Annual percentage cost of discount
Ap123
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.
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.
0
Comments

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
sandy@sandyhood.com
www.sandyhood.com0 
Thanks.0

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.0 
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
sandy@sandyhood.com
www.sandyhood.com0 
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
sandy@sandyhood.com
www.sandyhood.com0 
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.0 
I advise ignoring the £700
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
sandy@sandyhood.com
www.sandyhood.com0 
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?0 
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.
(I made the answer to the previous example 50.2% APR)
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 your customers tend to pay on time according to the existing terms of sale
 and you've not heard about any risk of insolvency
 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
sandy@sandyhood.com
www.sandyhood.com0 
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?0 
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
sandy@sandyhood.com
www.sandyhood.com0
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