4 DAR Percentages
Objectives
In this section, we will discuss:
The three numbers that you will need to calculate Days in AR.
What those three numbers mean and where to find them.
The steps in the calculation of Days in AR.
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4.1 Overview of Percentages
Just like fractions and decimals, percentages are a way to describe parts of a whole. When you are using percentages, the whole is considered to be made up of a hundred equal parts. It’s easy to work out the percentage when there are 100 individual parts making up the whole, but what if there are more or less? The answer is that you convert the parts of the whole into a percentage. For example, if there are 200 parts, each percentage (1%) is two parts, and every part would be half a percent (0.5%).
The general rule for finding a given percentage of a given whole is to work out the value of 1%, then multiply it by the percentage you need to find.
4.1.1 Percentages as Decimals and Fractions
One percent is one hundredth of a whole. It can therefore be written as both a decimal and a fraction. To write a percentage as a decimal, simply divide it by 100. For example, 50% becomes 0.5, 20% becomes 0.2, 1% becomes 0.01 and so on.
We can calculate percentages using this knowledge. 50% is the same as a half, so 50% of 10 is 5, because five is half of 10 (10 ÷ 2). The decimal of 50% is 0.5. So another way of finding 50% of 10 is to say 10 × 0.5, or 10 halves.
20% of 50 is the same as saying 50 × 0.2, which equals 10.
17.5% of 380 = 380 × 0.175, which equals 66.5.
The conversion from decimal to percentage is simply the reverse calculation: multiply your decimal by 100.
0.5 = 50% 0.875 = 87.5%
To write a percentage as a fraction, put the percentage value over a denominator of 100, and divide it down into its lowest possible form.
50% = 50/100 = 5/10 = 1/2 20% = 20/100 = 2/10 = 1/5 30% = 30/100 = 3/10
4.1.2 Percentages of a Whole
So far we have looked at the basics of percentages, and how to add or subtract a percentage from a whole.
Sometimes it is useful to be able to work out the percentages of a whole when you are given the numbers concerned.
For example, let’s suppose that an organisation employs 9 managers, 12 administrators, 5 accountants, 3 human resource professionals, 7 cleaners and 4 catering staff. What percentage of each type of staff does it employ?
Start by working out the whole.
In this case, you do not know the ‘whole’, or the total number of staff in the organisation. The first step is therefore to add together the different types of staff.
9 managers + 12 administrators + 5 accountants + 3 HR professionals + 7 cleaners + 4 catering staff = 40 members of staff.
Work out the proportion (or fraction) of staff in each category.
We know the number of staff in each category, but we need to convert that to a fraction of the whole, expressed as a decimal. The calculation we need to do is:
Staff in Category ÷ Whole (See our division page for help with division sums or use a calculator)
We can use managers as an example:
9 managers ÷ 40 = 0.225
Convert the fraction of the whole into a percentage
0.225 is the fraction of staff that are managers, expressed as a decimal. To convert this number to a percentage, we need to multiply it by 100. Multiplying by 100 is the same as dividing by a hundred except you move the numbers the other way on the place values scale. So 0.225 becomes 22.5.
In other words, 22.5% of the organisation’s employees are managers.
We then do the same two calculations for each other category.
12 administrators ÷ 40 = 0.3. 0.3 × 100 = 30%. 5 accountants ÷ 40 = 0.125. 0.125 × 100 = 12.5%. 3 HR professionals ÷ 40 = 0.075. 0.075 × 100 = 7.5%. 7 cleaners ÷ 40 = 0.175. 0.175 × 100 = 17.5%. 4 catering staff ÷ 40 = 0.1. 0.1 × 100 = 10%.
4.2 Step-by-Step Example
In this section, I’ll demonstrate the calculation for the optimal proportions (as percentages) of GCt and EARB needed for \(x\) DAR. We’ll use the data in the table below. Our Days in AR target (DARt) is 35 days:
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4.2.1 Calculate the Actual Percentages
First, we need to calculate the percentage of GCt and that of EARB. To calculate a percentage of two numbers, we first need to add the two numbers together to create the whole that we’ll be extracting the individual parts from.
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Add GCt and EARB together to get the whole.
1 + 1.5## [1] 2.5
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To find what percentage GCt and EARB are of this whole we will divide each by the whole and then multiply by 100:
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Divide GCt and EARB by the whole, then multiply by 100.
(1 / 2.5) * 100## [1] 40
(1.5 / 2.5) * 100## [1] 60
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So GCt is 40% and EARB is 60% of the whole of them added together. These are the “Actual” percentages. Let’s update our table:
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4.2.2 Calculate the Ideal Percentages
Now we need to calculate the “Ideal” percentages of GCt and EARB needed for a DARt of 35 days. Again, we need to add two numbers together to create the whole that we’ll be taking the parts from.
This time we will create our whole(s) by adding one to the Ideal Ratio for each of the NDiPs:
# NDiP is 28
1 + 1.25## [1] 2.25
# NDiP is 30
1 + 1.166666667## [1] 2.166667
# NDiP is 31
1 + 1.129032258## [1] 2.129032To get our Ideal percentages, we’ll divide 1 and the Ideal Ratio (remember, those were our original parts) for each NDiP by this whole and multiply by 100:
# NDiP is 28
(1 / 2.25) * 100## [1] 44.44444
(1.25 / 2.25) * 100## [1] 55.55556
# NDiP is 30
(1 / 2.166666667) * 100## [1] 46.15385
(1.166666667 / 2.166666667) * 100## [1] 53.84615
# NDiP is 31
(1 / 2.129032258) * 100## [1] 46.9697
(1.129032258 / 2.129032258) * 100## [1] 53.0303
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4.2.3 Calculate the Ideal Dollar Amounts
Finally, we’ll take the whole of our actual amounts (2.5) and multiply it by both Ideal Percentages (in decimal form) to find our Ideal Dollar Amounts:
# NDiP is 28
2.5 * 0.444444444444444## [1] 1.111111
2.5 * 0.555555555555556## [1] 1.388889
# NDiP is 30
2.5 * 0.461538461538461## [1] 1.153846
2.5 * 0.538461538461538## [1] 1.346154
# NDiP is 31
2.5 * 0.469696969696970## [1] 1.174242
2.5 * 0.530303030303030## [1] 1.325758
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4.3 Relationship Between EARB and GCt
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EARB & GCt Optimal Percentages for a DARt of 39.445 Over 365 Days.
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4.4 31-Day NDiP Comparison
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EARB & GCt 12-Month Comparison.
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EARB & GCt 12-Month Comparison REDO.
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As you can see, these percentages are independent of the GCt and EARB dollar amounts. And, from looking through the data to just where the DAR crosses from passing to failing, we can see that, for an NDiP of 31, the optimal percentage for GCt is approximately 44.01%, while EARB’s optimal percentage is 55.99%.
The optimal difference between the two amounts is 11.99%. If GCt falls below 44.01%, the DAR is failing. If EARB rises above 55.99%, the DAR is failing. If the difference between the two rises above 11.99%, the DAR is failing.
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The DAR Fails IF:
GCtfalls below 44.01%EARBrises above 55.99%the Difference between
GCtandEARBrises above 11.99%
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4.5 CROSSTALK TEST 2
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Visualization of Ending AR Balance & total Gross Charges Across 12 Months.
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4.5.3 31-Day NDiP
The following is a table of sample data wherein each row contains a 31-day month’s financial activity, sorted by DAR in descending order. In addition to the DAR Ratio measurements, there are several new figures included.
Under the Percentages spanner, the first two figures represent the individual proportions of Gross Charges and Ending AR to the whole of those two figures added together. The Difference percentage is that of the difference between the Gross Charges and Ending AR in relation to the whole figure as well.
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EARB & GCt 12-Month Comparison.
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