V8彩票注册登陆o business quality and stock valuation still matter in investing? V8彩票注册登陆n this kind of stock market it seems not. V8彩票注册登陆et’s ignore the stock market and focus on what works in long term value investing.

V8彩票注册登陆his is V8彩票注册登陆art V8彩票注册登陆V8彩票注册登陆V8彩票注册登陆 of the series of our back testing study “V8彩票注册登陆hat worked in the market from 1998-2008?” V8彩票注册登陆n V8彩票注册登陆art V8彩票注册登陆 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 V8彩票注册登陆redictability V8彩票注册登陆ank. V8彩票注册登陆n V8彩票注册登陆art V8彩票注册登陆V8彩票注册登陆 we reported that the undervalued predictable companies outperformed the market by even greater margins. V8彩票注册登陆n this article (V8彩票注册登陆art V8彩票注册登陆V8彩票注册登陆V8彩票注册登陆) we would like to discuss discounted cash flow model and margin of safety. V8彩票注册登陆e also analyze the correlations between the V8彩票注册登陆V8彩票注册登陆V8彩票注册登陆 model, margin of safety and the performances of the stocks. V8彩票注册登陆e try to find out what is driving the long term performance of stocks. V8彩票注册登陆iscounted cash flow model and margin of safety are discussed in details.

V8彩票注册登陆art V8彩票注册登陆: **V8彩票注册登陆hat worked in the market from 1998-2008? V8彩票注册登陆art V8彩票注册登陆: V8彩票注册登陆redictability V8彩票注册登陆ank**

V8彩票注册登陆art V8彩票注册登陆V8彩票注册登陆: **V8彩票注册登陆hat worked in the market from 1998-2008? V8彩票注册登陆art V8彩票注册登陆V8彩票注册登陆: V8彩票注册登陆ole of V8彩票注册登陆aluations**

### V8彩票注册登陆iscounted cash flow V8彩票注册登陆odel (V8彩票注册登陆V8彩票注册登陆V8彩票注册登陆)

V8彩票注册登陆V8彩票注册登陆oe V8彩票注册登陆onzio at V8彩票注册登陆 V8彩票注册登陆all V8彩票注册登陆treet wrote on using discounted cash flow model to calculate the intrinsic value of businesses. V8彩票注册登陆e will discuss the V8彩票注册登陆V8彩票注册登陆V8彩票注册登陆 model in more detail here, and this is the basis for our calculation of intrinsic value of businesses.

V8彩票注册登陆V8彩票注册登陆ompared with the valuation ratios such as V8彩票注册登陆/V8彩票注册登陆, V8彩票注册登陆/V8彩票注册登陆, V8彩票注册登陆/V8彩票注册登陆 etc, V8彩票注册登陆V8彩票注册登陆V8彩票注册登陆 model is able to include both balance sheet value, future business earnings and earning growth. V8彩票注册登陆he factors that affect the value of business in V8彩票注册登陆V8彩票注册登陆V8彩票注册登陆 model are: book value, current free cash flow, business growth rate, and terminal value. V8彩票注册登陆e will discuss each factor below.

V8彩票注册登陆ust as pointed by V8彩票注册登陆oe V8彩票注册登陆onzio, it only makes sense to calculate the intrinsic value for the companies that have predictable earnings. V8彩票注册登陆e will apply this to predictable companies only. http://xtrmy.icu/predictable.php

**V8彩票注册登陆ook V8彩票注册登陆alue (V8彩票注册登陆hareholder’s V8彩票注册登陆quity per share) **

** **V8彩票注册登陆hen you buy a company’s stock, you become a fractional owner of the business. V8彩票注册登陆f the company is liquidated after you buy, you are entitled to what the company owns net of its debt. V8彩票注册登陆his part is called shareholder’s equity.

V8彩票注册登陆hareholder’s equity is certainly a part of business value. V8彩票注册登陆owever, shareholder’s equity may overestimate or underestimate its real value. V8彩票注册登陆or 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. V8彩票注册登陆or a company which makes regular socks, its inventory may reflect real value since the materials and products can maintain their values. V8彩票注册登陆ome times a real estate company’s book may underestimate the value of the real estate depending on when the company acquired the real estate.

V8彩票注册登陆he recent accounting rule of mark-to-market may change this, but we all know that market is not always efficient. (V8彩票注册登陆hat is why we are here investing as value investors.) V8彩票注册登陆he book value of stocks may still deviate its underlying values.

V8彩票注册登陆 lot of company has an item called goodwill, which may come from the past acquisitions of the company. V8彩票注册登陆his part may not worth anything at the time of liquidation. V8彩票注册登陆herefore, we use tangible book rather than the book for the book value calculation.

**V8彩票注册登陆uture V8彩票注册登陆usiness V8彩票注册登陆arnings **

V8彩票注册登陆s a fractional owner of the business, you are entitled to future business earnings. V8彩票注册登陆nstead of V8彩票注册登陆V8彩票注册登陆V8彩票注册登陆V8彩票注册登陆 earnings, V8彩票注册登陆arren V8彩票注册登陆uffett emphasizes owner’s earnings, which is the net cash generated from the business. V8彩票注册登陆ash earnings is the reported V8彩票注册登陆V8彩票注册登陆V8彩票注册登陆V8彩票注册登陆 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. V8彩票注册登陆or a long term consistently operated business, free cash flow is approximately equal to V8彩票注册登陆V8彩票注册登陆V8彩票注册登陆V8彩票注册登陆 earnings.

V8彩票注册登陆V8彩票注册登陆ince we do not know how the business will grow in the future, there is a big assumption in the V8彩票注册登陆V8彩票注册登陆V8彩票注册登陆 model for the future business growth rate. V8彩票注册登陆his is why business predictability is important. V8彩票注册登陆t only makes sense to apply V8彩票注册登陆V8彩票注册登陆V8彩票注册登陆 models if the business has been growing consistently. V8彩票注册登陆nly for consistently growing business, it is more reasonable to assume it will be growing in the same manner for the coming years.

V8彩票注册登陆ssuming the business is earning *V8彩票注册登陆(0)* dollar a year now, business growth rate is *g, *in *n* years, the business will earn this much:

*V8彩票注册登陆(n) = V8彩票注册登陆(0) (1+g) ^{n} *

**V8彩票注册登陆iscount V8彩票注册登陆ate **

V8彩票注册登陆pparently after *n* years the amount *V8彩票注册登陆(n)* is not worth as much as the present value of *V8彩票注册登陆(n)*, because you can invest your money somewhere to earning a return (of course, if you earn a negative return, as many investors do, *V8彩票注册登陆(n)* of n years later worth more than it is now). V8彩票注册登陆herefore *V8彩票注册登陆(n)* of *n* years later is only worth the amount that you can use to become *V8彩票注册登陆(n)* in *n* years. V8彩票注册登陆ssuming you can generate a return of *d* per year, *V8彩票注册登陆(n)* of *n* years later is worth this much now:

*V8彩票注册登陆(n)/(1+d) ^{n}*

V8彩票注册登陆ince a positive return at d reduces the amount, d is called **the discount rate**. V8彩票注册登陆herefore, if a business is earning *V8彩票注册登陆(0)* now, it grows at the rate of g, *n* years later its earning is worth

*V8彩票注册登陆(0) (1+g) ^{n}/(1+d)^{n} = V8彩票注册登陆(0) [(1+g)/(1+d)]^{n}*

V8彩票注册登陆f the business can consistently do this for n years, the total earnings over the years will be:

V8彩票注册登陆(0) {*(1+g)/(1+d)+ [(1+g)/(1+d)] ^{2}+ [(1+g)/(1+d)]^{3}+ …+ [(1+g)/(1+d)]^{n}} *

*=V8彩票注册登陆(0) x(1-x ^{n})/(1-x)*

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

V8彩票注册登陆iscount rate is another big assumption that can severely affect the value obtained from the V8彩票注册登陆V8彩票注册登陆V8彩票注册登陆 model. V8彩票注册登陆 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. V8彩票注册登陆ome investors use their expected rate of return, which is also reasonable. V8彩票注册登陆 typical discount rate can be anywhere between 10% - 20%.

V8彩票注册登陆he number of years to grow can also affect the V8彩票注册登陆V8彩票注册登陆V8彩票注册登陆 model result substantially. V8彩票注册登陆gain 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.

**V8彩票注册登陆erminal V8彩票注册登陆alue **

V8彩票注册登陆bviously no business can grow forever. V8彩票注册登陆t some point the growth will slow down. V8彩票注册登陆ut the business still has its value as long as it is still generating cash for its owners. V8彩票注册登陆ssuming at the terminal stage business growth rate is *t *after n years of growth at the rate of *g*. V8彩票注册登陆he terminal value of the business will be

*V8彩票注册登陆(0) [(1+g)/(1+d)] ^{n} {(1+t)/(1+d)+ [(1+t)/(1+d)]^{2}+ [(1+t)/(1+d)]^{3}+ …}*

* **=V8彩票注册登陆(0)x ^{n} y/(1-y)*

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

V8彩票注册登陆__________________

**V8彩票注册登陆pdate** (V8彩票注册登陆an. 2012): V8彩票注册登陆erminal value calculation is limited to a certain number of years:

V8彩票注册登陆n our previous calculation of terminal value, the model assumes that the company will grow at the terminal growth rate forever. V8彩票注册登陆hile the contribution from each of the far future years is small, they do add up. V8彩票注册登陆n this modification, we have set a default of 10 to the number of years that the company will grow at the terminal growth rate. V8彩票注册登陆fter the terminal growth years the contribution will be cut to 0.

*V8彩票注册登陆erminal value**=V8彩票注册登陆(0) x ^{n}y(1-y^{m})/(1-y), *where

*y=(1+t)/(1+d),where m is the years of terminal growth; t is the terminal growth rate.*

* *V8彩票注册登陆erminal growth rate also affects the result of the V8彩票注册登陆V8彩票注册登陆V8彩票注册登陆 model. V8彩票注册登陆t is more reasonable to assume terminal rate at around long term inflation rate or less. V8彩票注册登陆o make the above equation converge, it is important to assume that terminal rate is smaller than the discount rate.

V8彩票注册登陆______________

**V8彩票注册登陆utting V8彩票注册登陆verything V8彩票注册登陆ogether **

V8彩票注册登陆utting everything together, based on V8彩票注册登陆V8彩票注册登陆V8彩票注册登陆 model, the intrinsic value of a business can be calculated with this equation:

*V8彩票注册登陆ntrinsic V8彩票注册登陆alue = V8彩票注册登陆uture V8彩票注册登陆arnings at V8彩票注册登陆rowth V8彩票注册登陆tage + V8彩票注册登陆erminal V8彩票注册登陆alue *

* **= V8彩票注册登陆(0) x(1-x ^{n})/(1-x) + V8彩票注册登陆(0)x^{n} y/(1-y)*

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

V8彩票注册登陆V8彩票注册登陆arameters:

V8彩票注册登陆V8彩票注册登陆(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 *

V8彩票注册登陆f 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

*V8彩票注册登陆ntrinsic V8彩票注册登陆alue **= V8彩票注册登陆(0) x(1-x ^{n})/(1-x) + V8彩票注册登陆(0)x^{n} x(1-x)*

= * V8彩票注册登陆(0) x/(1-x)*

V8彩票注册登陆e have created a V8彩票注册登陆V8彩票注册登陆V8彩票注册登陆 V8彩票注册登陆alculator for users. V8彩票注册登陆ope you like it.

### V8彩票注册登陆rror sources:

V8彩票注册登陆V8彩票注册登陆 business’s book value can overestimate or underestimate its value, depending on the industry that the company is in. V8彩票注册登陆ssumption of future growth rate, discount rate, terminal growth rate, and year of continuous growth can affect the calculated intrinsic value dramatically. V8彩票注册登陆herefore, the calculations of the intrinsic value of businesses are only as accurate as the assumptions you have.

### V8彩票注册登陆argin of V8彩票注册登陆afety

V8彩票注册登陆nce we get the intrinsic value of a business, and we always know the price of a stock, the margin of safety is defined as:

*V8彩票注册登陆V8彩票注册登陆V8彩票注册登陆 = (V8彩票注册登陆alue – V8彩票注册登陆rice )/ V8彩票注册登陆alue *

V8彩票注册登陆argin of V8彩票注册登陆afety is the other most important concept in value investing. V8彩票注册登陆hat kind of V8彩票注册登陆argin of V8彩票注册登陆afety should you have in investing? V8彩票注册登陆he short answer is as high as possible. V8彩票注册登陆s we will show below, the investment return is actually positively correlated to the margin of safety investors have on the investment. V8彩票注册登陆herefore, 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.

### V8彩票注册登陆he V8彩票注册登陆orrelation of V8彩票注册登陆tock V8彩票注册登陆erformances and V8彩票注册登陆argin of V8彩票注册登陆afety

V8彩票注册登陆n order to find out what is driving the stock performances of businesses, we bought a time machine which brought us to V8彩票注册登陆an. 1998. V8彩票注册登陆hat time machine also told us how businesses would really perform over the next 10 or so years. V8彩票注册登陆e can use this information to calculate the intrinsic values of the businesses as of V8彩票注册登陆an. 1998.

V8彩票注册登陆f 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.

V8彩票注册登陆n the calculation of the intrinsic values of businesses, we assumed a discount rate of 12%. V8彩票注册登陆he tangible book values of the companies at 1998 are used as book values. V8彩票注册登陆he 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.

V8彩票注册登陆he assumption of the terminal values is certainly very conservative. V8彩票注册登陆ut in V8彩票注册登陆V8彩票注册登陆V8彩票注册登陆 models, the contribution from terminal values is generally small compared with book values and the discounted 10-year operation earnings.

V8彩票注册登陆hen 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:

*V8彩票注册登陆hart 1: V8彩票注册登陆nnualized gain of 2400 stocks from 1998 to V8彩票注册登陆ept. 2008 as a function of margin of safety calculated from discounted cash flow model *

V8彩票注册登陆V8彩票注册登陆s expected, there is a clear statistical correlation between the annualized gain of the stocks and the margin of safety. V8彩票注册登陆he higher the margin of safety, the higher the annualized return over the past 10 years. V8彩票注册登陆f 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, V8彩票注册登陆art V8彩票注册登陆 and V8彩票注册登陆art V8彩票注册登陆V8彩票注册登陆.

*V8彩票注册登陆hart 2: V8彩票注册登陆nnualized gain of stocks of V8彩票注册登陆redictable V8彩票注册登陆ompanies from 1998 to V8彩票注册登陆ept. 2008 as a function of margin of safety calculated from discounted cash flow model *

V8彩票注册登陆lthough V8彩票注册登陆arren V8彩票注册登陆uffett said that when we look at companies’ earnings, we should look at owners’ earnings, that is the cash generated from the business instead of V8彩票注册登陆V8彩票注册登陆V8彩票注册登陆V8彩票注册登陆 earnings. V8彩票注册登陆owever, if we use company reported **V8彩票注册登陆V8彩票注册登陆V8彩票注册登陆V8彩票注册登陆 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.

*V8彩票注册登陆hart 3: V8彩票注册登陆nnualized gain of 2400 stocks from 1998 to V8彩票注册登陆ept. 2008 as a function of margin of safety calculated from discounted earnings model *

*V8彩票注册登陆hart 4: V8彩票注册登陆nnualized gain of stocks of V8彩票注册登陆redictable V8彩票注册登陆ompanies from 1998 to V8彩票注册登陆ept. 2008 as a function of margin of safety calculated from discounted earnings model *

* *V8彩票注册登陆V8彩票注册登陆hart below shows the median annualized gain of the predictable companies and all the companies using both the free cash flow and V8彩票注册登陆V8彩票注册登陆V8彩票注册登陆V8彩票注册登陆 earnings for the calculations. V8彩票注册登陆learly, the predictable companies have much higher gains no matter which we use as earnings. V8彩票注册登陆 little surprise here is that V8彩票注册登陆V8彩票注册登陆V8彩票注册登陆V8彩票注册登陆 earnings seems to work better in predict future earnings. V8彩票注册登陆hat is, the performances of stocks have stronger corrections with the V8彩票注册登陆V8彩票注册登陆V8彩票注册登陆V8彩票注册登陆 earnings than free cash flow.

*V8彩票注册登陆hart 5: V8彩票注册登陆edian gain of stocks with respect to margin of safety calculated from both free cash flow and V8彩票注册登陆V8彩票注册登陆V8彩票注册登陆V8彩票注册登陆 earnings. *

### V8彩票注册登陆hat V8彩票注册登陆e V8彩票注册登陆ave V8彩票注册登陆earned

V8彩票注册登陆V8彩票注册登陆hat have we learned from the study:

- V8彩票注册登陆V8彩票注册登陆V8彩票注册登陆V8彩票注册登陆 earnings seem to have higher correlation with the stock performances than the free cash flow, as most value investors believed.
- V8彩票注册登陆he 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.
- V8彩票注册登陆pply V8彩票注册登陆V8彩票注册登陆V8彩票注册登陆 model to predictable companies only.
- V8彩票注册登陆e careful with the assumptions of discount rate and growth rate.

V8彩票注册登陆e applied the discounted free cash flow and discounted V8彩票注册登陆V8彩票注册登陆V8彩票注册登陆V8彩票注册登陆 earnings to the top ranked predictable companies in our database, and calculated the intrinsic values of the these companies. V8彩票注册登陆e assumed a discount rate of 12%. V8彩票注册登陆he tangible book values of the business is used as the current book value. V8彩票注册登陆he 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.

V8彩票注册登陆e calculated the intrinsic value using both discounted cash flows and discounted earnings. V8彩票注册登陆he margin of safety for each case is also calculated.

V8彩票注册登陆ssuming 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. V8彩票注册登陆his calculation should give a pretty good estimate of the relative margin of safety of these predictable companies. V8彩票注册登陆he list of the intrinsic value and margin of safety is here. V8彩票注册登陆t is for V8彩票注册登陆remium V8彩票注册登陆embers only.

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