Days to Pay by Method and What the Gap Buys You

Why this matters

The argument about whether card payments are worth their fee is usually had in two different units at once. One side says "it costs us nearly four percent". The other says "we get paid the same day instead of waiting a month". Both are true and neither answers the other, because a percentage of a bill and a number of days are not the same kind of thing. Days to pay by method is what lets you convert one into the other, and once you have done that conversion the answer is often the opposite of what either side expected.

What the two averages are computed over

For every payment received in the window, take the number of days from the invoice's issue date to the date the payment landed. Then split those values by how the money arrived, and average each group separately. Card is one group; check, bank transfer and cash are the other, and it is worth keeping them apart from each other too once you have four quarters of data.

Two composition points before any number is read:

• It only contains payments that happened. An invoice never paid contributes nothing, so both lines are computed over the customers who did eventually pay. That is the same survivor bias the time-to-invoice card owns, and here it flatters both methods rather than one, so it distorts the levels and mostly leaves the gap intact. The gap is the useful part, which is convenient.
• It is measured from the issue date, not from completion. A job billed three weeks late and paid immediately shows one day to pay. That is correct for this metric and it is why it must be read beside the billing-speed number rather than instead of it.

The median is not a refinement here, it is the reading

The card line in particular is wrecked by a small number of payments against old invoices, and a shop that reads only the mean will conclude its card payments are slower than they are.

Take 100 card payments in a month. Ninety-six were taken at or near the point of billing and averaged 0.85 days. Four were customers clearing old balances through a payment link, against invoices issued an average of 57 days earlier.

• The 96 contribute 96 times 0.85, which is 81.6 payment-days.
• The 4 contribute 4 times 57, which is 228 payment-days.
• Total 309.6 payment-days over 100 payments, so the mean is 3.1 days.
• Ninety-six of the 100 sat at or near one day, so the median is 1.0 day.

Those 4 payments are 4 percent of the card payment count and carry 228 of the 309.6 payment-days, which is 74 percent of the card payment-day total. Both figures are about the same 100 card payments. A metric where 4 percent of the rows carry three quarters of the weight is a metric you read on the median.

The non-card line has the opposite shape: its mean of 34.8 days sits above its median of 29.0 days because of a long tail of slow payers rather than a handful of extremes. That difference between the two lines is itself diagnostic. Read both, and when they disagree, the mean is telling you about your worst accounts and the median about your normal ones.

This shop's two lines

Terms are net 30. The shop's realized card rate is 3.9 percent of card money collected, computed as total processing fees over total card money; the sibling card below owns how that figure is built and why it runs above the quoted rate.

Gap on the medians: 29.0 minus 1.0, which is 28.0 days. Gap on the means: 34.8 minus 3.1, which is 31.7 days. Use the median gap of 28.0 days for every decision below, because the mean gap is inflated by four payments on one side and a tail on the other, and those two distortions do not cancel.

Putting the fee and the speed on one scale

Here is the conversion the argument needs. The shop pays 3.9 percent of the bill to be paid 28.0 days sooner. Annualize it: 3.9 percent for 28 days is 3.9 times 365 over 28, which is 50.8 percent a year.

That is the price of the money, and it settles one half of the argument immediately. So at any cost of capital a shop can actually borrow at, the speed alone does not justify the fee - a line of credit is a small fraction of 50.8 percent a year - and the single exception is the shop with no line left to draw, whose marginal cost of money is whatever is actually available to it. That case is worked at the end, and it is the only one where the 28 days comes close to carrying the fee on its own. Anyone else defending card acceptance purely on "we get the money faster" has lost the argument on arithmetic, and it is worth knowing that before the conversation rather than during it.

What the conversion does not say is that card is not worth paying for. It says the 28 days is not what you are buying.

What actually pays for the fee

Three things do, and they have to be put in the same unit as the fee, which is a share of the bill.

The bridge you have to supply yourself is how many fully-loaded office hours your average invoice is worth. Divide your average invoice by your fully-loaded office hourly cost. For this shop it is about 6 office-hours, and every conversion below rests on that one ratio, so get it roughly right before trusting any of them.

Office labour. A non-card invoice on net 30 consumes about 0.35 office-hours across the reminder, the statement, the phone call and posting the payment. A card payment taken at the point of billing consumes about 0.05. Both of those figures are illustrative rather than measured, and together they form the largest term in the whole stack, so time your own office against five invoices of each kind before you let this ratio decide a payments policy. The difference is 0.30 office-hours per invoice. Against an average invoice worth 6 office-hours, that is 0.30 over 6, which is 5.0 percent of the bill. Note the other direction of the same ratio: 3.9 percent of a 6-office-hour invoice is 0.234 office-hours, so the fee costs 0.234 office-hours and buys back 0.30, and on labour alone it is 78 percent of what it saves.

Bad debt avoided. Money taken at the point of billing does not go bad. If card acceptance reduces the share of billed money eventually written off by 1.2 percentage points, that is 1.2 percent of the bill. Measure this one on your own book rather than assuming it, by comparing eventual write-off rates on invoices that settled by card against those that did not, over at least a full year.

Financing. 28.0 days of earlier cash at a line-of-credit rate of 12 percent a year is 12 times 28 over 365, which is 0.92 percent of the bill.

Add them: 5.0 plus 1.2 plus 0.92 is 7.12 percent of the bill, against a fee of 3.9 percent of the bill. All four figures are shares of the same bill, per invoice, so they can be added and compared. The trade is worth about 1.83 times what it costs, and the financing term is the smallest of the three at 0.92 percent, which is 13 percent of the 7.12. The thing everybody argues about is the least of what you are buying.

Two levers sit outside this stack and both are worth knowing before you decide to stop accepting card. The federal one is a floor you already have: under 15 USC 1693o-2(b)(3) a merchant may set a minimum transaction amount of up to 10 dollars for CREDIT card acceptance without breaching its network agreement, and that same provision permits no minimum on debit. The other is surcharging or a cash discount, and it is not a simple yes: a cash discount is broadly permitted federally under 15 USC 1666f, while a credit-card surcharge is governed by the networks' own registration, disclosure and cap rules, which are contract rather than law, and is separately restricted or banned by a small number of states, so get your state's current position and your processor's registration requirement before you add a line to an invoice.

The blended non-card line is usually a fiction

The fee argument is the loud use of this metric. The quieter one is that the non-card line, once you split it, tells you where 28 days actually went.

In this shop, 40 percent of non-card payments came from residential customers with a median of 14 days, and 60 percent came from commercial and property-management accounts with a median of 38 days. Those pool to the 29.0 day blended median quoted above, and 29.0 days describes nobody. The residential customers pay at roughly half of the terms they were given. The commercial ones pay about 8 days past net 30.

That split moves the work somewhere useful, because the two groups respond to completely different things.

The commercial line is not moved by reminders. It is moved by getting into the approval cycle cleanly: the correct purchase-order or work-order number on the invoice, submitted to the person or portal that actually processes it, with whatever backup that customer requires attached the first time. An invoice rejected on first submission restarts the clock, and the shop usually does not find out for a fortnight, so the days show up in this metric with no visible cause. Measure the share of commercial invoices returned or rejected on first submission; above about 5 percent of commercial invoices submitted, the fix is a submission checklist rather than a collections push, and no amount of chasing will move the median until it is fixed.

The residential line is moved by asking at the point of billing, which is exactly what taking a card at the door is. That is the same lever the fee argument is about, arriving from the other side.

Two shops where the rule collapses

The stack above is arithmetic, not a law, and two real shops break it in opposite directions. Both are worth recognising because the answer flips entirely.

The shop with no bad debt and an idle office. All commercial accounts, on terms, who always pay. The bad-debt term is genuinely zero. The office is salaried and not at capacity, so the 0.30 office-hours saved per invoice are hours already paid for that nobody will be let go over, and they do not become money this year. If the shop also carries no borrowing, the financing term is zero as well. The whole stack collapses to something near zero against a 3.9 percent cost, and the correct policy is to stop pushing card on those accounts and offer terms instead. The saved hours only become value when the office is the constraint, and on that shop it is not.

The shop at its credit limit in peak season. Here the financing term is the one that explodes, because 12 percent a year is the rate on credit it does not have. Its marginal source of money is whatever is actually available: a merchant advance, a supplier stretched past terms, an early-payment discount forgone, or a job it cannot start because it cannot buy the materials. If the marginal cost of money is four times the line rate, the financing term goes from 0.92 to 3.68 percent of the bill. For that shop, during that season, the 28 days alone very nearly carries the fee: 3.68 percent against a 3.9 percent cost, so it still falls just short on its own and needs about a 4.24 times marginal rate to cross, at which point the other two terms are pure gain.

Both shops should compute the same stack. The inputs differ, and that is the point: this is a calculation each shop does with its own numbers, not a rule anyone can hand you. What travels is the method and the ordering of the three terms, and the finding that the speed is almost never the biggest of them except when the shop has run out of money.

References

• See related: universal-the-effective-card-rate-is-not-the-rate-you-were-quoted, which owns how the 3.9 percent realized rate is built and why it runs above the quote.
• See related: universal-what-share-of-collections-arrives-by-card, for the arrival-date anchor both figures share and for splitting card into its three channels.
• See related: universal-time-to-invoice-only-counts-the-invoices-you-sent, which owns the survivor-bias explanation and covers the billing-speed number this metric must be read beside.
• See related: universal-the-aging-buckets-and-what-each-one-actually-costs, for the write-off rates the bad-debt term should be measured from.