Investment Appraisal Discounted Cash Flow – Annuities and Perpetuities

ACCA F9 lectures ACCA F9 notes


  1. Profile photo of Satiam says

    In example 5 on annuity… when we get the answer 80440 as u did in the video, do we not have to discount it further to get a present value in year 0..?
    its like we calculated the value in year 4 but year 0 (now) we didn’t..

    • Profile photo of John Moffat says

      The first receipt is at time 4, and because there are 10 receipts, the last receipt is at time 13.

      You can get the answer in one of two ways – it doesn’t matter which, so whichever you find more obvious.

      One way is the take the annuity factor for 13 years (which would give a PV for all 13 years) and subtract the annuity factor for 3 years. That leaves you with a factor for time 4 to time 13.

      The alternative is to take the annuity factor for 10 years (because there are 10 years of flows), and then discount by the ordinary present value factor for 3 years (because the annuity starts 3 years at time 4 instead of time 1).

      Both ways give the same answer (they will be a little different because of the roundings in the tables, but that is irrelevant in the exam).

      (If you are still unsure it will help you to watch the relevant F2 lectures because it is revision of F2)

    • Profile photo of John Moffat says

      First, there is no such thing as an ‘advanced perpetuity’! I can only guess that you mean a perpetuity that starts later than at time 1 – but that is still a perpetuity by definition!!

      Second, it is extremely rare for perpetuities to occur investment appraisal questions at Paper F9 (they are relevant when calculating cost of equity, but that is dealt with in the lectures on the cost of equity). You will find it difficult (if not impossible) to find any past exam questions in the past five years that have a perpetuity existing in an investment appraisal question. We are teaching to pass the exam, not simply play around with numbers.

      Thirdly, dealing with annuities (which do occur often in F9) and perpetuities (which don’t) are both pure revision from Paper F2, so if you have forgotten how to deal with them then you should watch the relevant F2 lectures.

    • Profile photo of John Moffat says

      The 13 year annuity factor is the total of the discount factor from years 1 to 13 inclusive.

      We want the total factor for years 4 to 13, so we need to remove the total for years 1 to 3, i.e. the 3 year annuity factor.

      • Profile photo of John Moffat says

        The first receipt is in 4 years time – time 4.

        The second receipt is at time 5
        The third receipt is at time 6.

        If you carry on (and use your fingers to count!) then if there are 10 receipts the last receipt is at time 13.

  2. avatar says

    I think the interpretion on Qn 5 pg 40 is wrong:Look at how i think it should be counted and end of the tenth year would year 14 and not 13
    Receivable in 4 years time:
    year 1 2 3 4 5 6 7 8 9 10 11 12 13 14
    There after for total 10 years 1 2 3 4 5 6 7 8 9 10
    Am i correct to think this way????

    • Profile photo of John Moffat says

      I know that the wording may confuse, but it is likely wording in the exam.

      The first receipt is in 4 years time – time 4 – and there are 10 receipts in total (not 10 receipts in addition).

      So for 10 receipts in total, the receipts are at times 4 5 6 7 8 9 10 11 12 and 13.

  3. avatar says

    hi, john. trying to calculate the answer to Q7 on page 41 by using the other method, and the answer was different. the way i’ve done it was: if there will be receiveables from year 5 to infinity, then on year 5 the discount factor will be:
    1/0.05 x 0.784= 15.68 . i agree the way that have been shown in the vid is less confusing and if i was right then the figures should be the same. can you help, please? thank you!

    • avatar says

      The formula 1/r is the discount factor for perpetuities.
      So if you assume receivables happen from time=0 to time=infinity, the discount factor for this example is 20, and the present value of 18,000 annually in perpetuity is 18,000×20 = 360,000. (This means if you put 360,000 in the bank now you will get 18,000 every year)

      The only thing you are left with now, is to remove years 1-4.
      You can do this by removing each year individually (by multiplying 18,000 by the 1,2,3 and 4 year discount rate in the present value table) or by removing years 1-4 in one lump sum by multiplying 18,000 by the discount rate in the annuity table for year 4.

      The Annuity table is simply the present value table, summed to include all preceding years.

      In this example…
      Year 1 discount factor = 0.952
      Year 2 = 0.907
      Year 3 = 0.864
      Year 4 = 0.823

      Because net cash flow is the same each year (18,000), instead of multiplying 18,000×0.952, and 18,000×0.907, and 18,000×0.864 and 18,000×0.823, we can instead say that it is the same as 18,000x(0.952+0.907+0.864+0.823) = 18,000 x 3.546.

      So the answer would be (18,000 x 1/0.05) – (18,000 x 3.546).

    • Profile photo of John Moffat says


      I may be mistaken, but lukedavidizard seems to be just repeating what is in the video lecture!

      The approach that you are trying to take is fine, but you have made one error.

      The discount factor for a perpetuity is certainly 1/r, and if the perpetuity started in 1 years time then this would give the present value (the amount now).
      However, the perpetuity starts in 5 years time, which is 4 years later. So multiplying by 1/r would give a value 4 years later – i.e. at time 4. To get back to the present value you would then need to multiply by the ordinary discount factor for 4 years (not 5 years as you have written).

      If you do this then you will get the same answer. (In fact it will probably be a little different, but this will be simply due to rounding and does not matter).

      • Profile photo of John Moffat says

        hasanali95 is correct – since you are given tables you do not need to calculate.
        However, I would try and sort out your calculator – you will need to do other things with it even though you will not need to calculate the discount factors (which are not percentages by the way!) :-)

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