collection ratio problem

Hello ...
I am doing some cash flow analysis for a company and I just looked deeper at what is usually called the "collection ratio".
According to the theory, the collection ratio measures the average
amount of time it takes for a company to collect its sales. The formula is : receivable/(sales/365). Now lets take for fun a simple example :
During a week, a company named ABC sold 1$ of merchandise per day to a client named XYZ :
sunday : sold merchandise for 1$ (invoice 001) monday : sold merchandise for 1$ (invoice 002) tuesday : sold merchandise for 1$ (invoice 003) wednesday : sold merchandise for 1$ (invoice 004) thursday : sold merchandise for 1$ (invoice 005) friday : sold merchandise for 1$ (invoice 006) saturday : sold merchandise for 1$ (invoice 007)
On saturday, ABC received payments for invoice 001 and invoice 002.
According to the classical formula applied to a period of one week, the average time ABC takes to collect 123 is
5$/(7$/7) = 5 days
where 5$ is the receivable, 7$ is the revenue for a week and 7 is the amount of days for the targeted period.
Sorry but that does not work.
If we all agree invoice 001 was collected in 6 days and invoice 002 in 5 days the formula should be :
(5 days + 6 days) / 2 = 5.5 days
If we extend our method, the collection ratio should be a sum where each sale is an item weighted by its collection delay and its importance in terms of money.
Any comments?
SES
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In the real world you would not have the luxury of averaging each individual collection, which is what you have done to arrive at 5.5 days. The collection ratio is an indicator of collection efficiency. The difference between the two methods is exaggerated because of the small size of your sample.
Cheers, Rusty

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Well ... doing that calculation is something trivial for an accounting system ... I was actually able to do it in 30 minutes using a script of my own.
Your comment on the exageration of the difference "because of the small size of my example" is mathematicaly completely wrong.
First, the classic ratio calculates the delay of *invoices* collection ... which is useless, since an analyst will be more interested in money collection delays (set invoice 002 amount to 100$ instead of 1$ and you will undertsand).
Second, the result of the classic formula is not the mathematical limit of my formula. Therefore, the "difference" between the 2 calculation methods will not get closer by increasing the amount of invoices. This can be easily demonstrate.
SES
Rusty wrote:

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steven wrote:

Ratios' are only guides. The more exact you become with your data the less exact the outcome becomes. Calculating ratios on a larger group of data i.e. over a year will give you a more accurate ratio calculation. You need to calculate for ratio over a month. If a customer buts every day and then stops buying and the recommecnes buying over a month you will have wild swings in your ratio if they also slow up in payment.
As most customers pay a group of invoices at a time, each invoice will have a different payment day, but you can calculate the average over a group of invoices. Applying tight mathematical formuale will give you results that are of little use to you. A bigger timescale will go you an average, but not an exact result.
If you have hundreds of invocies and customers, is it worth the time trying to calculate the pay days per invoice sand then work out an average for that customer.
If you have credit terms for each customer, are they paying on time or are they going over those terms, this information to me is more useful. How efficent at collecting my money against my terms am I.
Is 1/2 a day (5.5 v 5 worth the effort?) - What is the cost benefit analysis of the results.
Also these are general ratios'. If your company requires more accurate results then your results are not wrong it is just the general ones are very guide guides but not exact.
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