An FI has purchased (borrowed) a one-year $10 million Eurodollar deposit at an annual interest rate of 6 percent. It has invested these proceeds in one-year Euro (€) bonds at an annual rate of 6.5 percent after converting them at the current spot rate of €1.75/$. Both interest and principal are paid at the end of the year. What is the spread earned by the bank if the end-of-year exchange rate is €1.77/$?

Question

BlackTom AI · Accepted Answer

Convert the dollar borrowing into euros, apply the euro interest, then convert back to dollars and compare to the dollar obligation.

Relevant concepts:
- Currency conversion: initial euros = dollars × spot rate (€/ $).
- Euro investment grows by (1 + i_euro).
- At year end convert euros back to dollars using the new €/$ rate: dollars_received = euros_end / S1 (or equivalently multiply by S0/S1).
- Spread = final dollar value net of cost of funds (compare final dollar amount to the dollar repayment owed).

Step-by-step calculations:
1) Borrow $10,000,000 at 6% → amount owed at year end = $10,000,000 × (1 + 0.06) = $10,600,000.
2) Convert $10,000,000 into euros at the initial spot S0 = €1.75/$:
   euros_invested = $10,000,000 × 1.75 = €17,500,000.
3) Invest at 6.5% for one year → euros at year end:
   euros_end = €17,500,000 × (1 + 0.065) = €17,500,000 × 1.065 = €18,637,500.
4) Convert euros back to dollars at S1 = €1.77/$ (i.e., $ per euro = 1/1.77):
   dollars_received = €18,637,500 / 1.77 = $10,532,203.39 (intermediate).
5) Net dollar profit (loss) = dollars_received − amount owed = $10,532,203.39 − $10,600,000 = −$67,796.61.
6) Express as a percentage of the $10,000,000 principal: spread = (−$67,796.61 / $10,000,000) × 100% = −0.6779661% ≈ −0.68%, which rounded to the answer choices is −0.70%.

Why this is correct:
- The euro investment earned 0.5 percentage points more in interest (6.5% vs 6.0%), but the euro depreciated against the dollar (S rose from 1.75 to 1.77 €/$), so when converting back the bank lost value; the combined effect yields a small net loss of about 0.68 percentage points.
Why other choices are incorrect:
- a. −1.00% is too negative (overstates the FX loss or double-counts effects).
- c. −0.25% and e. +0.20% are too small (they ignore the full FX depreciation impact).
- d. 0.00% would require exact offset of interest differential and FX movement; here they do not offset.

Conclusion: The spread is approximately −0.68%, which corresponds to choice b. −0.70 percent.

类似问题

A project has a required return of 12.6 percent, an initial cash outflow of $42,100, and cash inflows of $16,500 in Year 1, $11,700 in Year 2, and $10,400 in Year 4. What is the net present value?

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