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What worked in the market from 1998-2008? Intrinsic Value, Discounted Cash Flow and Margin of Safety

November 30, 2008
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gurufocus

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Do business quality and stock valuation still matter in investing? In this kind of stock market it seems not. Let’s ignore the stock market and focus on what works in long term value investing.

This is Part III of the series of our back testing study “What worked in the market from 1998-2008?” In Part I we found that companies with predictable revenues and earnings outperform the market averages, they also suffer lower probability of loss, hence we introduced the concept of Predictability Rank. In Part II we reported that the undervalued predictable companies outperformed the market by even greater margins. In this article (Part III) we would like to discuss discounted cash flow model and margin of safety. We also analyze the correlations between the DCF model, margin of safety and the performances of the stocks. We try to find out what is driving the long term performance of stocks. Discounted cash flow model and margin of safety are discussed in details.

Part I: What worked in the market from 1998-2008? Part I: Predictability Rank
Part II: What worked in the market from 1998-2008? Part II: Role of Valuations

Discounted cash flow Model (DCF)

Joe Ponzio at F Wall Street wrote an excellent series on using discounted cash flow model to calculate the intrinsic value of businesses. We will discuss the DCF model in more detail here, and this is the basis for our calculation of intrinsic value of businesses.

Compared with the valuation ratios such as P/E, P/S, P/B etc, DCF model is able to include both balance sheet value, future business earnings and earning growth. The factors that affect the value of business in DCF model are: book value, current free cash flow, business growth rate, and terminal value. We will discuss each factor below.

Just as pointed by Joe Ponzio, it only makes sense to calculate the intrinsic value for the companies that have predictable earnings. We will apply this to predictable companies only. http://www.gurufocus.com/predictable.php

Book Value (Shareholder’s Equity per share)

When you buy a company’s stock, you become a fractional owner of the business. If the company is liquidated after you buy, you are entitled to what the company owns net of its debt. This part is called shareholder’s equity.

Shareholder’s equity is certainly a part of business value. However, shareholder’s equity may overestimate or underestimate its real value. For instance, for a consumer electronics maker, the inventory on its book may overestimate its market value, because consumer electronics becomes obsolete quickly and their market value declines. For a company which makes regular socks, its inventory may reflect real value since the materials and products can maintain their values. Some times a real estate company’s book may underestimate the value of the real estate depending on when the company acquired the real estate.

The recent accounting rule of mark-to-market may change this, but we all know that market is not always efficient. (That is why we are here investing as value investors.) The book value of stocks may still deviate its underlying values.

A lot of company has an item called goodwill, which may come from the past acquisitions of the company. This part may not worth anything at the time of liquidation. Therefore, we use tangible book rather than the book for the book value calculation.

Future Business Earnings

As a fractional owner of the business, you are entitled to future business earnings. Instead of GAAP earnings, Warren Buffett emphasizes owner’s earnings, which is the net cash generated from the business. Cash earnings is the reported GAAP earnings plus non-cash expenses such as depreciation and amortization less the cash maintenance expense on equipment and properties, this can be very close to the free cash flow. For a long term consistently operated business, free cash flow is approximately equal to GAAP earnings.

Since we do not know how the business will grow in the future, there is a big assumption in the DCF model for the future business growth rate. This is why business predictability is important. It only makes sense to apply DCF models if the business has been growing consistently. Only for consistently growing business, it is more reasonable to assume it will be growing in the same manner for the coming years.

Assuming the business is earning E(0) dollar a year now, business growth rate is g, in n years, the business will earn this much:

E(n) = E(0) (1+g)n

Discount Rate

Apparently after n years the amount E(n) is not worth as much as the present value of E(n), because you can invest your money somewhere to earning a return (of course, if you earn a negative return, as many investors do, E(n) of n years later worth more than it is now). Therefore E(n) of n years later is only worth the amount that you can use to become E(n) in n years. Assuming you can generate a return of d per year, E(n) of n years later is worth this much now:

E(n)/(1+d)n

Since a positive return at d reduces the amount, d is called the discount rate. Therefore, if a business is earning E(0) now, it grows at the rate of g, n years later its earning is worth

E(0) (1+g)n/(1+d)n = E(0) [(1+g)/(1+d)]n

If the business can consistently do this for n years, the total earnings over the years will be:

E(0) {(1+g)/(1+d)+ [(1+g)/(1+d)]2+ [(1+g)/(1+d)]3+ …+ [(1+g)/(1+d)]n}

=E(0) x(1-xn)/(1-x)

where x=(1+g)/(1+d).

Discount rate is another big assumption that can severely affect the value obtained from the DCF model. A reasonable discount rate assumption should be at least the long term average return of the stock market, which is about 11%, because investors can always invest passively in an index fund and get an average return. Some investors use their expected rate of return, which is also reasonable. A typical discount rate can be anywhere between 10% - 20%.

The number of years to grow can also affect the DCF model result substantially. Again if a business had consistent growth over a long time, it is safer to assume it will do it over another extended period of time.

Terminal Value

Obviously no business can grow forever. At some point the growth will slow down. But the business still has its value as long as it is still generating cash for its owners. Assuming at the terminal stage business growth rate is t after n years of growth at the rate of g. The terminal value of the business will be

E(0) [(1+g)/(1+d)]n {(1+t)/(1+d)+ [(1+t)/(1+d)]2+ [(1+t)/(1+d)]3+ …}

=E(0)xn y/(1-y)

where y=(1+t)/(1+d)

__________________

Update (Jan. 2012): Terminal value calculation is limited to a certain number of years:

In our previous calculation of terminal value, the model assumes that the company will grow at the terminal growth rate forever. While the contribution from each of the far future years is small, they do add up. In this modification, we have set a default of 10 to the number of years that the company will grow at the terminal growth rate. After the terminal growth years the contribution will be cut to 0.

Terminal value=E(0) xny(1-ym)/(1-y), where y=(1+t)/(1+d),where m is the years of terminal growth; t is the terminal growth rate.

Terminal growth rate also affects the result of the DCF model. It is more reasonable to assume terminal rate at around long term inflation rate or less. To make the above equation converge, it is important to assume that terminal rate is smaller than the discount rate.

______________

Putting Everything Together

Putting everything together, based on DCF model, the intrinsic value of a business can be calculated with this equation:

Intrinsic Value = Future Earnings at Growth Stage + Terminal Value

= E(0) x(1-xn)/(1-x) + E(0)xn y/(1-y)

where x=(1+g)/(1+d), and y=(1+t)/(1+d)

Parameters:

E(0) – current earnings

g – growth rate
d – discount rate
t – growth rate at terminal state
n – number of years at the growth rate of g

If the growth rate is equal to terminal rate, which means that the company is growing at a constant rate forever, x=y in the above equation, which then becomes

Intrinsic Value = E(0) x(1-xn)/(1-x) + E(0)xn x(1-x)

= E(0) x/(1-x)

We have created a DCF Calculator for users. Hope you like it.

Error sources:

A business’s book value can overestimate or underestimate its value, depending on the industry that the company is in. Assumption of future growth rate, discount rate, terminal growth rate, and year of continuous growth can affect the calculated intrinsic value dramatically. Therefore, the calculations of the intrinsic value of businesses are only as accurate as the assumptions you have.

Margin of Safety

Once we get the intrinsic value of a business, and we always know the price of a stock, the margin of safety is defined as:

MOS = (Value – Price )/ Value

Margin of Safety is the other most important concept in value investing. What kind of Margin of Safety should you have in investing? The short answer is as high as possible. As we will show below, the investment return is actually positively correlated to the margin of safety investors have on the investment. Therefore, if you have an investment that you think you have enough margin of safety, everything else is equal, you should try to find another one that has even higher of margin of safety.

The Correlation of Stock Performances and Margin of Safety

In order to find out what is driving the stock performances of businesses, we bought a time machine which brought us to Jan. 1998. That time machine also told us how businesses would really perform over the next 10 or so years. We can use this information to calculate the intrinsic values of the businesses as of Jan. 1998.

Of course nowhere could we have bought this time machine, but this exercise helps us to understand the correlations between stock performances, the intrinsic value and margin of safety.

In the calculation of the intrinsic values of businesses, we assumed a discount rate of 12%. The tangible book values of the companies at 1998 are used as book values. The real business performance numbers such as earnings, free cash flows from 1998 to 2008 are used to calculate the value, also we assumed the terminal values of business are all 0.

The assumption of the terminal values is certainly very conservative. But in DCF models, the contribution from terminal values is generally small compared with book values and the discounted 10-year operation earnings.

When we use the free cash flow data to calculate the intrinsic value of the 2403 companies that have been continuously traded since 1998, the correlation between the investment performance and the margin of safety is shown below:

Chart 1: Annualized gain of 2400 stocks from 1998 to Sept. 2008 as a function of margin of safety calculated from discounted cash flow model

As expected, there is a clear statistical correlation between the annualized gain of the stocks and the margin of safety. The higher the margin of safety, the higher the annualized return over the past 10 years. If we just look at the predictable companies, i.e. the companies that have never lost money from 1998-2008, we see similar correlations, but clearly, the predictable companies have higher gain and lower probability of loss than the unpredictable companies, as we reported in the series of this research, Part I and Part II.

Chart 2: Annualized gain of stocks of Predictable Companies from 1998 to Sept. 2008 as a function of margin of safety calculated from discounted cash flow model

Although Warren Buffett said that when we look at companies’ earnings, we should look at owners’ earnings, that is the cash generated from the business instead of GAAP earnings. However, if we use company reported GAAP earnings data instead of free cash flow to calculate the intrinsic value, the correlation between the intrinsic value and the margin of safety is even stronger, as the data shows smaller standard deviation from the mean.

Chart 3: Annualized gain of 2400 stocks from 1998 to Sept. 2008 as a function of margin of safety calculated from discounted earnings model

Chart 4: Annualized gain of stocks of Predictable Companies from 1998 to Sept. 2008 as a function of margin of safety calculated from discounted earnings model

Chart below shows the median annualized gain of the predictable companies and all the companies using both the free cash flow and GAAP earnings for the calculations. Clearly, the predictable companies have much higher gains no matter which we use as earnings. A little surprise here is that GAAP earnings seems to work better in predict future earnings. That is, the performances of stocks have stronger corrections with the GAAP earnings than free cash flow.

Chart 5: Median gain of stocks with respect to margin of safety calculated from both free cash flow and GAAP earnings.

What We Have Learned

What have we learned from the study:

  1. GAAP earnings seem to have higher correlation with the stock performances than the free cash flow, as most value investors believed.
  2. The higher margin of safety you apply to your investment ideas, the higher discount the stock price is, the higher return you may achieve from this investment.
  3. Apply DCF model to predictable companies only.
  4. Be careful with the assumptions of discount rate and growth rate.

We applied the discounted free cash flow and discounted GAAP earnings to the top ranked predictable companies in our database, and calculated the intrinsic values of the these companies. We assumed a discount rate of 12%. The tangible book values of the business is used as the current book value. The growth rate for the next 10 years are assumed to be the same as the average growth rate of the past 10 years, and the terminal values of the businesses are ignored.

We calculated the intrinsic value using both discounted cash flows and discounted earnings. The margin of safety for each case is also calculated.

Assuming the growth rate of the next 10 years the same as the past 10 years may overestimate the intrinsic value, and ignoring the terminal value may underestimate it. This calculation should give a pretty good estimate of the relative margin of safety of these predictable companies. The list of the intrinsic value and margin of safety is here. It is for Premium Members only.

Related Articles:

Part I: What worked in the market from 1998-2008? Part I: Predictability Rank
Part II: What worked in the market from 1998-2008? Part II: Role of Valuations

Links:

These features are for Premium Members only. Take a Free Trial of GuruFocus Premium Membership.

 

About the author:

gurufocus
GuruFocus - Stock Picks and Market Insight of Gurus

Rating: 2.9/5 (163 votes)

Comments

rozer
Rozer - 5 years ago
Thank you for an excellent post. Would it be possible to provide some examples showing your calculations? Concrete examples are the best way to provide instruction.

thanks again.
gurufocus
Gurufocus premium member - 5 years ago
Thank you Rozer!

Try these links:

Target DCF or JNJ
lsmith49
Lsmith49 - 5 years ago
I'm not sure i quite understand them charts. Annualized gain measured from -1 to 1? and Margin of safety measured in percent, right? Surely you would expect the annualized gain to also be measured in percent? Or am i missing something quite badly here, lol.
tmacpherson1966
Tmacpherson1966 premium member - 5 years ago
Great article. Thanks so much guys. This is really helpful.
richday101
Richday101 premium member - 5 years ago
> I'm not sure i quite understand them charts. Annualized

> gain measured from -1 to 1? and Margin of safety measured

> in percent, right? Surely you would expect the annualized

> gain to also be measured in percent? Or am i missing

> something quite badly here, lol.

Lsmith, Margin of Safety (MS) ranges from -1 to +1 and Annualized Expected Gain (AEG) is in perceentages ranging from -20% to +50% in the first 4 charts. If we look at Chart 5 which is the clearest with less points and scatter, for a MS=0.75 the average AEG=15%, for MS=0.50 the AEG=10%, and for MS=0.25 the AEG=5%. In other words, More margin of safety the more the expected return.
buffetteer17
Buffetteer17 premium member - 5 years ago
Nice article! I would quibble with one part of your value equation: Intrinsic Value = Book Value + Future Earnings at Growth Stage + Terminal Value.

I would substitute Excess Assets for Book Value, for several reasons.

- book value is often not reflective of current value, as you already pointed out

- much of the assets, esp. PP&E, are used to produce the cash flow and shouldn't be counted in addition to the cash flow

- a fresh competitor would need to replicate some of the current assets to start up a business, and it is the cost of this replication rather than the current book value that needs to be set aside as necessary assets to run the business.

To illustrate this, let's consider at the value of a simple copy shop. They own an expensive copying machine, do we include it in their intrinsic value? No, because without that copying machine, they would not be able to produce the cash flow. Look at it another way. If they didn't own a copying machine, they would have to lease one. The lease payments would reduce free cash flow. You are double counting if you add the cash flow and the value of the copying machine, unless you subtract the cash flow they could get by simply leasing out their machine.

On the other hand, they might own a valuable lot of commercial property. That we can include, to the extent that the value of such property exceeds what they would have to pay to buy a similar lot. Or they might have cash in the bank beyond what they need for working capital, which we could include in the intrinsic value.

Figuring excess assets precisely is hard, and often unnecessary, as future cash flows tend to greatly exceed excess assets. I would say excess assets are Current Market Value of Assets minus Cost to Replicate Capital Required to Operate. Sometimes it is easy to get a rough handle on this. Freightcar America (RAIL) is a small cap manufacturer of railroad cars. They have cash and other current assets of $336M and total long term liabilities $262M, a difference of $74M. Revenues are around $100M. The surely do not require $74M of working capital for a business of this size. I would happily include about $50-55M of the current assets in their intrinsic value. With 11 million shares out, it seems reasonable to start them off with $5/share before considering the free cash flow.
batbeer2
Batbeer2 premium member - 5 years ago
Statistics is not my thing so please forgive me my ignorance but I have two problems with the research.

1) Only the companies that are still around are included in the sample.

Lets say WCG is gone 2 years from now but CROX survives and is still here in 2018. The 2018 chart will only show CROX. The owner of the very cheap WCG who lost it all, is eliminated from the data. This would account in part for the fact that most of the cheap companies in the graph are winners. This would have some impact on the averages.

2) Annualised losses are presented on a linear axis with annualised gains. Well I for one think a 50% loss is more meaningfull than a 50% gain. IMO an exponential axis would better visualise reality.

To be fair, some takeovers where investors made a lot of money are probably eliminated and some partial liquidations where investors did well are represented as losses.

Or am I mistaken ?
mikeynet
Mikeynet premium member - 5 years ago
Folks, you can't claim both the book value (as a liquidation value) and the value of future cash flows!! You don't receive cash flow if you liquidate. You're double counting.
batbeer2
Batbeer2 premium member - 5 years ago
>> you can't claim both the book value (as a liquidation value) and the value of future cash flows!!


So what do you propose ? If a company has 1B of debt and 1B of cash flow how would IV be different from a similar company with 1B of exces cash assuming both have a bright future ?
batbeer2
Batbeer2 premium member - 5 years ago
IMO the sums make sense for a "non distress" company. You see if someone would want to buy the company as a whol he/she would have to pay for "exces" assets as well as future owner earnings. You buy a company with 1B of owner earnings for 10B and if for some reason it had 10B of cash on the balance sheet or some 15B building they don't really need, you have a pretty good deal.

IMHO the price an intelligent and informed owner would pay for the company as a whole is the definition of IV.
mplummer
Mplummer - 5 years ago
For your Terminal Value Calculator, you don't seem to multiple to numerator by (1+t)

Also, why do you discount by (1+d) twice? I thought the Terminal Value (FV) formula was

FCF(n) * (1+t) / (d-t)

where in your case FCF would be

E(0) * (1+g) ^ n

so the PV would be

[ E(0) * (1+g)^n * (1+t)] / [ (d-t) * (1+d)^n ]

What am I missing?

psimon55
Psimon55 - 5 years ago
To add or not add the co's tangible book value is a really tough question. As previous posts point out, tangible book would only turn into excess cash flows in the event of liquidation. But a business with a healthy balance sheet should be worth more than one with a crappy one. I think MSFT is a good example of how excess cash in the balance sheet enabled larger cash flows to the owners (it paid a special dividend). I would suggest two approaches:

1. Replace the terminal value (usually based on a 3-5% growth perpetuity) with the current tangible book value.

- OR -

2. Boost your FCF projections by your estimate of excess cash presently in the balance sheet spread over 5-10 years and still slap the terminal value at the end.

This way you are not double-counting and the balance sheet counts in your intrinsic value calculation. This site's suggestion to simply add the co's tangible book value without any discounting and adding a terminal value is plain wrong.
batbeer2
Batbeer2 premium member - 5 years ago
>> This site's suggestion to simply add the co's tangible book value without any discounting and adding a terminal value is plain wrong.

I disagree.

The assumption here is that the model for calculating IV should reflect a certain (real) proces. Newtons models (called laws) do not pass that test. The proces that makes an apple fall from a tree is still not well understood and is not reflected in the simplicity of Newtons model.

All we know is that Newtons laws under the right conditions have some use in predicting the speed of an apple in free fall. Important parameters (friction etc) are well known and are taken into account when neccesary (designing parachutes).

IMO your suggestions do not enhance the quality or accuracy of this DCF model.

All I ask of a model for the selection of stocks is that:

- It has use in deteriming if a stock a cheap or expensive.

- The parameters, variables and assumtions that go into the model are clear.

The model is fine by me.

Every single stock I have looked at in earnest has significant liabilities and/or assets that just don't show up in the financial statements.
psimon55
Psimon55 - 5 years ago
>>> All I ask of a model for the selection of stocks is that:

- It has use in deteriming if a stock a cheap or expensive.

- The parameters, variables and assumtions that go into the model are clear.

Wow, that's not asking much of a model. Then why not just use P/E or P/B? They pass your two parameters quite well.

Since the world's most successful investor does not plug in the co's tangible book value without any discounting, I will follow his reasoning. I am a CFA Charterholder and was taught to add in the book value without discounting. I see today that what I was taught was wrong. Going through Morningstar's methodology, I noticed that they do not add it either.

Of course this is a free country and folks should do what they feel is correct. Also, the more people that value assets based on lousy methods and impulse, the more inefficient the market will be which is great for all of us who know what we are doing.

Have fun and prosper.
investdata
Investdata - 5 years ago
sir thanks for the work well done, but the process of computing this DCM is long and complicated. what are the items one can pick from the company balance sheet and PAT reports.
Evan
Evan - 5 years ago
To the author of this study,

Why did you limit your sample to just ten years? It seems like you put a lot of time and effort into the study, which is good, but the size of your sample is so small that it might (might) not be a good representation of what works generally in investing.
batbeer2
Batbeer2 premium member - 5 years ago
>> Then why not just use P/E or P/B? They pass your two parameters quite well.

Do they ?
LUIS FELIPE AHUMADA
LUIS FELIPE AHUMADA - 4 years ago
A DCF calculation is exactly that - a model that discounts cashflows. The cashflows are the result of the earnings power of the assets; so adding book value is double counting. If there is excess cash or other assets that aren't necessary for the business to operate and produce the projected cashflow, then and only then can those assets be added to the calculation. A DCF of unlevered cashflows (before interest payments) will give you the enterprise value (EV) of the operating assets of the firm - this calculation should be compared with the market's EV = Net Debt (Debt - excess cash) + Mkt Cap, to determine if the company is under / over-valued. In theory one could subtract the value of non-operating assets on the balance sheet in the market EV calculation in order to account for excess assets, as well; but one should not subtract the entire tangible net asset value since they are needed to operate the firm and produce the cashflows.
hondafan78
Hondafan78 - 4 years ago
Time and time again, value investing proves it is the best way for most investors to make gains! Margin of Safety!!!! Buy at a discount!!! Those slogans are good advice in any economic climate.
dos122
Dos122 - 4 years ago
This is not how a discounted cash flow model is done.

"Cash earnings is the reported GAAP earnings plus non-cash expenses such as depreciation and amortization less the cash maintenance expense on equipment and properties, this can be very close to the free cash flow. For a long term consistently operated business, free cash flow is approximately equal to GAAP earnings."

To clarify, owner earnings is not very close to free cash flow, it is free cash flow. The last statement in this is a generalization that can really get you into trouble. If free cash flow was apprx. close to EPS, then it wouldn't be a necessary calculation. "Earnings" is a foggy subject and the classification as to what "earnings" is ranges from company to company. The reason we use free cash flow as a basis for calculating this model is because cash cannot be faked, there's no cloud as to what constitues cash: cash is cash. (Source: The Essays of Warren Buffet - Lessons for Corporate America)

If the greatest investor in the world warns us against using earnings or EPS as a measure for corporate performance, why is this website using this Fair Value estimator using EPS as a starting point?

superguru
Superguru - 4 years ago
Gurufocus,

"When we use the free cash flow data to calculate the intrinsic value of the 2403 companies..."

where can I see intrinsic value for companies using free cash flow on gurufocus site?
gurufocus
Gurufocus premium member - 4 years ago


"When we use the free cash flow data to calculate the intrinsic value of the 2403 companies..."

where can I see intrinsic value for companies using free cash flow on gurufocus site?
It only makes sense to use the DCF model if the company business is predictable, because we have to assume the future growth rates. The results for the Predictable companies are shown in Undervalued Predictable Companies

[/i]Dos122[i] wrote: If the greatest investor in the world warns us against using earnings or EPS as a measure for corporate performance, why is this website using this Fair Value estimator using EPS as a starting point?

We certainly understand that DCF model uses free cash flow. However, as described in detail in this article, our backtesting study found that in the 10-year period the performances of the stocks have better correlation with the discount earning model than the discount cash flow model, that is why we use earning as the starting point for fair value calculation.

But you can always put free cash flow number in if you like to use it.
Benoit
Benoit premium member - 4 years ago


Hi,

The fair value calculated by your DCF model is the fair value of a stock for now, for the next 12 months, in 12 months, or ...

Thank you.
filosofem
Filosofem - 4 years ago
The total earnings formula

E(0) (1-xn+1)/(1-x) have a error.

Corrected variant is


E(0) (1-xn)/(1-x)
filosofem
Filosofem - 4 years ago


This TV formula is also not correct:

E(0)(1+g)(1+t)/[(1+d)2n (d-t)]


The results, calculated by the DCF calculator and this formula, does not match.
gbtjom
Gbtjom - 4 years ago
The TV formula is incorrect....from a mathematics stand point.

As Mplummer pointed out more than a year ago, the TV is discounted TWICE in the formula. That is incorrect. I think the correct equation should be:

TV = E(0)(1+g)/[(1+d)n (d-t)]

You don't multiply by (1+ t) nor do you discount twice (the 2n exponent). Therefore, the DCF Calculator is also incorrect. If I'm wrong can someone please explain.

The other equation is incorrect as well for Discount Rate:

E(0) (1-xn+1)/(1-x) should have been : E(0) (1-x(n+1))/(1-x) The exponent should have been (n+1)
gurufocus
Gurufocus premium member - 4 years ago
Dear Mplummer and Gbtjom,

For the terminal value, we did not discount twice, we just discount in two steps. Since the terminal value is calculated from the end of the growth period, therefore, we need to discount first to the end of the growth period, then we need discount from the end of the growth period to current.

By doing the two step discount, we bring all numbers to current dollar.

We did have a type in the formula, as pointed by Filosofem, we have corrected it.

thank you for the comment.

gbtjom
Gbtjom - 4 years ago
Hello and thanks for responding.

"we need to discount first to the end of the growth period, then we need discount from the end of the growth period to current."

I guess I'm uncertain as to what you are trying to do as I don't follow your above quote. I assumed that the way this normally works is that you have a high growth period for n years at "g". At the end of the n years you lower the growth rate to something less "t". But I guess my question is what is the period of the growth rate at "t"? I assumed looking at your formula that is was forever (in perpetuity) because the denominator has (d-t) in it. A perpetuity that grows at "t" and is discounted by "d" with an after first year payment of "C" is equal to : C/(d-t). So if that is the case then that amount needs to be discounted back "n" years from there. So you'd have:

PV = E(0)*(1+t)/[(1+d)^n * (d-t)] where E(0) * (1+t) is the "after first year payment C", (1+d)^n is the discount from year "n" back to the present and the (d-t) is the perpetuity. BTW, I was incorrect above where I said it was (1+g)...it should have been (1+t).

I guess the bottom line from my POV is that you don't need to do the discount in sections since the (d-t) is a discount from "forever" to "n" years from now...it's already done. THEN you discount using (1+d)^n to get to the present. :D

investdata
Investdata - 4 years ago
Earnings remains a vital parmeter for measuring companies strenght because profitability drives price and at the same determines what accures to investors in form of dividend.
batbeer2
Batbeer2 premium member - 4 years ago
Earnings remains a vital parmeter for measuring companies strenght because profitability drives price and at the same determines what accures to investors in form of dividend.

Ehm..... the problem with that is that the record is based on PAST earnings while it is FUTURE profitability that drives price from now on.
filosofem
Filosofem - 4 years ago
E(0) (1-xn+1)/(1-x) should have been : E(0) (1-x(n+1))/(1-x) The exponent should have been (n+1)

I think, corrected variant of formula is:

CashFlowValue = E(0) (1-x(n+1))/(1-x) - E(0)

Because we sum next n-year cash flows, excluding E(0).

For terminal value we can also use this formula:

TerminalValue = E(10)(1-x(n+1))/(1-x) - E(10)

Finally:

IntrinsicValue = BookValue + CashFlowValue + TerminalValue

cm1750
Cm1750 premium member - 4 years ago
IntrinsicValue = BookValue + CashFlowValue + TerminalValue




I hate to beat a dead horse, but adding BV is just wrong. Anyone who has taken a basic finance course should know this, and even if not, it is common sense.

Buffetteer did a good job explaining why with his copy shop example. You can add the market value of excess assets - for example, if the copy shop had $5,000 of artwork that contributed no ongoing FCF, you can add that back, as well as excess cash over that needed to run the business.

Gurufocus should also remove BV from its DCF formula and have a place where a user can enter excess assets.
Peticolas
Peticolas - 1 year ago
The strong result here seems to be that predictable companies outperform unpredictable companies across the board. Margin of safety, however calculated, seems to matter not at all until you get to margins of safety above .2. At that point, they seem to matter.

Interesting to look at the charts. I suspect a regression of any of those charts would yield insignificant results (except for the predictable vs others). Yet there is still some information in the charts.
mjreige
Mjreige - 8 months ago
Would you please provide the latest variation of the formula with all the corrections made to the Terminal Value, etc.
rrurban
Rrurban premium member - 6 months ago

There are many opinions on whether to add back book value or tangible book value on top of the discounted cash flow value. My opinion is to at least add back LIQUIDATION VALUE onto your DCF value. Then to be safe, do not add in the terminal DCF value. I prefer a 15% discount rate and then a 25-50% MOS based on the risks of the business, competitive advantages and predictability of cash flows.

nhadautu20
Nhadautu20 - 2 months ago

Thanks so much

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