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

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

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

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!

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

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.

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!

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!