I thought after playing with numbers for more than 9 months, I've got a little experience, however small, to talk about the perils of the calculation of intrinsic value. There are so many ways that we can evaluate the intrinsic value. In our need to place a certain number to our uncertain analysis, there could be a risk where the investor places too much confidence on what I call GIGO - Garbage In Garbage Out. However, armed with this magic number generated from fundamental data (that is, from the financial statements), the investor feels more confident than is justified and thus begins his (possible) sorrowful journey with the company.

I used to believe greatly on the certainty of the numbers, believing it will give me the ultimate decision to decide if a company's price is worthy of its value. It couldn't be further from the truth when the real test of investor - bear market - begins to maul down all the calculations made.

Here's an example of how an investor could 'justify' his purchase.

Company A had the following data:

Impressive! Pretty good ROE of around 17.5% averaged over 4 years, high gross margins of around 24%, PATMI margins of 20% and had very low debts ratio of 20 to 30% compared to equity. Closing at $1.750 today, the investor almost jumps out of joy when he realised that the company also gave dividend, amounting to a dividend yield of 8.5% (inclusive of specials and based on FY07)!

Mr. Investor immediately logged in to his online brokerage account and started keying in his order when he suddenly remembered that as an investor, he ought to at least do out a DCF or other forms of valuation so that he can find out the price to value discrepancy. Didn't Benjamin Graham and Warrent Buffett keep harping about margin of safety? How could he, a practioner of safe and long term investing, forgot to do that? Tsk tsk.

So on he went, opening his excel and begin putting in the numbers. Since long term is 5 years to him, he started putting in the DCF with EPS for the next 5 years, projected at an EPS growth rate of 20% and discount rate of 4%. Mr.Investor used an EPS growth rate of 20% because from historical data, the PATMI per share is growing at a CAGR of 19.5% over 4 years, so it's reasonable to project this for another 5 years. 4% discount rate is because the long term SG treasury bonds is around 4%. Since Mr. Investor did not do out terminal value, which accounts for a huge bulk of the value, he thinks that it's very conservative already.

Here's what Mr.Investor did:

The current closing price is $1.75 but the intrinsic value is $1.25. Company A is actually overvalued! Mr.Investor tried checking the inputs for any mistakes but couldn't find any. As such, he reasoned that there is no reason why the earnings will stop after 5 years, so he could be too conservative. He decided to extend his timeframe to 10 years.

Here's what Mr. Investor did after extending to 10 years:

Now, the intrinsic value changes to $3.82. With current closing price of $1.75, that represents a margin of safety of 54.2%! Being a skeptic, Mr. Investor started thinking. If it is grossely undervalued, why is everyone not buying it? He started to feel insecure about his figures. Perhaps the EPS growth rate of 20% is too high. Over 10 years, it's highly unlikely that earnings will continue to grow at such a high rate, he reasoned. As such, he decides to do another valuation. This time, the EPS growth rate is changed to 10% (though the historical CAGR over 4 years is 19.5%) - conservative estimate!

Here goes:

Ahh..this sounds more reasonable, at $2.21. The current price gives a margin of safety of nearly 20%. For such a high quality company with low debts, strong margins and good yields, it's worth it! Besides, Mr. Investor already had 3 layers of safety margin:

a. The valuation assumes that the company folds over in 10 years. Since it is unlikely, the intrinsic value is supposedly higher than the calculated one. There is no perpetual or terminal value, which forms the bulk of the DCF value. As such, the value erred on the conservative side.

b. EPS growth rate of 10% is so much lower than historical growth rate of 19.5%. Conservative again.

c. Mr. Investor bought at a 20% discount to intrinsic value. As such, he had a 20% buffer against unforeseeable adverse circumstances.

Mr. Investor happily bought it, satisfied of having done a thorough analysis to Company A before buying. He can sleep soundly everyday knowing that he had done his valuation and bought with several layers of margin. So what's wrong with this?

With the right combination of earnings growth rate, discount rates and period of investment, DCF can make any purchase at any price justified, even with a margin of safety built into it.

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## 15 comments :

LP,

Nice post ! That's one reason why I don't use DCF, because it assumes a terminal value ! Companies have an infinite life (look at Boustead, 180 years and still going strong !), and to assume a terminal value based on 5 or 10 years is unrealistic at best; inaccurate at worst.

Also, stuff like EPS growth rate into the future are purely hypothetical and cannot be based on past growth data (a company tends to grow faster initially but will slow down as it gets larger and "clumsier"). Also, ROE gets harder and harder to remain high as the company's equity base increases with successive years of profit. The discount rate one uses is another variable.

So with so many "problems" with DCF, it's no wonder the intrinsic values can differ so much !

This is why I advise factoring in intangibles and qualitative aspects too, to justify a purchase. Relying on numbers alone to invest would be suicide as numbers sometimes don't tell the full story.

Cheers,

Musicwhiz

Hi mw,

Actually the terminal value assumes that the company will continue growing at a certain growth rate to infinity. I don't like to include that because it's already hard to determine the growth rate of 5 to 10 years, why make it harder to project the growth rate to infinity? As such, I'm happy to treat the company as having a limited shelf life.

I do agree that the EPS growth rate cannot be extrapolated from past growth rates, otherwise companies like IBM would have shot up to the sky already! There's an element of prediction here which makes the intrinsic value based on DCF a range, rather than an exact numbers. Nevertheless, we can still get a rough range using different scenario of EPS growth. The different scenarios itself will be an invaluable tool in gauging the value of the company when they grow at different pace.

Relying on numbers really would be suicidal - which is the point of this post. I think one needs to check on the figures itself, to see if it makes sense. For example, if the EPS projected in 2017 is so and so, we can find out the revenues that need to be be incurred in order to have that amount of EPS. Sometimes, based on current market share, it's impossible to have that kind of revenue! That's what the numbers fail to tell you.

Thks for your comments!

Hi LP/MW,

I think u folks have highlighted the prb with DCF very well. I'm not sure if computing a range with DCF is even reasonable though, given that the discrepancy can be huge depending on your assumptions.

Just wondering... If u folks distrust DCF, what other valuation methods do you usually use to compute the intrinsic value?

Thanks for enlightening a newbie.

- caseyc

Hi caseyc,

I still use it though :) It's good to know a rough figure of that value, as long as the inputs are not aggressively optimistic nor pessimistic.

I use PE too, you can look at my post here: http://bullythebear.blogspot.com/2008/09/perils-of-pe.html

I still think my concept of:

Portfolio return = 20% alpha + 80% beta.

A good stock picker may outperform the market, say his portfolio is down 30% while the market is down 40%.

But what's the point? End of the day we retail investors just want to earn absolute return.

As long as the overall market is weak, this 80% beta pull the portfolio return down drastically.

I still think cash is king.

I had written this article today:

http://www.commoditiestradingpro.com/2008/09/where-is-s-500-index-heading-to-part-2.html

Thks brendan, read your post. I think it's true that stock market is +ve correlated to interest rates. This is funny considering how textbooks say otherwise.

It's the usual academics vs practitioners kind of battle again. I'll believe the practitioners anytime.

That's the way man!

Hi

Referring to Company A revenue's CAGR of 11.4%, did u use number of periods (n) as 3 or 4?

Hi Shud'n,

This is how I calculated:

CAGR = ((64747/46894)^(1/3) - 1)*100

= (1.1135-1)*100

= 11.35%

= 11.4% (3 sf)

I used the number of periods as 3 because 2004 to 2005 is the first period, 2005 to 2006 is the second, 2006 to 2007 is the third.

LP, this is where I get confused. Isn't FY2004 from 2003-2004, which is already 1 year? Pls enlighten me. Other companies will be using 3 years as well if given this case as I saw their annual reports.

Hi Shudn'n,

You misunderstood me. I am merely answering your question as to whether the period (n is 3 or 4. I didn't say that FY2004 is from 2004 to 2005. As to the actual financial year, it varies from company to company, but it has nothing to do with the calculation of CAGR. Some company start their financial year in June, some start in Dec.

The n in the formula refers to the number of intervals between the data pts. 2004 to 2005 is the first interval, 2005 to 2006 is the second interval, 2006 to 2007 is the third interval, hence n is 3. I did not mean to say that the FY04 starts from 2004 to 2005. The actual period where the financial year starts is immaterial to the calculation of CAGR as long as they did not change the start and end date of their financial year.

To make it crystal clear, consider the sequence:

10,18,22,23,34,35

How many intervals are there?

There are 5 intervals. The calculation of CAGR would be:

[(35/10)^(1/5)-1]x100

=28.47%

The calculation is the same as this sequence:

10,15,20,25,30,35 too.

LP,

Ok from 2004-2007, it should be:

1st period: 1st jan 2004 - 31 dec 2004

2nd period: 1st jan 2005 - 31 dec 2005

3rd period: 1st jan 2006 - 31 dec 2006

4th period: 1st jan 2007 - 31 dec 2007

n = number of periods right? So, isn't it 4?

Using a real-life example, let's say a student starts his secondary school education in 2004. In 2004, he's in Sec 1. 2005-Sec 2. 2006-Sec 3. 2007-Sec 4. So, it's a total of 4 years of secondary school education even though there are only 3 intervals.

Pls correct me if I'm wrong.

Hi Shud'n,

"Ok from 2004-2007, it should be:

1st period: 1st jan 2004 - 31 dec 2004

2nd period: 1st jan 2005 - 31 dec 2005

3rd period: 1st jan 2006 - 31 dec 2006

4th period: 1st jan 2007 - 31 dec 2007

n = number of periods right? So, isn't it 4? "

If you want to treat it this way, then you need the data pt on 31-dec 2003. 5 data pts will then give you 4 intervals.

"Using a real-life example, let's say a student starts his secondary school education in 2004. In 2004, he's in Sec 1. 2005-Sec 2. 2006-Sec 3. 2007-Sec 4. So, it's a total of 4 years of secondary school education even though there are only 3 intervals."

Yes, I agree with you that there are 4 years but 3 intervals. That doesn't change the fact that when using the formula, you should treat n as the intervals, not the no. of years. Intervals, again, is defined as the spaces between the data pts.

Have you seen how others calculate?

Here's a few:

1. http://en.wikipedia.org/wiki/Compound_annual_growth_rate

2. http://allfinancialmatters.com/2006/06/08/how-to-compute-compound-annual-growth-rate-cagr/

For e.g 2, $10,000 is actually at year 1985 because that's the year where they use the starting value in the calculation.

LP now I get it! Thank you so much! This has always been bugging me for some time already!

Hi Shud'n,

Glad to be of help :)

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