Functions & Formulae

Each applied formula has its own function page, with a signature, implementations, and tests.

Net days in accounts receivable function for a provider paid claim by claim

d(AR, R, D) = DAR

Maps a provider's net patient receivables, its net patient service revenue and the calendar days of the revenue period to net days in accounts receivable, the receivables balance expressed as days of average daily net revenue. The measure belongs to providers paid claim by claim, under fee-for-service or case-based payment such as the case-weighted payment per case of HE-FM-CWT-002, where every episode of care becomes a receivable until it is collected. HE-FM-DAR-001 gives the measure and HE-CF-DAR-001 builds its denominator from monthly revenue and actual calendar days as HFMA MAP Key FM-1 requires. Split by payer group, the overall figure is the revenue-weighted mean of the groups' own figures, the weighted mean of HE-FM-CRAT-001 and of the first part of HE-FM-CWT-001 with daily revenue in place of member or case numbers, so it is not drafted again. Since the balance equals r_bar times DAR, the cash released when collection shortens is r_bar times the fall in days, and the annual cost of carrying the balance at a cost of capital i is i times the receivables balance, the same rate-times-balance product as the return R_t = r * B_t on the balance still tied up in HE-CF-ANLS-002. The article's other use of released cash, held as cash and divided by daily cash operating expenses to give extra days cash on hand, is an alternative to the saving, not an addition to it. DAR equals the mean time a unit of revenue waits for cash, the W of Little's law in HE-FM-DES-003, only in a steady state with constant daily revenue, where the closing balance equals the time-average balance (derived); away from that state the two differ. Notation follows the Days in Accounts Receivable article.

  • Net days in accounts receivable from net receivables and average daily net patient revenue

    r_bar = R / D; DAR = AR / r_bar

    Divides the net patient receivables on the balance sheet at the end of a period by the average daily net patient service revenue of the same period, the HFMA MAP Key FM-1 net days in accounts receivable, so that receivables of providers of any size read on one scale of days. The measure applies to providers paid claim by claim, where each episode of care has to be coded, billed, adjudicated and collected before it turns into cash. Applied to one payer group the same formula gives that group's own days figure, and the overall figure is the revenue-weighted mean of the group figures by the weighted-mean identity of HE-FM-CRAT-001. Multiplying DAR by r_bar returns the receivables balance, the input to the carrying cost and the cash released that HE-FN-DAR-001 describes.