Discontinued perpetuity cash flow (DPCF) - Need help with formula

Hello together,

I am new to this forum and fundamental analysis, so hopefully I am not doing any doublepost here.
I am trying to understand the DCF Intrinsic value calculator and I have a problem understanding the Discounted Perpetuity CF part.

In the calculator and in the book the following formula is used from year 11 to perpetuity:

DPCF= $1000*( (1+0.06)^11 *(1.03)/(0.1-0.03))*(1/(1+0.1)^11))

I would expect:

DPCF= $1000*( (1+0.06)^10 *(1.03)/(0.1-0.03))*(1/(1+0.1)^11))

Since I take the last FCF value calculate the growth for the next year and discount it in the end.

On a morningstar page I would find the same approach. Do I have a flaw in my logic?
http://news.morningstar.com/classroom2/course.asp?docId=145102&page=5&CN=

Thanks in advance!

JH_Analyst


Also thanks for all the great content. With these practical approach I am learning way faster!!!

Comments

  • I guess the Equation is based on the Gordon Growth Model. But I would assume that I take the last CF from year 10 instead of 11. And discount it then to the present value
  • Hey JH_Analyst,

    Let me see if I understand you correctly:
    - You are using the DCF model to find the value of something (probably a business)
    - You have 2 portions of DCF model: 1) the pro forma (forecast) of cash flows (which looks to be 10 yrs), 2) the value of the company beyond year 10 to infinity (otherwise known as the 'terminal value).

    I found this post that could help with the terminal value part. I find it easier to separate the 2 portions of the model.
    http://www.wallstreetmojo.com/terminal-value-formula-method-calculations-in-excel/

    Sorry - maybe this doesn't help with your question. I personally find it difficult to asses your issue by simply looking at the formula you wrote.

    Kindly,
    RJ
  • Hey RJ_Michell,

    thanks for your answer. Unfortunately it does not solve my problem and even supports my doubt in the intrinsic value calculation on buffettsbooks.com.

    I try to be more precise this time:
    I am looking only for the terminal value calculated by using the Gordon Growth Method.
    My values are the following with the calculator:

    Year 1 2 3 4 5
    FCF $1060 $1124 $1191 $1262 $1338
    DF 1.10 1.21 1.33 1.46 1.61
    DFCF $964 $929 $895 $864 $831
    Sum of DFCF $4480
    Discontinued perpetuity cash flow (DPCF) $11782

    Shortterm annually was 6%
    Discount rate 10%
    Long term Growth rate 3%

    Now I am seeking to check the DPCF of $11782.

    With the equation on your website --> (FCFF_5 * (1 + Long term GR))/( DR - LtGR)
    and by discounting it further to the prensence I calculate:

    DPCF = ((1338 * 1,03)/(0,1-0,03))/(1,1^5) = $12224,5

    $11782 != $12225
    I somewhere have a major flaw in my understanding!
    I probably cannot see the forrest with all this trees around!!!


    Thanks for your patience and your help!
  • Hey JH_Analyst

    OK - got it.

    Let's make sure I have this right:
    - Year 6 FCF = 1,378 (1,338*1.03)
    - Perpetuity Factor = 7% (10% - 3%)
    - This equals = 19,688 (1,378 / 7%)
    - Discount rate = 10%
    - Discounted perpetuity/terminal value = 12,225 (19,688 discounted @ 10% over 5 years)
    Which matches what you have

    If I discount the 19,688 by another year (i.e. 6 years), then it equals 11,113 - not a match
    If I don't add the 3% growth rate to the 1,338, then I get 11,868 (using the steps above)

    I wouldn't be surprised if this came down to some rounding in the buffetsbooks calculations
  • Okay, actually it's not a rounding mistake.
    I read the accounting book and their formula is as follows.

    1338 * 1.06 * 1.03 / 0.07 * 1/1.1^11

    So they use both growth rates as if they jump one period ahead. Its like I take the FFCF of period 11 with short term growth factor and then from there calculate the terminal value in period 12 . In my perception they do it because of a passive approach. But It lacks an explanation. Neither on the website nor in the book an explanation of the Equation is given.
  • It's a 4% difference in the terminal value. And in my opinion it's exactly one period of FCF they just leave out.
    They calculate for example t=1...5 and terminal value of t=7......infinity and leave out t=6

    Hope my logic is clear. Thanks for your answer!
  • GOT IT - nice to hear you found the issue :smile:
  • Hi all,

    I'm also new to this forum. I've got one question to ask regarding DCF: What if the average free cash flow value is minus? I can't do the calculation because the calculator couldn't compute the number. What does a minus value signify?

    Thanks in advance!
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