Tolerable Deviation Rates
Asset-based lenders usually lend at less than 100 percent of book value. Since verifications are sent out regularly and negative verifications are normally investigated on subsequent field examinations, the lender can then assume a certain level of risk, preferably either five percent or ten percent.
The second step is to determine the tolerable deviation rate, or the amount of uncollectible accounts receivable that a lender deems acceptable. This number (expressed as a percentage of the dollar value of the sample) should be no greater than 1/3 the difference between the collateral value (book value x advance rate) and the book value. Therefore, if the advance rate is 85 percent of book, the tolerable deviation rate should be no greater than five percent; for an 80 percent advance rate, a tolerable deviation rate of no more than seven per cent should be considered. Note that the effective advance rate (book value-ineligibles x advance rate) is not used when determining the tolerable deviation rate, for reasons of conservatism.
The third and final step in determining sample size is to quantify the expected deviation rate. Since a lender expects that an accounts receivable aging submitted as collateral is complete and accurate, the expected deviation rate should be zero. Once the lender has quantified the risk of over reliance, the tolerable deviation rate, and the expected deviation rate, the tables in Exhibit I may be employed to determine the sample size. For example, if the risk of over reliance equals five percent, the tolerable deviation rate is five percent, and the expected deviation rate is zero percent, then 59 of the invoices in the aging should be verified. If the tolerable deviation rate rises to seven percent, then 42 invoices would be verified.
Note that when these tables are used, the number of invoices in the population has no effect on sample size. This is because large swings in population size generally result in much smaller changes in sample size. Depending on the three variables described above, one population 1,000 times larger than another could result in less than a doubling of the sample. Therefore, for simplicity as well as conservatism, all populations are considered large or infinite. Selecting the sample
Once the sample size has been determined, the lender must select the invoices to be verified. This process is divided into two steps, calculating the interval and selecting the first invoice. To calculate the interval, divide the total number of invoices on an aging (an estimate may be used) by the sample size. Therefore, if the number of invoices on an aging equals 1,000, and the sample size equals 59, then every 17 invoices will be verified. Because the first invoice selected will determine which others will be included in the sample, a lender should choose this invoice randomly. This is easily accomplished using a random number table, such as the one detailed in Exhibit 2. If the first column of the tables is used, then in January, the 47th invoice would be chosen, while in February, the 104th invoice, and then the 75th in March. The table can be used from left to right, right to left, or any other direction. The sample should also be expanded to include significant or unique invoices, such as large dollar invoices or rounded dollar amount (i.e., invoices rounded to the nearest thousand or ten thousand) invoices.
Account Receivables
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