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  • Annual percentage cost of discount

    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.
    Last edited by Ap123; 10-02-08, 20:22.

  • #2
    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.
    Last edited by SandyHood; 10-02-08, 21:22.
    sandy@sandyhood.com

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    • #3
      Thanks.

      Comment


      • #4
        Originally posted by SandyHood View Post
        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!!

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        • #5
          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@sandyhood.com

          Comment


          • #6
            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@sandyhood.com

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            • #7
              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.

              Comment


              • #8
                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@sandyhood.com

                Comment


                • #9
                  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?

                  Comment


                  • #10
                    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
                    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@sandyhood.com

                    Comment


                    • #11
                      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?

                      Comment


                      • #12
                        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 will be different from the compounding method. Compounding is a geometrical calculation.
                        sandy@sandyhood.com

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