Receivables Turnover & Days Sales Outstanding

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\text{Receivables turnover} = \frac{\text{Revenue}}{\text{Average receivables}} \qquad DSO = \frac{365}{\text{Receivables turnover}}

$\text{Revenue}$: total sales for the year (assume all on credit, the standard simplification when a credit-sales split isn't given)
$\text{Average receivables}$: the accounts-receivable balance, averaged between the start and end of the year
$\text{Receivables turnover}$: how many times per year the average receivable balance was collected and reissued
$365$: days in a year — the unit conversion from 'cycles per year' to 'days per cycle'
$DSO$: days sales outstanding: the average wait between a sale and its cash collection

Why it must be true

A sale on credit is not yet cash — it is a customer's promise. Receivables turnover asks: how many times per year does that promise get collected and re-extended? A turnover of 8 means the average receivable balance was fully collected and reissued eight times over the year — customers pay fast, capital recycles quickly.

DSO restates the same fact in a unit anyone can feel: days. Turnover of 8 becomes "customers take about 46 days to pay." The two are the same measurement wearing different clothes — one built for comparing efficiency across companies, the other for reading a collections calendar.

The derivation

Revenue is a flow measured over the whole year; the receivables balance is a snapshot. Bridge them with the average balance, so the ratio compares a year's sales to the capital that financed them:

\text{Receivables turnover} = \frac{\text{Revenue}}{\text{Average receivables}}

To convert a turnover count into a days-per-cycle figure, divide the days in the year by how many cycles fit inside it — the same logic as converting "3 loads of laundry a week" into "one load every 2.3 days":

DSO = \frac{365}{\text{Receivables turnover}}

Faster turnover (more cycles) always means fewer days per cycle — the two move in exact, mechanical opposition.

When to reach for it

Judging how efficiently a company collects what it's owed, or converting between a 'times per year' efficiency ratio and a 'days to collect' operating figure.

Listen for

“receivables turnover / accounts receivable turnover”“days sales outstanding (DSO) / average collection period”“how long customers take to pay”“credit and collections efficiency”

Back-of-the-envelope

Estimate it in your head first — then the calculator only confirms.

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Turnover and DSO are reciprocal-flavored: a HIGHER turnover always means a LOWER DSO. If both move the same direction in a distractor, one of them is wrong.
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Quick sanity bands: DSO under 30 days is fast (cash-heavy retail); 45–60 is typical B2B; well over 90 signals either generous credit terms or a collections problem.
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Round trip check: turnover × DSO should equal 365 almost exactly (small rounding aside) — a fast way to verify an answer choice.

Traps in applying it

✗Using the ending receivables balance instead of the average — the ratio compares a full year of sales to a full year's typical balance, not one snapshot.
✗Forgetting which way the reciprocal runs: DSO = 365 / turnover, not turnover / 365.
✗Applying the ratio when a large cash-sales portion exists without adjusting revenue to the credit-sales figure the question actually gives.

Limits & criticisms

The ratio averages away everything interesting: a single giant overdue account can hide inside an otherwise healthy average, and seasonal businesses show a distorted number if measured at the wrong point in the year. It also says nothing about collectibility — receivables can turn over on schedule right up until a customer defaults. Aging schedules (a breakdown by how overdue each invoice is) catch what the single average cannot.

Where it came from

Alexander Wall's 1919 study for the Federal Reserve Board ("Study of Credit Barometrics") was among the first to argue that no single ratio judges a company — a system of ratios, including collection measures, was needed to size up a borrower. Trade-credit departments and bank lending officers turned "days to collect" into a standing scorecard decades before formal equity analysis existed, and it remains one of the first numbers a CFO's dashboard shows: a rising DSO is often the earliest sign that revenue quality is slipping before it shows up anywhere else.

One identity, 2 questions

The exam can hide any variable. Each face below is the same equation solved for a different unknown — drill them separately.

Times collected per year

\text{Receivables turnover} = \frac{\text{Revenue}}{\text{Average receivables}}

The efficiency face: how many times a year the credit-sales cycle completes.

Drill this face →

Days to collect

DSO = \frac{365}{\text{Receivables turnover}}

The calendar face: the same cycle speed, read as an average wait in days.

Drill this face →

On the BA II Plus

Worked example: Revenue was $1,100.00m; receivables stood at $30.00m at the start of the year and $85.00m at the end. How many days sales outstanding does that imply?

1.(30 [+] 85) [÷] 2 [=]average receivables
2.1100 [÷] [RCL] [=]receivables turnover
3.365 [÷] [RCL] [=]days sales outstanding

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Where it leads

Master this and the following come almost for free:

Cash Conversion Cycle Inventory Turnover & Days of Inventory on Hand Total Asset Turnover

Drill this formula Back to the library