Question 20.3: The Row Cannery wants to borrow $2 million for one month. Us...
The Row Cannery wants to borrow $2 million for one month. Using its inventory as collateral, it can obtain a 12% (APR) loan. The lender requires that a warehouse arrangement be used. The warehouse fee is $10,000, payable at the end of the month. Calculate the effective annual rate of this loan for Row Cannery.
Plan
The monthly interest rate is 12%/12 = 1%. We need to compute the total cash flows Row will owe at the end of the month (including interest and the warehouse fee). By scaling those cash flows by the amount of the loan, we will have a total monthly cost for the loan that we can then convert to an EAR.
Execute
At the end of the month, Row will owe $2,000,000 × 1.01 = $2,020,000 plus the warehouse fee of $10,000.
The cash flows are shown here on a timeline:
The actual one-month interest rate paid is:
\frac{2,030,000-2,000,000}{2,000,000} =1.5\%Expressing this as an EAR gives 1.015^{12}-1=0.196, or 19.6\%
Evaluate
The warehouse arrangement is quite costly: The EAR on the loan itself is (1.01)^{12}-1=.1268, or 12.68\%, but the warehouse arrangement raises it to 19.6%!
