# Annual percentage cost of discount

Registered Posts: 2 New contributor ?
Say the average customer invoice is £3k and normal terms of trade are 30 days from invoice date.

If the company is considering 3% settlement discount for payments within 7 days, How do you calculate the annual percentage cost of this discount?

can anyone show me how I would work this out, thanks.

I cant find the formula anywhere.

• Registered, Moderator Posts: 2,034
I teach this in a number of professional accounting courses.

The annual percentage cost is the equivalent to the APR a store card or credit card might charge you.
By offering this early settlement discount you are asking for cash 23 days earlier than you would normally get it.
So you need to find how many lots of 23 days are in a year
365 = 15.8696 (Leave that in your calculator)
.23

We are going to deduct 3% of the invoice amount, so we will receive 97% of the total. The 3% represents
3 = 3.09% You can express this as 1.0309 (to include the principle)
97
If you could deposit money in the bank at 3.09% £1 will become £1.0309.

Now, does your calculator allow you to do calculations to the power of something?

If it does, the annual discount rate calculation is 1.0309 to the power of 15.8696 less 1.

I make it 62.2%

And would recommend against such a move in almost all cases, as bank overdraft finance comes at a miuch lower apr. The rare case where 62% is acceptable might be the floundering business customer where you can get the money owed to you before they go into administration.
Sandy
[email protected]
www.sandyhood.com
• Registered Posts: 2 New contributor ?
Thanks.
• Registered Posts: 13 Regular contributor ⭐ ? ⭐
SandyHood wrote: »
I teach this in a number of professional accounting courses.

The annual percentage cost is the equivalent to the APR a store card or credit card might charge you.
By offering this early settlement discount you are asking for cash 23 days earlier than you would normally get it.
So you need to find how many lots of 23 days are in a year
365 = 15.8696 (Leave that in your calculator)
.23

We are going to deduct 3% of the invoice amount, so we will receive 97% of the total. The 3% represents
3 = 3.09% You can express this as 1.0309 (to include the principle)
97
If you could deposit money in the bank at 3.09% £1 will become £1.0309.

Now, does your calculator allow you to do calculations to the power of something?

If it does, the annual discount rate calculation is 1.0309 to the power of 15.8696 less 1.

I make it 62.2%

And would recommend against such a move in almost all cases, as bank overdraft finance comes at a miuch lower apr. The rare case where 62% is acceptable might be the floundering business customer where you can get the money owed to you before they go into administration.
Hi, a search I did has brought up this old thread, as it's something that I can't get my head round - when asked to calculate annualised cost of discount and it says "the average customer invoice is £X000"... I can't figure out how to use that "average invoice amount". I just ignored the invoice amount in the Sim, with disastrous results! (I did discount divided by 100 minus discount; then 365 divided by old period minus new period: that times that times 100 equals my answer. Which was wrong.) I've got access to a scientific calculator assuming I can find out how to use it!! But where/how do I use that invoice amount please? Thanks for looking!!
• Registered, Moderator Posts: 2,034
Bear in mind that there are longer methods than the one I put forward, but the annual percentage rate doesn't need the average invoice amount.
Sandy
[email protected]
www.sandyhood.com
• Registered, Moderator Posts: 2,034
As this was part of the webinar course yesterday I've added this post so it is near the first page for current Unit 15 students.
Sandy
[email protected]
www.sandyhood.com
• Registered Posts: 34 ? ? ?
i would appreciate any help.

annual percentage cost of disocount
Usually 60 day terms on an invoice of £700
5% discount to those who pay in 14 days.
That would be...
365/46 = 7.94

and i get lost from here.
• Registered, Moderator Posts: 2,034
This firm can claim a 5% discount from their supplier provided they pay in 14 days rather than 60

So they'll pay 95% of the bill but have to pay 46 days earlier than they would have done

The supplier is effectively borrowing 95% of the invoice value and paying 5/95ths as the interest (for 46 days)

As there 7.94 periods of 46 days in a year you can use this to find the annual percentage rate
0.052632
7.934783
50%

5/95 = 5.263%
So you say (1+ 5.263%)^7.935 - 1
In other words 1 represents the amount borrowed
So 1 + the rate of interest for 46 days to the power of 7.935 less the 1 (amount borrowed) gives the APR

Did that help?
Sandy
[email protected]
www.sandyhood.com
• Registered Posts: 34 ? ? ?
Hi, thanks yeah that;s a little clearer

This is based on offering a discount, not receiving a discount, don't know if that matters.

The annual percentage rate is...the annual discount given correct?
• Registered, Moderator Posts: 2,034
The calculation remains the same:
offering or being offered
the interpretation and subsequent decision will obviously be different because we would be either receiving a rate of interest of xx% or having to pay interest at that rate.

As a general rule of thumb, early settlement discount questions tend to produce answers which have high APRs.
Obviously borrowing money from banks etc can be subject to lots of things, they'll look at the risk they are taking if they lend and they'll not always agree to a loan. But if
1. your customers tend to pay on time according to the existing terms of sale
2. and you've not heard about any risk of insolvency
3. and your bank are willing to lend to you (through the overdraft) at say 8% APR
Then you'll probably be better off, not offering an early settlement discount (of 50.2%)
And you'll probably be better off accepting a supplier's offer of an early settlement discount (of 50.2%)
Sandy
[email protected]
www.sandyhood.com
• Registered Posts: 8 Regular contributor ⭐ ? ⭐
I'm having real problems with this!

I can't do 'to the power of' on my calculator so I have been using a different method from the Kaplan book but it gives a completely different answer to the example above.

(5/95) x (365/46) x 100 = 41.76%

This is the method I used in my simulation but it was wrong. Can anybody help?
• Registered, Moderator Posts: 2,034
To be honest, try and get a calculator with a "to the power of button" for Christmas.

The method you have highlighted is an arithmetical calculation and [size=+1]will[/size] be different from the compounding method. Compounding is a geometrical calculation.
Sandy
[email protected]
www.sandyhood.com