# CASH MANAGEMENT - The annual cost of cash or settlement discouting

RichardK
Well-KnownRegistered Posts:

**107**
I am going to explain the meaning and use of the cash settlement discounting formula. You can find this formula on page 183 of the Osborne Cash management book.

I have attempted to remove all errors and would appreciate any comments if you find any.

Originally composed by RichardK (AAT full member) and proof read and edited Rowan B (BSc Stats)

Remember that when you deal with this sort of formula, you can not do the calculations in any order. The calculations must follow a particular order. This means if you have a formula like (d/100-d) you have to do the part which says 100-d first. Then you can divide it into d. You can not do it any other way or the answer will be incorrect. Please bear this in mind.

Firstly we need to look at what each part of the settlement or cash discounting formula means

(d/100-d) x (365/N-D)

d = settlement discount percentage

N = normal settlement period in days

D= settlement period for early payment

To simplify the formula and help your understanding I am first going to look at the left hand side part called (d/100-d)

Here (d divided by 100-d) represents how much the discount, which was applied to the invoice, is worth in percentage compared to the discounted invoice overall. 100 *(d/ (100 – d)) = percentage value of discount relative to discounted invoice (percentage interest rate for the number of days the payment is reduced by).

Here I am going to put some numbers in to give you an idea as to what is happening as follows……………

I am going to let d=£20 so the left hand part of the formula will look like this……….

(20/100-20) which can be simplified as 20/80 and simplified further as ¼. All of these are the same as saying 25%.

IMPORTANT: When you express a percentage, it is always relative to something else. Therefore it follows that £25 expressed as a percentage of £100 equals 25% and likewise £20 expressed as a percentage of £80 is also 25%.

Therefore we are saying that a discount of 20% on an invoice of £100 is 25% of the discounted invoice of £80 or ¼ (one quarter or 0.25) of the discounted invoice. Another way of looking at it is as follows………..

£20 expressed as a percentage of £100 = 20%

£20 expressed as a percentage of £80 = 25%

We can even put these numbers in the formula to help your understanding as follows………

(£20/£100-£20) which means £100 was the original invoice and £20 was the discount on the invoice. Therefore £20 represents 25% or one quarter of the discounted invoice of £80.

To help your understanding further I am going to apply a discount of 50% as follows…………

(£50/£100-£50)=1 or 100%

So now the complete formula will go from looking like this………..

(d/100-d) x (365/N-D) x100%

To looking like this……………

1 x (365/N-D)

I have applied a discount of 50% so that the left hand side will equal 100% and we can put this side of the formula to one side and work on the right hand side. At this stage you can assume that we are always going to apply a discount of £50 to the original invoice of £100 until I say otherwise.

We can now move on to the right hand side of the formula which looks like this

(365/N-D)

I need to look at the number of days in the normal invoice period (let us say 30 days) and take away from that the number of days in the invoice period that permits a discount to be applied (let us say 7 days).

So it will cost us £50 to reduce the payment period by 23 days. This make sense right? It will cost us £50 to get the customer to pay up 23 days early.

THIS £50 IS THE COST OF DISCOUNTING FOR GETTING PAID 23 DAYS EARLY.

However, we need to convert this £50 over a 23 day period it into a yearly percentage so we can compare it with how much it would cost us to borrow £50 over the period of 1 year so that we can compare it with yearly borrowing rates. In other words IS IT CHEAPER TO DISCOUNT AN INVOICE BY 50% AND GET THE CUSTOMERS MONEY INTO YOUR ACCOUNT 23 DAYS EARLY OR SHOULD WE BORROW THE MONEY FROM THE BANK?

This is where the right hand side of the formula comes in.

So we know already that if the customer pays within 7 days he will get the discount of 50%. We are always using 50% until I change it later.

So the right hand side of the formula now looks like this……….

(365/30-7)

= (365/23)

= 15.86 worth of 23 day periods in 1 year.

This tells us how many periods of 23 days are in 1 year. Effectively, this is used to convert the percentage rate which the left hand side of the equation represents into an annualised percentage rate.

We can now look at our formula overall and put all the numbers in that we have calculated as follows:

(50/100-50) x (365/30-7) x100%

= 1 x 15.87 = 15.87. This equates to a 1587% ((15.87 * 100) %) cost per annum to offer the discount.

You can now see that if we put different numbers in the left hand side of the formula we can reduce the 15.86 on the right hand side of the formula as follows. So now I am going to HALVE the discount rate from 50% to 25% as follows……..

(£25/ £100-£25) x 15.87

= 0.333 x15.87 = 5.29 (to 2 d.p.). This equates to a 529% ((5.29*100) %) cost per annum to offer the discount.

So you can see how the effect of applying different discounts for the same period will have different results.

In this case halving the discount will reduce the annual cost to one third of what it was, presuming discount payment term remains the same.

I hope this helps.

I have attempted to remove all errors and would appreciate any comments if you find any.

Originally composed by RichardK (AAT full member) and proof read and edited Rowan B (BSc Stats)

Remember that when you deal with this sort of formula, you can not do the calculations in any order. The calculations must follow a particular order. This means if you have a formula like (d/100-d) you have to do the part which says 100-d first. Then you can divide it into d. You can not do it any other way or the answer will be incorrect. Please bear this in mind.

Firstly we need to look at what each part of the settlement or cash discounting formula means

(d/100-d) x (365/N-D)

d = settlement discount percentage

N = normal settlement period in days

D= settlement period for early payment

To simplify the formula and help your understanding I am first going to look at the left hand side part called (d/100-d)

Here (d divided by 100-d) represents how much the discount, which was applied to the invoice, is worth in percentage compared to the discounted invoice overall. 100 *(d/ (100 – d)) = percentage value of discount relative to discounted invoice (percentage interest rate for the number of days the payment is reduced by).

Here I am going to put some numbers in to give you an idea as to what is happening as follows……………

I am going to let d=£20 so the left hand part of the formula will look like this……….

(20/100-20) which can be simplified as 20/80 and simplified further as ¼. All of these are the same as saying 25%.

IMPORTANT: When you express a percentage, it is always relative to something else. Therefore it follows that £25 expressed as a percentage of £100 equals 25% and likewise £20 expressed as a percentage of £80 is also 25%.

Therefore we are saying that a discount of 20% on an invoice of £100 is 25% of the discounted invoice of £80 or ¼ (one quarter or 0.25) of the discounted invoice. Another way of looking at it is as follows………..

£20 expressed as a percentage of £100 = 20%

£20 expressed as a percentage of £80 = 25%

We can even put these numbers in the formula to help your understanding as follows………

(£20/£100-£20) which means £100 was the original invoice and £20 was the discount on the invoice. Therefore £20 represents 25% or one quarter of the discounted invoice of £80.

To help your understanding further I am going to apply a discount of 50% as follows…………

(£50/£100-£50)=1 or 100%

So now the complete formula will go from looking like this………..

(d/100-d) x (365/N-D) x100%

To looking like this……………

1 x (365/N-D)

I have applied a discount of 50% so that the left hand side will equal 100% and we can put this side of the formula to one side and work on the right hand side. At this stage you can assume that we are always going to apply a discount of £50 to the original invoice of £100 until I say otherwise.

We can now move on to the right hand side of the formula which looks like this

(365/N-D)

I need to look at the number of days in the normal invoice period (let us say 30 days) and take away from that the number of days in the invoice period that permits a discount to be applied (let us say 7 days).

So it will cost us £50 to reduce the payment period by 23 days. This make sense right? It will cost us £50 to get the customer to pay up 23 days early.

THIS £50 IS THE COST OF DISCOUNTING FOR GETTING PAID 23 DAYS EARLY.

However, we need to convert this £50 over a 23 day period it into a yearly percentage so we can compare it with how much it would cost us to borrow £50 over the period of 1 year so that we can compare it with yearly borrowing rates. In other words IS IT CHEAPER TO DISCOUNT AN INVOICE BY 50% AND GET THE CUSTOMERS MONEY INTO YOUR ACCOUNT 23 DAYS EARLY OR SHOULD WE BORROW THE MONEY FROM THE BANK?

This is where the right hand side of the formula comes in.

So we know already that if the customer pays within 7 days he will get the discount of 50%. We are always using 50% until I change it later.

So the right hand side of the formula now looks like this……….

(365/30-7)

= (365/23)

= 15.86 worth of 23 day periods in 1 year.

This tells us how many periods of 23 days are in 1 year. Effectively, this is used to convert the percentage rate which the left hand side of the equation represents into an annualised percentage rate.

We can now look at our formula overall and put all the numbers in that we have calculated as follows:

(50/100-50) x (365/30-7) x100%

= 1 x 15.87 = 15.87. This equates to a 1587% ((15.87 * 100) %) cost per annum to offer the discount.

You can now see that if we put different numbers in the left hand side of the formula we can reduce the 15.86 on the right hand side of the formula as follows. So now I am going to HALVE the discount rate from 50% to 25% as follows……..

(£25/ £100-£25) x 15.87

= 0.333 x15.87 = 5.29 (to 2 d.p.). This equates to a 529% ((5.29*100) %) cost per annum to offer the discount.

So you can see how the effect of applying different discounts for the same period will have different results.

In this case halving the discount will reduce the annual cost to one third of what it was, presuming discount payment term remains the same.

I hope this helps.

## Comments

2,453107These are now being deleted.

Thank you

526Regards,

Andrea.

1072,034A clear posting, and I hope you don't take any criticism I make personally.

Calculating the annual percentage rate requires 3 key calculations:

This is assessed on a lot of courses, and

sadlyassessed differentlyBut AAT do assess this in a way that is accurate

And it is exactly the same way as both RichardK and Osborne describe as far as calculations 1 and 2 are concerned

Where AAT's marking scheme differs from the method outlined is in calculation 3

[email protected]

www.sandyhood.com

2,034The approach above assumes that the discounted amount can be converted into an APR using a simple interest approach.

But interest rates grow on a compound basis, so instead of (50/100-50) x (365/30-7) x100%, we need to look at compounding the 50/(100-50)

And this is done using the power button on the calculator not the times

(1+(discount rate/proportion payable)) to the power of the number of time periods in a year.

[email protected]

www.sandyhood.com

2,034The interest rate calculated (i.e. discount%/net payable%) needs to be converted to an annualised percentage rate using the formula

R=((1+r)^(365/reduction period))-1

A simple way of estimating the annual cost is to simply multiply the interest rate calculated by the reduction period. This does not take into account the effect of c ompound interest and is therefore technically incorrect but can be used as a rough and ready measure.

To pass the task a correct calculation was required.

I hope this helps.

The quote is not word for word from the mark sheme as the mark scheme refers to the actual numbers in that test and I used generic names for the terms so the approach can be used in all questions.

[email protected]

www.sandyhood.com

2,034But if you are asked by your boss should we take an early settlement discount offered by a supplier? or

Should we offer customers an early settlement discount?

Please use the compound approach AAT examine - it is more accurate.

[email protected]

www.sandyhood.com

107Hi Sandy, please do not confuse people with compound interest formula. The compound interest formula is not stated in the Osborne books.

I have written this thread according to the AAT Osborne books based on the simple interest calculations.

Calculations regarding compound interest (interest on interest) can be found on the web in most maths forums.

Please also appreciate that is has been proof read and edited by RowanB (BSc stats)

Your comments may help to confuse people and detract from the Osborne AAT books.

2,034Thank you

The point you make is the same point that Osborne has made, but it is not correct. Candidates who use simple interest will not be marked as correct in the skills test.

[email protected]

www.sandyhood.com

107I presume you do not speak for the whole of the UK AAT courses?

In which case, please let students put this point to their individual tutors. After which they can apply the appropriate method and formula.

Also not all loans are based on the compound interest formula so you would not be comparing like with like if you used it under some circumstances.

2,034It is a shame when the books and the mark schemes do not agree (we had one on VAT in the college where I work very recently), but the assessor sets the threshold and that is used to judge competence or otherwise.

[email protected]

www.sandyhood.com

107Hi,

Thank you. I appreciate your comments but I am just going by the Osborne and Kaplan AAT book on this occasion. If you would like me to add some information to the original Thread to mention this can you please post it here.

As stated, not every loan is based on the compound interest formula. If you use the compound interest formula to compare with the cost of borrowing on a simple interest loan, you will not be comparing like with like.

2,034I quite accept that many loans are on simple interest rates, but this task is not in that category. When it says annualised percentage rate it is looking for compounding. It is similar to credit card monthly interest and APRs.

[email protected]

www.sandyhood.com

107Can we agree,

"If in doubt consult your tutor"

Regards

158This was my fault. I wrote that. I thought it was an annualised percentage rate. Otherwise, I think the task is perfectly solved using the simple interest formula.

2,415Perhaps you are unaware of Sandy's qualifications and peer status amongst the usual AAT posters Richard, but I can assure you it is held in much higher regard than yours. I guess that maybe you're unaware that Sandy is an award winning senior lecturer from Chichester college who runs tutorial courses all over the country, a status - again I'm guessing - probably goes way beyond your own. Maybe you should add your own achievements on here so we can judge who should 'be more respected'?

158107Hi,

i'm (we are) not here to score points with qualifications or otherwise.

Please appreciate that the information has been edited and approved by RowanB (BSc Maths & Stats).

You can take the information or leave it. That is your choice.

If you do not like the posts, please do not read them.

158If you remove that sentence, I'm not sure the explanation is flawed at all. Then again, I'm obviously not an expert.

488Just my opinion for what. It is worth.

107Hi, thank you,

your feedback is important. However, regarding the accuracy and content of the thread, it does stand up mathematically. It has been edited and approved by the BSc Maths & Stats graduate "RowanB".

I welcome anyone to give their comments.

As the old saying goes "There are many ways of skinning a cat"

This subjectivity often plays a part in accountancy where two accountants with the same data produce slightly different results.

275Well said, Glynis.

I applaud you!

And i'm affraid I have not read ALL the thread's but I have to say, no disrespect to anyone else, but if Sandy and Steve tell you something...you and pretty much bet your life on it they are right!

488107Thank you.

The post is not only credible but correct. If anyone has any positive comments on how to enhance or improve the original text, it is most welcome.

I would appreciate positive comments from anyone whether they are a STUDENT or tutor.

158107Hi Rowan,

you did do the corrections in your sleep, so please give yourself a break. You pass exams in your sleep!

In future can you make the corrections whilst awake.

997Hi Richard

I think when you are offering advice on forums it is best to receive positive and negative feedback. I'm not saying the advice questioning your post is critical advice but as you say there are occasions when two accountants will often differ. I am lecturing to 65 qualified accountants in London on Wednesday and I am expecting (in fact somewhat hoping) some of them will challenge my views because this then allows me to consider everyone's viewpoint. The same principles are involved in offering advice on forums - sometimes people will agree, others will disagree but I don't think you can ask for positive responses all the time because negative ones will often be very valid, as in Sandy Hood's case.

Your post will undoubtedly help other students and the posts challenging the content may also offer food for thought.

Kind regards

Steve

2,415Well, that line has been added on since I first read this post. Perhaps Richard you can advise me how I'm able to know in advance if I'm going to like or dislike by a post before I read it? Now if you're asking me not to comment on a thread I dislike, then that's a different issue but if someone's talking bollocks about something, I often feel the need to interject.

For once Glynis, I agree with you. I'd rather trust the comments of Sandy who's been a proven asset to this forum for several years and thus doesn't feel the bullish need to 'prove his worth' rather than that of someone who argues the experiences of others even though they won't qualify their own.

158Thanks