For the year just ended, LuLu’s Pies had an average of $50,000 in accounts receivable. Credit sales were $500,000. LuLu’s factors its receivables by discounting them 3 percent—in other words, by selling them for 97 cents on the dollar. What is the effective interest rate on this source of

Question

For the year just ended, LuLu’s Pies had an average of $50,000 in accounts receivable. Credit sales were $500,000. LuLu’s factors its receivables by discounting them 3 percent—in other words, by selling them for 97 cents on the dollar. What is the effective interest rate on this source of short-term financing?

Accepted Answer

To determine the interest rate, we first have to know the accounts receivable, or average collection, period. During the year, LuLu’s turned over its receivables $500,000/$50,000 = 10 times. The average collection period is 365/10 = 36.5 days.
The interest paid here is a form of discount interest (discussed in Chapter 6). In this case, LuLu’s is paying 3 cents in interest on every 97 cents of financing. The interest rate per 36.5 days is .03/.97 = .0309, or 3.09%. The APR is 10 × 3.09% = 30.9%, but the effective annual rate is:

EAR = 1.0309[latex]^{10}[/latex] − 1 = .356, or 35.6%

Factoring is a relatively expensive source of money in this case.
We should note that, if the factor takes on the risk of default by a buyer, then the factor is providing insurance as well as immediate cash. More generally, the factor essentially takes over the firm’s credit operations. This can result in a significant savings. The interest rate we calculated is therefore overstated, particularly if default is a significant possibility.

Question 18.3: For the year just ended, LuLu’s Pies had an average of $50,0...

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