[Beginner's Guide] Deriving the Core Model of Stock Valuation from Scratch: The Discounted Free Cash Flow Model, with Tencent as an Example for Valuation

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Introduction#

The previous article elaborated on the entire value investment system from the perspective that buying stocks is equivalent to buying companies. In the chapter on margin of safety, it mentioned that once you understand a company, you can estimate its value, and based on that, consider the margin of safety before deciding whether to buy or sell stocks.

This article will serve as a supplement to the previous one, establishing from scratch the most basic and core model for estimating the intrinsic value of assets in the investment field: the Discounted Free Cash Flow Model, and using Tencent's 2022 profits for its valuation, ultimately explaining the applicable conditions of this model.

Let's get started.

Discounted Free Cash Flow Model#

What is the intrinsic value of a company? To put it simply, if you were to acquire a company, the amount you are willing to pay is its intrinsic value. Suppose there is a restaurant at the entrance of your community, with a net profit of 300,000 this year, and its earnings will increase by 8% each year. You are willing to pay 3 million to buy it; in your view, its intrinsic value is 3 million.

Intuition is based on feelings, and feelings can sometimes be unreliable. So, is there a reliable method to calculate a company's intrinsic value?

Yes.

In the words of Warren Buffett:

The value of stocks, bonds, or businesses depends on the sum of the discounted free cash flows over the remaining life of the assets, discounted at an appropriate rate.

This sentence fully explains the method for calculating a company's intrinsic value. However, for investment novices, to learn how to calculate it, one must first understand two concepts in this sentence: Free Cash Flow and Discounting.

What is Cash Flow#

The restaurant at the entrance of the community received a total of 2,000 yuan in cash today (inflow), while the total expenses for raw materials, rent, and employee salaries amounted to 1,000 yuan (outflow). Therefore, the cash flow for the restaurant today is 1,000 yuan.

For a company, the cash that flows into the company at a certain moment is called cash inflow; the cash that flows out of the company at a certain moment is called cash outflow. The algebraic sum of cash inflow and cash outflow is called cash flow.

What is Free Cash Flow#

Returning to the restaurant, although there is a cash flow of 1,000 yuan today, the cautious owner would definitely not dare to spend all of it. Because he needs to set aside some cash to purchase raw materials for the next day; otherwise, the restaurant cannot open.

Suppose the owner spends 300 yuan on new raw materials, leaving 700 yuan for personal use. This 700 yuan is the free cash flow.

Thus, the difference between free cash flow and cash flow is that free cash flow is very flexible, to the extent that it can be considered dispensable without significantly affecting the company's operations.

The precise definition of free cash flow is: the cash flow remaining after meeting the company's reinvestment needs. This portion of cash flow is the maximum amount available for distribution to the company's capital providers without affecting the company's development.

For this restaurant, the capital provider is the owner himself, as he is the only one funding it. For publicly traded companies, capital providers include all individuals and institutions holding the company's stock.

How to Calculate Free Cash Flow#

For a simple small business like a restaurant, free cash flow is the cash flow generated from opening the store that day, minus the funds needed to maintain operations for the next day.

For publicly traded companies, it is not that simple. Public companies have various business models, and to accurately record the company's financial status, they must rely on accounting standards based on the accrual basis.

Typically, free cash flow can be calculated as the net cash flow from operating activities in the financial statements minus capital expenditures, such as cash paid for constructing fixed assets, intangible assets, and other long-term assets, namely:

Free Cash Flow = Net Cash Flow from Operating Activities - Capital Expenditures (1)

The net cash flow from operating activities is calculated using the following formula:

Net Cash Flow from Operating Activities = Net Profit After Tax + Depreciation and Amortization - Increase in Working Capital (2)

Substituting (1) into (2), we get the final formula for calculating free cash flow:

Free Cash Flow = Net Profit After Tax + Depreciation and Amortization - Increase in Working Capital - Capital Expenditures (3)

When calculating free cash flow, it is important to remember one thing: we focus on real cash, not money owed to us, nor unsold products.

Below is a brief explanation of the reason for each item in the formula.

Why Add Depreciation and Amortization#

When calculating net profit after tax, depreciation of equipment and amortization of costs are deducted. However, depreciation and amortization do not cause a loss of cash flow for the company, so this portion must be added back when calculating free cash flow.

Why Subtract the Increase in Working Capital#

Working capital equals current assets minus current liabilities.

Current assets affecting working capital include inventory, accounts receivable, and prepaid expenses. These items either delay the receipt of cash for the company or require the company to pay cash in advance, thus reducing the cash currently available to the company.

Current liabilities affecting working capital include deferred revenue and accounts payable. These items either allow the company to receive cash in advance or delay cash payments, thus increasing the cash currently available to the company.

An increase in working capital, meaning the current working capital is greater than the previous period's working capital, indicates that the growth of current assets exceeds that of current liabilities, which will reduce the cash currently available to the company.

However, when calculating net profit after tax, the increase in working capital is counted as part of the profit, while the increase in working capital is caused by increases in inventory, accounts receivable, and prepaid expenses. The increased portion does not bring cash to the company, so when calculating free cash flow, the increase in working capital must be subtracted. Note that it is the increase in working capital that is subtracted, not the working capital itself.

What is Discounting#

Before explaining the concept of discounting, let's consider the following question.

The Aladdin's lamp tells you: you are a good child who loves to learn, and I will reward you with 1 million cash. I can give it to you now, or I can give it to you five years later. Do you want it now or later?

Most people would definitely prefer to receive the 1 million cash now.

Because once you have the 1 million cash, you can deposit it in the bank. Assuming the interest rate is 3%, in five years, 1 million will become $100\times(1+0.03)^5=1.159 million$. The process of money increasing reflects the time value of money.

In other words, in your eyes, the 1.159 million five years later is equivalent to 1 million now. That is, the 1.159 million five years later, when discounted back to now, equals 1 million.

Therefore, discounting is defined as the process of converting the value of future funds to present value. It can be understood colloquially as a discount; the same amount of money is worth less in the future than it is now, so future money must be discounted to convert it to present value.

The discount rate is the proportion of the expected return on future funds converted to present value, reflecting the time value of money. For example, in the above case, the annual discount rate is 3%, because of the existence of interest, the principal increases by 3% each year.

General Discounted Free Cash Flow Valuation Model Calculation Formula#

Having understood the concepts of free cash flow and discounting, we can further explore how to use the discounted free cash flow model to calculate a company's intrinsic value.

First, let's review what the discounted free cash flow model is:

The value of stocks, bonds, or businesses depends on the sum of the discounted free cash flows over the remaining life of the assets, discounted at an appropriate rate.

This sentence describes what the discounted free cash flow model is and indicates how to calculate a company's intrinsic value using free cash flow.

Assuming the company can operate for n more years, with future cash flows for years 1, 2, 3, ..., n being $C_1, C_2, C_3... C_n$, and the discount rate for each year being $r$, the present values of these cash flows are $\frac{C_1}{1+r}, \frac{C_2}{{(1+r)}^2}, \frac{C_3}{{(1+r)}^3}... \frac{C_n}{{(1+r)}^n}$. Listing this data in a table gives:

Years from Now	Free Cash Flow for the Year	Present Value of Free Cash Flow
1	$C_1$	$\frac{C_1}{1+r}$
2	$C_2$	$\frac{C_2}{{(1+r)}^2}$
3	$C_3$	$\frac{C_3}{{(1+r)}^3}$
...	...	...
n	$C_n$	$\frac{C_n}{{(1+r)}^n}$

By summing all the present values of free cash flow in the table, we obtain the intrinsic value of the company:

\begin{aligned} Intrinsic Value of the Company = \frac{C_1}{1+r} + \frac{C_2}{{(1+r)}^2} + \frac{C_3}{{(1+r)}^3} + ... + \frac{C_n}{{(1+r)}^n} \\ = \sum_{t=1}^{t=n} \frac{{C_t}}{(1+r)^{t}}(4) \end{aligned}

Where:

$n$ is the remaining life of the asset
$t$ is the years from now
$C_t$ is the free cash flow in year $t$
$r$ is the discount rate

Formula (4) is the most basic form of the discounted free cash flow model, which I will refer to as the General Formula.

The general formula "looks" concise and perfect, and the underlying theory of discounted free cash flow can withstand scrutiny. However, since it is so beautiful and the calculation method is simple—just addition—why do so many people still incur losses in the stock market? Logically, if you calculate a company's intrinsic value using this formula, as long as you buy when the price is below intrinsic value, you shouldn't incur losses.

Because to use the general formula, you need to know the company's free cash flow for the next n years.

First, you cannot accurately know how long the company will survive; it might become a century-old business, or it might collapse immediately after experiencing a black swan event. Secondly, you cannot predict the future n years of free cash flow. Perhaps you can predict the free cash flow for the next three to five years based on a deep understanding of the company, but no one can predict the company's free cash flow for the next ten or even several decades.

Thus, the general formula is not very useful.

Two-Stage Discounted Free Cash Flow Valuation Model Calculation Formula#

To make the general model more practical, some have made improvements. The idea behind the improvement is that since we cannot accurately predict the company's free cash flow for the next n years, we can divide the time into two stages: the first stage, where we can estimate free cash flow more accurately, and the second stage, where we can only estimate it roughly. The length of the first stage is usually 3 to 5 years, while the second stage is assumed to be perpetual.

When estimating the free cash flow for the second stage, we assume that the growth rate of free cash flow remains constant at $g$ each year, and this perpetually growing growth rate is also known as the perpetual growth rate.

For example, we use the two-stage method, with the first stage lasting 3 years and the second stage lasting (n-3) years, with a discount rate of $r$ and a perpetual growth rate of $g$. The predicted free cash flows for the first three years are $C_1, C_2, C_3$, and according to the definition of the perpetual growth rate, the free cash flows for the second stage are $C{_3}(1+g), C{_3}(1+g)^2... C{_3}(1+g)^{n-3} ...$.

It is important to note that since we will no longer directly predict free cash flow after three years, but instead use the free cash flow from the third year to calculate future free cash flows, we will multiply by $C_3$.

The present values of the future n years of free cash flow are as follows:

Years from Now	Free Cash Flow for the Year	Present Value of Free Cash Flow
1	$C_1$	$\frac{C_1}{1+r}$
2	$C_2$	$\frac{C_2}{{(1+r)}^2}$
3	$C_3$	$\frac{C_3}{{(1+r)}^3}$
4	$C{_3}(1+g)$	$\frac{C{_3}(1+g)}{{(1+r)}^4}$
5	$C{_3}(1+g)^2$	$\frac{C{_3}(1+g)^2}{{(1+r)}^5}$
6	$C{_3}(1+g)^3$	$\frac{C{_3}(1+g)^3}{{(1+r)}^6}$
...	...	...
n	$C{_3}(1+g)^{n-3}$	$\frac{C{_3}(1+g)^{n-3}}{{(1+r)}^n}$
…	…	…

Based on the calculation method of the general discounted free cash flow model, summing all the present values of free cash flow in the table gives:

\begin{aligned} Intrinsic Value of the Company = \frac{C_1}{1+r} + \frac{C_2}{{(1+r)}^2} + \frac{1}{(1+r)^2}\frac{C_3}{r-g}\\& =\frac{C_1}{1+r} + \frac{C_2}{{(1+r)}^2} + \frac{1}{(1+r)^2}\frac{C_3}{r-g} + ... (5) \end{aligned}

The value from the second half of equation (5), starting from $\frac{C_3}{{(1+r)}^3}$, can be calculated using the infinite geometric series summation formula. Note that when n is large, we can consider it to have infinitely many terms, so we can use the infinite geometric series formula for summation.

\begin{aligned} \frac{C_3}{{(1+r)}^3} + \frac{C{_3}(1+g)}{{(1+r)}^4} + \frac{C{_3}(1+g)^2}{{(1+r)}^5} + \frac{C{_3}(1+g)^3}{{(1+r)}^6} + ... + \frac{C{_3}(1+g)^{n-3}}{{(1+r)}^n} + ... \\ =\frac{1}{(1+r)^2}\frac{C_3}{r-g}(6) \end{aligned}

Substituting equation (6) into equation (5) yields the final formula for calculating the intrinsic value of a company using the two-stage method:

Intrinsic Value of the Company = \frac{C_1}{1+r} + \frac{C_2}{{(1+r)}^2} + \frac{1}{(1+r)^2}\frac{C_3}{r-g}(7)

How to Choose the Perpetual Growth Rate and Discount Rate#

Predicting the future is a task with a low success rate, so we simplify the prediction of free cash flow for each year to only predicting the free cash flow for the next three years, and for the free cash flow after three years, we use the perpetual growth rate for a very rough estimate.

The choice of perpetual growth rate varies by person and asset class. For individual investors using spare money for investment, the following considerations can be made.

Through certain research, you have a thorough understanding of a company's business model and core competitiveness, and you believe that the company can still maintain a certain competitive advantage in the future. Therefore, the company's annual free cash flow growth rate will not be lower than the risk-free rate of return, so the risk-free rate can be used as the perpetual growth rate.

In the era of fiat currency, lending money to the government is the safest investment method, so the yield on ten-year government bonds is often used to determine the risk-free rate of return in society.

The current ten-year government bond yield is 2.85%, rounding up gives 3%.

For the discount rate, as mentioned earlier, the discount rate is the proportion of the expected return on future funds converted to present value, which essentially reflects the investor's expectation of future returns. Now, simply buying government bonds can yield a 3% return, so what return do you think is appropriate for taking on the greater risk of stocks? In other words, how high does the return need to be to compensate for the risk?

This is also a matter of personal preference. For me, I expect the overall future return to reach twice the risk-free rate, which is 6%.

Valuation Example with Tencent#

The year 2022 was a tumultuous year for China's internet industry, with many internet companies experiencing sharp declines in profits and stock prices halving repeatedly. Tencent faced anti-monopoly regulations, restrictions on game licenses, and financial controls, with a profit of 115.6 billion yuan last year, down 7%, and free cash flow of 88.4 billion yuan. Additionally, it holds equity in listed and unlisted companies worth approximately 770 billion.

After announcing its annual report on March 22, 2023, Tencent's stock price rose by 8%. Microeconomically, the market believes that after the third quarter's performance turned positive and the fourth quarter's profit grew by 19%, Tencent's performance has reached a turning point. Macroeconomically, with the lifting of pandemic restrictions, consumer spending rebounded, and the government's attitude shifted from restricting platform economic development to encouraging platforms to grow stronger, the attitude towards private entrepreneurs has also changed dramatically in a short period.

Without delving into excess information, let's return to the main line of valuing Tencent. Tencent's valuation can be viewed in two parts: the first part is the main business, such as gaming, advertising, fintech, and cloud and enterprise services, which can be valued using the discounted free cash flow method; the second part mainly includes the equity in listed and unlisted companies obtained through annual profits. The market value of this equity can be directly added to the valuation of the first part to obtain Tencent's total valuation.

First, we predict the free cash flow for the next three years. Considering that Tencent has passed its darkest hour, the macro environment continues to improve, and the company's competitive advantages remain stable, with promising growth in mini-programs and WeChat short videos, we set the annual growth rate of future free cash flow at 20%. Therefore, the free cash flows for 2023, 2024, and 2025 are 106 billion ($884\times{1.2}$), 127.2 billion ($884\times{1.2}^2$), and 152.7 billion ($884\times{1.2}^3$).

Next, we determine the perpetual growth rate and discount rate. As one of China's top-quality companies, Tencent's future free cash flow growth rate will not be lower than the risk-free rate of return, so we use a 3% risk-free rate as the perpetual growth rate. The discount rate is set at twice the risk-free rate, which is 6%.

Finally, based on the discounted free cash flow method, we calculate the intrinsic value of Tencent's operating business (see formula (7)):

\begin{aligned} Intrinsic Value of Operating Business &=\frac{C_1}{1+r} + \frac{C_2}{{(1+r)}^2} + \frac{1}{(1+r)^2}\frac{C_3}{r-g}\\& =\frac{1060}{1+0.06} + \frac{1272}{{(1+0.06)}^2} + \frac{1}{(1+0.06)^2}\frac{1527}{0.06-0.03} \\& =47450 \end{aligned}

Thus, the total valuation is the intrinsic value of the operating business plus the market value of the equity held, totaling 55,150 billion yuan (47450 + 7700 = 55150).

Although we have obtained a valuation, what price should we buy at? Should we buy at the stock price corresponding to the valuation?

We should not, because we can candidly acknowledge one point: our predictions about the future are often wrong, at least not entirely correct. Think about what has happened in the financial markets this year; all sorts of bizarre events could happen in the future. To allow for errors, we need to apply the concept of margin of safety again, meaning we should not buy based on valuation but rather apply a significant discount.

My suggestion is to buy at half the valuation, for instance, buying when Tencent's market value is 27,575 billion yuan, corresponding to a Hong Kong stock price of 327.5 HKD, while the current stock price is 385.4 HKD (April 9, 2023, click to view real-time stock price).

If you ask me why I didn't buy at last year's lowest point of 180 HKD, I would say that there is only one bottom, and those who buy are all gods.

(Note: All analyses should not be considered as investment advice)

When to Use the Discounted Free Cash Flow Model#

There is no silver bullet in the investment world; any model is only correct under certain conditions, and the discounted free cash flow model is no exception.

According to the calculation formula of the two-stage discounted free cash flow model:

Intrinsic Value of the Company = \frac{C_1}{1+r} + \frac{C_2}{{(1+r)}^2} + \frac{1}{(1+r)^2}\frac{C_3}{r-g}(8)

It provides two important pieces of information:

First, only companies that meet the following conditions are suitable for the discounted free cash flow model:

When valuing, we focus on how much cash the company can distribute to shareholders in the future, not just the numbers fluctuating on the K-line chart, nor merely the profits the company earns, because profit does not equal cash. For example, goods sold to others on credit generate profits, but if the buyer defaults, it leads to bad debts. This requires us to invest in companies that can generate real cash.
When valuing, we believe that the company can survive for a long enough time n in the future, hoping that the company can generate free cash flow every year during its existence and distribute it to us. This requires us to invest in companies with sustainable competitiveness and free cash flow.
As shareholders, we hope that the cash flow generated by the company each year can be distributed to us without needing to finance from other sources, and that it can distribute cash to us next year that is similar to the previous year. This requires us to invest in companies that do not require significant investment to maintain current profitability.

Therefore, the discounted free cash flow model is suitable for companies with real profits, sustainable free cash flow, and that do not require much investment to maintain current profitability; other companies are not suitable for valuation using this model.

Second, only funds that meet these conditions are suitable for the discounted free cash flow model

Since we focus on the free cash flow generated during the company's existence, companies that meet the above conditions can usually survive for many years. This requires us to view the company's valuation from a long-term perspective, and to match this long-term perspective, we also need to use long-term funds.

Long-term funds refer to money that will not be used in the short term, such as in three to five years.

Imagine that when Tencent's stock price fell from its peak of 740 HKD to 327.5 HKD, a drop of 55%, you thought the stock price was low enough and borrowed money from the bank to buy a large amount of Tencent stock, blindly confident that the price would rise in the short term. However, after buying, instead of rising, the price continued to fall, eventually dropping to 180 HKD. At this point, your paper loss is 45%, and the bank starts to urge you to repay the loan, forcing you to sell your stocks and raise money from other sources to repay the bank.

This illustrates that the discounted free cash flow model requires us to use long-term idle funds and not to use leverage (borrowing money for investment is a form of leverage) because in extreme market panic, prices can drop to any level. Only by using long-term funds can we shield ourselves from Mr. Market's erratic pricing and avoid being forced to sell assets due to urgent situations.

Thus, it is often said that the discounted free cash flow model is more of an investment philosophy than a valuation method, as it tells us what kind of companies to invest in and what type of funds to use for investment.

Summary#

The two forms of the discounted free cash flow model were derived, with the two-stage model being more practical, and a valuation calculation was performed using Tencent as an example.
The discounted free cash flow model essentially reflects an investment philosophy, indicating that one should use long-term funds to invest in companies with real profits, sustainable free cash flow, and that do not require much investment to maintain current free cash flow.

References#

Tang Chao. Value Investment Practice. China Economic Publishing House, 2019.
A Discussion on the Cash Flow Discounting Method
Discount Rate Defined: How It's Used by the Fed and in Cash-Flow Analysis
Geometric Series Summation Formula - Baidu Encyclopedia
Old Tang's Valuation Method Q&A (Continued)
Old Tang's Valuation Method Q&A Continued
Tencent Announces Q4 and Full Year 2022 Results
Tencent Returns to Bull Market | Zhike
Old Tang's Weekly Journal March 25, 2023 Free Edition: Brief Review of Tencent's Annual Report, Trading Arrangements for Next Week, and Reading for This Month