Question

Toyota Motor Company, headquartered in Japan, needs US$10,000,000 for three years to finance working capital for its plant in Long Beach, CA. Toyota has two alternatives for borrowing:

1. Borrow $10,000,000 in New York at 3.00% per annum.
2. Borrow ¥1,200,000,000 in Tokyo at 1.00% per annum, and exchange these yen at the present exchange rate of ¥120/$ for U.S. dollars.

For both loans, Toyota will make no payments until the end of three years, when principal and accumulated interest will be paid.

At what ending exchange rate would Toyota be indifferent between borrowing U.S. dollars and borrowing yen?

Answer 1

Borrowing US dollars

Amount to repay after 3 years = amount borrowed + (amount borrowed * interest rate * number of years)

Amount to repay after 3 years = $10,000,000 + ($10,000,000 * 3.00% * 3)

Amount to repay after 3 years = $10,900,000

Borrowing Yen

Amount to repay after 3 years = (amount borrowed + (amount borrowed * interest rate * number of years)) / ending exchange rate

Amount to repay after 3 years = (¥1,200,000,000 + (¥1,200,000,000 * 1.00% * 3)) / ending exchange rate

Toyota would be indifferent between borrowing U.S. dollars and borrowing yen if the amount repaid after 3 years is equal.

$10,900,000 = (¥1,200,000,000 + (¥1,200,000,000 * 1.00% * 3)) / ending exchange rate

ending exchange rate = (¥1,200,000,000 + (¥1,200,000,000 * 1.00% * 3)) / $10,900,000

ending exchange rate = ¥113.39/$

Toyota would be indifferent between borrowing U.S. dollars and borrowing yen if the ending exchange rate = ¥113.39/$