McDougan Associates, a U. S. based investment partnership, borrows EUR 80,000,000 at a time when the exchange rate is USD1.3460/EUR. The entire principal is to be repaid in three years, and interest is 6.250% per annum paid annually in euros. The euro is expected to depreciate vs. the dollar at 3% per annum. What is the effective cost of this loan for McDougan Associates?

The effective cost of this loan for McDougan Associates: 3.06%.

Explanation:

* The exchange rate over the 3-year of borrowing is:

Y1: USD/EUR: 1.3460 x (1 - 3%) = 1.3056

Y2: USD/EUR: 1.3460 x (1 - 3%) ^2 = 1.2665

Y3: USD/EUR: 1.3460 x (1 - 3%) ^3 = 1.2285

* Interest payment in USD at each year are and principal payment at the end of 3 years:

Y1: 80,000,000 x 6.250% x 1.3056 = $6,528,000

Y2: 80,000,000 x 6.250% x 1.2665 = $6,332,500

Y3: (80,000,000 x 6.250%+80,000,000) x 1.2285 = $104,422,500.

* Principal borrowing at the beginning in term of USD = 80,000,000 x 1.3460 = $107,680,000.

=> Effective cost of this loan (denoted as x) is equal to the discount rate of future repayment (in term of USD) that equalize the net present value of future repayment to its principal borrowing:

6,528,000 / (1+x) + 6,332,500 / (1+x) ^2 + 104,422,500 / (1+x) ^3 = 107,680,000 x = 3.06%

Thus, Effective cost of this loan is 3.06%.