# 4.7. Receivables and payables

## Days of account receivables – DAR

The days of account receivables state the average number of days that go from the date that the company issued an invoice until its paid. It is common to see the use of the following equation:

• $$DAR=\frac{Clients}{Revenue}\times365$$

However, despite being the most common calculation form, the above equation casts an error by comparing the clients account, which includes VAT, whereas the revenue does not. As such, whenever possible and applicable VAT rate are known, the following equation is better:

• $$DAR=\frac{Clients}{(Revenue)\times(1+VAT\ rate)}\times365$$

It is on every company’s best interest to take an effort to the reduce the average payment deadline, because while doing so the company will reduce its receivables.

#### Example case: Dutch Fabric Innovations

Consider the following items representative of DFI’s activity:

 Values in EUR 2020 2021 2022 2023 2024 Clients 0,00 246 728,11 537 453,82 1 007 275,27 1 585 265,75 Revenue 0,00 2 480 875,00 5 404 150,00 10 128 250,00 15 940 000,00 Days of accounts receivables 0,00 30,00 30,00 30,00 30,00

In 2020, DFI is not selling yet and, therefore, has a clients account equal to zero, as well as zero revenues. So Days of Accounts Receivables are zero too. From 2021 onwards, considering a VAT rate of 21%, the days of accounts receivables are

• $$DAR=\frac{246\ 728,11}{2\ 480\ 875,00\ \times\ (1+0.21)\ }\ \times\ 365=30,00$$

This means that, on average, the invoices issued by the company take 30 days to be paid.

#### Example case: Golden Days

Let’s take into account some items extracted from Golden Days’ balance sheet and income statement:

 Values in USD 2019 2020 2021 2022 2023 Clients – 59 116,43 117 821,91 145 052,05 162 369,86 Revenue – 719 250,00 1 433 500,00 1 764 800,00 1 975 500,00 Days of accounts receivables – 30,00 30,00 30,00 30,00

Golden Days only starts selling in 2020, therefore, it has a clients account equal to zero, as well as zero revenues in 2019. So Days of Accounts Receivables are zero too.

From 2020 on, the days of accounts receivables are constant and equal to 30, meaning that, on average, the invoices issued by the company take 30 days to be paid.

• $$DAR=\frac{59\ 116,43}{719\ 250,00\times(1+VAT)}\times365=30,00\$$

We must take into consideration that in the United States there is no VAT rate.

## Days of accounts payables – DAP

The days of accounts payables follows a logic that is similar to that of the accounts receivables, but applies to what the company owes to its suppliers and the purchase of consumables and operating expenses.

• $$DAP=\frac{Suppliers}{Inventory\ purchase+Operating\ expenses}\times365$$

As with the DAR, while calculating the DAP there may be a misfit between Suppliers, whose amounts include VAT and the acquisition of inventory and operating expenses that do not include. Hence it is best to apply the following equation:

• $$DAP=\frac{Supplies}{(Inventory\ purchase+Operating\ expenses)\times(1+VAT\ rate)}\times365$$

In what regards to the treasury and working capital investment of the company it is its interest to extend the deadline of the payments to its suppliers, thus extending the cyclical operating resources.

#### Example case: Dutch Fabric Innovations

Consider the following items representative of DFI’s activity:

 Year 2020 2021 2022 2023 2024 Suppliers 40 188,57 535 204,36 1 082 647,99 1 999 618,12 3 060 106,55 Inventory purchase – 1 635 843,83 3 656 070,00 6 373 017,67 9 852 705,48 Operating expenses 134 700,00 158 000,00 275 750,00 329 100,00 403 850,00 Days of accounts payables 90,00 90,00 90,00 90,00 90,00

In 2020, DFI has a suppliers account with the value 40 188,57€ and operating expenses of 134 700,00€. As for inventory purchases, they follow the formula:

• $$(inventory\ in\ the\ end\ of\ the\ year\ – inventory\ in\ the\ beginning) + cost\ of\ goods\ sold\$$

Regarding cost of goods sold, only raw materials and consumables are considered. Given this, with a zero cost in raw materials in 2020 and a VAT rate of 21%, the company will have

• $$DAP=\ \frac{40\ 188,57}{\left(0+134\ 700\right)\ \times\ (1+0.21)}\ \times\ 365=90,00$$

Following the same logic for the other years, the days of accounts payable will stay constant at 90.

#### Example case: Golden Days

Let’s consider once again some items from Golden Days’ balance sheet and income statement:

 Values in USD 2019 2020 2021 2022 2023 Suppliers 13 808,21 25 533,37 75 418,52 88 503,28 101 899,39 Inventory purchase – – 49 275,00 60 915,00 68 310,00 Operating expenses 84 000,00 155 328,00 409 521,00 477 480,00 551 578,00 Days of accounts payables 60,00 60,00 60,00 60,00 60,00

In 2019, Golden Days presents a suppliers account with the value 13 808,21$and operating expenses of 84 000,00$.

• $$(inventory\ in\ the\ end\ of\ the\ year\ – inventory\ in\ the\ beginning) + cost\ of\ goods\ sold\$$

However, Golden Days has no inventory, so only cost of goods sold remain, and for these only raw materials and consumables are considered. We must remember that the company only has costs with raw materials in 2021 and that in the United States there is no VAT. Given this,

• $$DAP=\ \frac{13\ 808,21}{(0+84\ 000,00)\times(1+VAT)}\times365=60,00\$$

Following the same logic for the other years, the days of accounts payables will stay constant at 60.

## Days of investment accounts payables – DIAP

The days of investment accounts payables is just like the DAP but applied to to the acquisition of investment.

• $$DIAP=\frac{Investment\ suppliers}{Investment\ acquisition}\times365$$

Or (when taking VAT in consideration):

• $$DAP=\frac{Investment\ suppliers}{(Investment\ acquisition)\times(1+VAT\ rate)}\times365$$

## Days of stock

The days of stock identifies the average number of days that stocks are held by the company until it is sold.

• $$Days\ of\ stock=\frac{Raw\ materials}{Inventory}\times365$$

#### Example case: Dutch Fabric Innovations

Consider the following items representative of DFI’s activity:

 Year 2020 2021 2022 2023 2024 Inventory – 179 543,83 387 713,83 742 031,50 1 162 836,98 Raw materials – 1 456 300,00 3 144 790,00 6 018 700,00 9 431 900,00 Days of stock 0,00 45,00 45,00 45,00 45,00

We know that in 2020, DFI does not register any inventory or raw materials since it only starts producing in 2021.

In 2021, however, it will present 45 days of stock:

• $$Days\ of\ stock=\frac{179\ 543,83}{1\ 456\ 300,00}=45,00$$

The company maintains 45 days of stock through the years, which means that DFI holds its stock 45 days before selling it.

#### Example case: Golden Days

 Year 2019 2020 2021 2022 2023 Raw materials – – 49 275,00 60 915,00 68 310,00 Inventory – – – – – Days of stock – – – – –

Golden Days holds no inventories because the type of business in which it is inserted is based on the offer of services and does not require inventories. Given this, it does not have stock as well and present zero days of stock.

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