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Discounted cash flow techniques (part 4) – ACCA (AFM) lectures

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  2. Hi John, really appreciate the material available on the site and the work you and your team have put in. This has helped me immensely.

    I have read comments which refer to example 6 and why the discount factor for year 3 of 0.579 was used rather than year 4. But I am still not clear. Please would you mind elaborating a bit further to help me understand.

    Many Thanks in advance.

    • After the 3 year the flows are 7,000 a year with inflation at 5% from year 4 through to infinity.

      Had they been 7,000 a year with inflation at 5% per year from year 1 to infinity then the growth formula would have given the PV ‘now’ (i.e. at time 0).

      Here, however, instead of the first flow being in year 1, it is in year 4, which is 3 years later. So they are exactly the same flows but all of them are 3 years later. Therefore using the formula gives the PV but the PV 3 years later i.e. at time 3 instead of time 0. So to get back to the PV at time 0 we need to discount the answer for 3 year.

  3. Hi John, regarding example 5, it says the cash flows have been forecast at $5000 p.a, and inflating at 4% p.a., does it means in year 1, we will get cash flow 5000*(1.04) straight away?
    Would it be possible to have $5000 in year 1 and then inflating at 4% (if it is the case, how would the wording be)?
    Thanks heaps in advance!

    • Yes – in example 5 the cash flow will be 5.000 x 1.04 in 1 years time.

      And yes it is possible to have an actual 5,000 at time 1 and for it then to inflate at 4% per year. It would be worded as you have done (or in the same sort of way as example 6 is worded).

      • Hi Mr. Moffat,

        To refresh my memory of the growth model, I would like to clarify that the growth model is assumed to use time 1 inflated cash flow ($5000 * 1.04) to discount to time zero. This assumes that there is no cash flow at time zero. If there is cash flow at time zero, do we add the cash flow at time zero plus the discounted perpetual cash flow at time 1 to zero?

        If it is $5,000 at time 1 and inflated thereafter, do we have to discount the inflated to time 1 and then discount both the $5,000 and the inflated at time 1 to time zero?

      • The numerator in the formula ( Do(1+g) ) is the dividend in 1 years time. If given the current dividend then the dividend in 1 years time is Do(1+g). If given the dividend in 1 years time then we use the same formula but use D1 as the numerator and do not multiply by 1+g.

  5. Hello sir, what if the inflation rate is higher than the discount rate and is this possible in any case? As the discount rate includes the impact of inflation, is it practically possible that the inflation rate be higher than the discount rate?

  6. Dear Sir,

    In example 6, why do we use the growth model formula starting in year 4 when the first flow is in year 3 (7,000) and inflating at a rate of 5% thereafter. So this way the formula would discount the perpetuity back to year 2 i/o year 3 as you explained in your workings.

    Thank you for your reply in advance!

    Regards,
    Peter

    • You should remember from Paper PM (was F9) that when dealing with an inflating perpetuity (which in Paper FM was usually inflating dividends) that if the inflating stream started at time 1, then in the formula we put as Do the current dividend that has just been paid (i.e. at time 0).

      Here, instead of the inflating stream starting at time 1, I have taken it as starting at time 4 (and discounting the time 3 flow separately). Therefore for Do in the formula we use the time 3 flow of 7,000.

      By all means use the formula for the stream starting at time 3 instead, and discount the answer for 2 years, but then you need to use D0(1+g) as being 7,000 (and not 7,000 x (1+g)). You will get the same answer:

      (7,000 / (0.20 – 0.05) ) x ((1/1.20)^2) = 32,407.

      This is the same as the PV of 7,000 in 3 years time, plus the PV of the inflating stream from time 4 onwards as in the lecture. 4,053 + 28,371 = 32,423

      (The difference is simply due to the rounding of the discount factors and is, as always, irrelevant in the exam)

    • The dividend valuation formula give the PV for any inflating perpetuity. If the first flow is in 1 years time then it gives a PV at time 0. If the first flow is in 4 years time then it gives a PV at time 3.

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