Question

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?

Answer 1

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

Step-by-step 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%.