Does 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 (Trades, Portfolio) 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-x ^{n})/(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)x ^{n} y/(1-y)*

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

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**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) 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.*

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.

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**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-x ^{n})/(1-x) + E(0)x^{n} 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-x ^{n})/(1-x) + E(0)x^{n} 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 (Trades, Portfolio) 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:

- GAAP earnings seem to have higher correlation with the stock performances than the free cash flow, as most value investors believed.
- 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.
- Apply DCF model to predictable companies only.
- 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**

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