Question 15.4: Calculating the Annual Percentage Rate of Short-Term Lender ...
Calculating the Annual Percentage Rate of Short-Term Lender Credit
The A. B. Good Company sells electrical supplies to building contractors on terms of net 60. The firm’s average monthly sales are $100,000; thus, given the firm’s 2-month credit terms, its average receivables balance is $200,000. The firm pledges all of its receivables to a local bank, which in turn advances up to 70 percent of the face value of the receivables at 3 percent over prime and charges a 1 percent processing fee on all receivables pledged. A.B. Good follows a practice of borrowing the maximum amount possible, and the current prime rate is 10 percent. What is the APR of using this source of financing for a full year?
STEP 1: Formulate a Solution Strategy
In this example, the same annual percentage rate formula is used. However, the key is identifying the correct characteristics to use as variables in the equation:
Annual percentage rate = \frac {interest}{principal} \times \frac{1}{time} (15-9)
Note that we can calculate interest by adding the interest expense plus the annual processing fee. The principal will be represented by the actual amount of credit extended. Finally, our time period should be over the full year:
APR = \frac {interest expense + processing fee}{ credit extended} \times \frac {1}{time}
STEP 2: Crunch the Numbers
Once we substitute the correct variables from above into the equation, we get the following result:
APR = \frac { \$ 18,200 + \$ 12,000} {\$ 140,000} \times {1}{ 360/360} = 0.2157 = 21.57%
where the total dollar cost of the loan consists of both the annual interest expense (0.13 × 0.70 × $200,000 = $18,200) and the annual processing fee (0.01 × $100,000 × 12 months = $12,000). The amount of credit extended is 0.70 × $200,000 = $140,000. Note that the processing charge applies to all receivables pledged. Thus, the A. B. Good Company pledges $100,000 each month, or $1,200,000 during the year, on which a 1 percent fee must be paid, for a total annual charge of $12,000.
STEP 3: Analyze Your Results
It appears that A. B. Good Company’s lender charges a rate of about 14 percent (13 percent interest and 1 percent annual processing fee) for the 70 percent of receivables for which it gives a receivables advance. In this example, the effective APR is actually more than this charge of 14 percent because of the discounted amount of the receivables advance. Since only 70 percent of the receivables are actually credited, the effective APR is increased to account for the 30 percent of receivables for which no advance is given.
One more point: The lender, in addition to making advances or loans, may be providing certain credit services to the borrower. For example, the lender may provide billing and collection services. The value of these services should be considered in computing the cost of credit. In the preceding example, A. B. Good Company may save $10,000 per year in credit department expenses by pledging all of its accounts and letting the lender provide those services. In this case, the cost of short-term credit is only:
APR = \frac {\$ 18,200 + \$ 12,000 – \$ 10,000} {\$ 140,000} \times \frac{1}{ 360/360} = 0.1443 = 14.43%