The firm needs to borrow $100,000 dollars. Ignore interest rate parity for the s

Question

The firm needs to borrow $100,000 dollars. Ignore interest rate parity for the sake of this problem. The firm can borrow in U.S. at 4% compounded annually, or the firm can borrow Yen at 3% compounded annually. The spot exchange rate is 108 Yen per dollar and the bank offers a one-year forward rate of 109 Yen per dollar. Both loans require repayment of the principal and interest at year end. Borrowing in which country is cheaper? How many dollars does the cheaper alternative save at year end (when compared to the alternative)?

Explanation / Answer

If it borrows in dollars at end of year it will pay 100,000*(1+4%)=$104,000

If it borrows in yen then spot conversion = 100,000*108 yen =10,800,000yen

after one year it is 10,800,00*(1+3%)=11,124,000

Conversion after one year @ 109 yen per dollar

=11,124,000/109=$102,055.05

The yen borrowing is cheaper and by this they save 104,000-102,055.05=$1,944.95

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