is $1.60. At the end of the year, assume the euro depreciates such that the spot rate of U.S. dollars per euro falls to $1.00. Which is nearest to the required spot rate of U.S. dollars per British pound at the end of the year in order for the bank to earn a net interest margin of 2.0%? (Note: this is a variation on Saunders' Question #11)
A
$1.40 per £1; i.e., GPBUSD
B
$1.50
C
$1.60
D
$1.70
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