Question

TropiKana Inc., a U.S firm, has just borrowed euro 1,000,000 to make improvements to an Italian fruit plantation and processing plant. Ifthe interest rate is 5.50% per year and the Euro appreciates against the dollar from $1.40/€ at the time the loan was made to $1.45/€ at the end of the first year, what is the before tax cost of capital if the firm repays the entire loan plus interest (rounded)?

Answer should be 9.27% but I am unsure of how to get there

Answer 1

TropiKana borrowed euro 1,000,000 at the starting of the year, which effectively means that they've borrowed $1,400,000 since the spot rate is  $1.40/€ which effectively means that for every euro you borrow, you have to give $1.4.

Since the interest rate is 5.5% per year, now you have to pay back euro 1,055,000 (55,000 as interest payment)

Now, since the lender is US based, he'd want his money back in US dollars, we convert back  euro 1,055,000 at $1.45/€ (since the euro has appreciated)
The dollar amount we pay after one year is $1,529,750
Which means we pay $129,750 as interest payment on $1,400,000 ($1,529,750 - $1,400,000 )

The effective cost of capital for one year is
= 129,750/1400000
or 9.27%