Question 15.2: Calculating the Effective Annual Cost of Short-Term Bank Cre...
Calculating the Effective Annual Cost of Short-Term Bank Credit
M&M Beverage Company has a $300,000 line of credit that requires a compensating balance equal to 20 percent of the loan amount. The rate paid on the loan is 10 percent per annum; $200,000 is borrowed for a 6-month period deposit with the lending bank. The dollar cost of the loan includes the interest expense and the opportunity cost of maintaining an idle cash balance equal to the 20 percent compensating balance. To accommodate the cost of the compensating-balance requirement, assume
that the added funds will have to be borrowed and simply left idle in the firm’s checking accounts.
STEP 1: Formulate a Solution Strategy
The amount actually borrowed (B) will be larger than the $200,000 needed. In fact, the needed $200,000 will constitute 80 percent of the total borrowed funds because of the 20 percent compensating-balance requirement; hence,
0.80B = $200,000, such that B = $250,000
Thus, interest is paid on a $250,000 loan, of which only $200,000 is available for use by the firm.³
Interest = principal × rate × time
= $250,000 × 0.10 × (180/360) = $12,500
Note that we use the $250,000 as the principal when calculating the interest payment. The reason is that the firm must borrow the 20 percent compensating balance of $50,000 that is left idle in the firm’s checking account.
The effective annual cost of credit, therefore, is calculated using the APR formula:
APR = \frac { interest}{ principal} \times \frac{1} {time}
STEP 2: Crunch the Numbers
Substituting the characteristics of M&M Beverage Company’s bank loan into the APR equation above, we get the following:
APR = \frac{\$ 12,500} {\$ 200,000} \times \frac {1} {180/360} = 0.125 = 12.5%
Note that we use $200,000 as the principal when calculating the annual percentage rate. This amount represents the available portion of the loan, or the effective portion; therefore, we use it to calculate effective annual cost.
STEP 3: Analyze Your Results
In the M&M Beverage Company example, the loan required the payment of principal ($250,000), which includes the 20 percent compensatory balance, plus interest ($12,500), a 10 percent rate, at the end of the 6-month loan period. The effective annual cost of credit was calculated using the ratio of interest ($12,500) to effective principal amount ($200,000). When annualized, this ratio produced an effective annual cost of bank credit of 12.5 percent.
Frequently, bank loans will be made on a discount basis. That is, the loan interest will be deducted from the loan amount before the funds are transferred to the borrower. Extending the M&M Beverage Company example to consider discounted interest involves reducing the effective loan proceeds ($200,000) in the previous example by the amount of interest for the full 6 months ($12,500). The effective rate of interest on the loan is now:
APR = \frac{\$ 12,500} {\$ 200,000 – \$ 12,500} \times \frac {1} {180/360} = 0.1333 = 13.33%
The effect of discounting interest was to raise the cost of the loan from 12.5 percent to
13.33 percent. This results from the fact that the firm pays interest on the same