The Working Capital Cycle: How to Compute the Days

The cash conversion cycle is computed from five figures: receivables over revenue, inventory over the cost of materials consumed, and payables over that same cost, each multiplied by 365, then combined as the first plus the second less the third. For Anjani Stationers' year two the three come to 128.4, 68.8 and 54.1 days, and the cycle to 143.1.

Here is what sits underneath that. Each of the three ratios compares a balance sitting on the balance sheet with the flow that produced it during the year, and the whole of the difficulty in this arithmetic is pairing each balance with the right flow. Receivables were produced by selling, so the flow underneath them is revenue. Inventory and payables were produced by buying, so the flow underneath both of them is the cost of materials consumedThe line reporting what the materials used up during the year cost, worked out as opening stock plus purchases less closing stock.. Multiplying by 365 turns each of those three fractions into a number of days, and the three day counts combine into the cash conversion cycleThe three day counts combined as collection plus inventory less payables, expressed as a single number of days. by adding the first two and deducting the third. The calculator computes those four numbers. Reading what a finished cycle says about a business is a separate subject from computing it.

What does this calculator produce?

Four numbers and one sentence. The four numbers are the three ratios in days and the cycle they combine into. The sentence names which balances were used, and it is part of the output rather than a courtesy. Five printed inputs go in and nothing else is needed: no rate, no assumption, no judgement about the business.

The shape of the arithmetic is one every household already does without naming it. A rice tin holding roughly ten kilograms, in a house that gets through about half a kilogram a day, holds twenty days of rice. A stock divided by a daily flow gives a number of days. A stock over a daily flow is the entire mechanic, done three times, with the daily flow worked out by dividing a full year’s figure by 365 rather than by watching the tin. Every one of the three ratios is a balance divided by a daily rate of flow, so the only thing that can go wrong is dividing by the wrong flow.

What are the three ratios, and what base does each one use?

Three divisions, two bases. Days sales outstandingTrade receivables divided by revenue and multiplied by 365, reported as a number of days. puts trade receivables over revenue. Days inventory outstandingInventories divided by the cost of materials consumed and multiplied by 365, reported as a number of days. puts inventories over the cost of materials consumed. Days payable outstandingTrade payables divided by the cost of materials consumed and multiplied by 365, reported as a number of days. puts trade payables over that same cost of materials consumed. Each result is multiplied by 365. The baseThe figure written underneath the line in a division, the flow the balance is being measured against. is the second of those two words in every case, and it is the step where this computation is lost or won.

Two of the three ratios divide by the cost of materials consumed and only one divides by revenue, and a calculator that puts revenue underneath all three will still return four tidy numbers. That is what makes this the expensive step. Nothing breaks, nothing errors, nothing looks odd. Anjani Stationers' inventory of Rs 28,00,000 over the revenue of Rs 2,70,00,000, multiplied by 365, gives 37.9 days, a perfectly well formed number that answers a question nobody asked. The stock in the godown was never sold at the selling price while it sat there; it was bought at cost and it is carried at cost, so the flow it has to be measured against is the cost flow.

Follow what the wrong base does to the finished cycle. The finished cycle does not behave the way people expect. Swap the base for inventory alone and the cycle drops from 143.1 days to 112.2, a shortfall of 30.9 days. Swap the base for both inventory and payables, the usual move for somebody working at speed, and the cycle comes to 136.6 days, only 6.5 days short. The payables error pushes back against the inventory error. The smaller miss is the more dangerous of the two: a cycle that is out by 31 days invites a second look, and one that is out by 6 does not.

Where is each of the five inputs found?

Two of the five come off the face of the statement of profit and loss and three off the balance sheet, and every one is a single printed line rather than something that has to be assembled. The field notes in the calculator say exactly where to look. One of them is worth saying twice. Revenue from operations is the first line on the face, not the total income line printed below it. The total adds other income, and other income was never sold to a customer on credit and has no receivable behind it.

Some preparers print purchases of stock in trade and changes in inventories of finished goods as separate lines beside the cost of materials consumed. Which of those lines belong in the base is then decided once, and the identical set is used in both ratios and in both years. All five inputs are printed lines in a filed set of accounts, so no number in the computation had to be estimated, apportioned or assumed.

Two precisions on the balance sheet side are worth writing on the sheet beside the inputs. Anjani Stationers carries a provision for doubtful debts of Rs 9,00,000 behind its receivables line, so the gross figure is Rs 95,00,000 and the net figure is Rs 86,00,000. The calculator uses the gross Rs 95,00,000. Which of the two is chosen decides nothing. Choosing the same one in every year decides everything. The second precision is the Rs 4,00,000 of advances the Sunrise Public School group has paid for notebooks not yet delivered. The advance sits in current liabilities next to trade payables and it is not a trade payable, so it does not enter the payables input.

Closing balance or average balance, and why must the choice be stated?

Both work, and the calculator has to be told which one it is running. The closing balanceThe amount standing on a balance sheet line on the last day of the year, exactly as printed. is what the balance sheet prints: Rs 95,00,000 of receivables on the last day of Anjani Stationers' year two. The average balanceThe opening and closing balances of a line added together and halved, used to smooth a balance that moved during the year. takes the opening and closing figures for the same line, adds them and halves them: Rs 78,00,000 plus Rs 95,00,000 gives Rs 1,73,00,000, halved to Rs 86,50,000. Revenue and the cost of materials consumed are already full year flows and have nothing to average, so the base underneath stays exactly where it was in both cases.

Run Anjani Stationers' collection ratio both ways and the difference is not small. Closing gives 128.4 days. Average gives 116.9 days. Eleven and a half days separate two correct computations of the same year from the same accounts. The gap is why the basis is written beside the number and not left to be guessed. A household reading a water tank faces the same thing. The reading taken on the last evening of the month and the reading obtained by averaging the first and the last are both honest readings, and when one neighbour quotes the first while another quotes the second, the two argue about the tank instead of about the water.

One practical limit is worth stating rather than working around. An average basis needs an opening balance for every line it touches, so it runs only for a year whose opening figures are in hand. Year one’s opening receivables are printed at Rs 30,00,000, but its opening inventories and payables are not. The calculator above therefore refuses to average that column and says so rather than filling the gap with a nil. Where a basis cannot be run for every year in a series, the basis that can be run is the one used, and it is stated.

What do Anjani Stationers' two years come to?

Here is the whole computation with nothing hidden: five inputs, three ratios and one cycle for each year, both on closing balances so the two columns are comparable. The middle column is the instruction and the two on the right are the output.

Two things in that table are worth checking. The first is the rounding convention. Each ratio is rounded to one decimal and the three rounded figures are then combined. Rounded that way, 128.4 plus 68.8 less 54.1 gives 143.1. Carrying every division to four decimals instead brings the same year to 143.2. Neither is a mistake, and a published number should say which convention produced it. The second is the year one column. Year one’s column uses year one’s own bases, Rs 2,40,00,000 of revenue and Rs 1,32,00,000 of cost, never year two’s.

The two cycles differ by 13.5 days, and because both columns were computed on the same basis with the same rounding, those 13.5 days are a movement in the business rather than a movement in the method. The components rather than the total show where the movement sits. Collection lengthened by 9.8 days and inventory by 16.3 days. Payables lengthened by 12.6 days, and payables are deducted, so those 12.6 days pull the other way. Adding 9.8 and 16.3 and deducting 12.6 gives 13.5. The sum matches the change in the cycle, a useful arithmetic check that all six ratios were computed correctly.

Who runs this computation, and what do they check first?

The people who run this arithmetic run it on somebody else's accounts, usually under time pressure, and each has one habitual first check. A credit officer sizing a working capital facility recomputes the days from the borrower’s filed accounts rather than accepting the sheet the borrower brought. A borrower’s own sheet has often used revenue for all three, so the base underneath the inventory and payables ratios is looked at first. An analyst rebuilding a series checks that every year in it is on one basis before comparing any of them.

A wrong base produces an answer that always looks reasonable, so every practitioner check is a check on the inputs and the basis, never on whether the answer looks reasonable. A finished cycle cannot be inspected to see whether it was computed correctly, since 112.2, 136.6 and 143.1 all look like plausible day counts for the same business. The only defence is that the five inputs were read off named lines and the basis was written down beside the answer.

Here are the readings the slider produces, written out. Year two's revenue of Rs 2,70,00,000 sits underneath every one of them, so a balance carried in from year one is being measured against year two's selling rather than year one's. On closing balances, a receivables balance of Rs 40,00,000 gives 54.1 days of collection and a cycle of 68.8 days. Rs 78,00,000 gives 105.4 days and a cycle of 120.1. Rs 95,00,000 gives the reported 128.4 days and 143.1. Rs 1,20,00,000 gives 162.2 days and 176.9, and Rs 1,40,00,000 gives 189.3 days and 204.0. The other two ratios never changed, so each of those cycles moves by exactly the number of days the collection ratio moved. No clearer demonstration exists that the cycle is an addition rather than a blend. Switch the basis to average at the reported balance and the set becomes 116.9, 57.8 and 45.5, a cycle of 129.2 days.

Anjani Stationers Private Limited, Chitra Binding Works Private Limited, Anjani Kulkarni, Meera Rao and the Sunrise Public School group are invented.
Educational material. Not advice on any investment, tax, budget or market position.