[Finance as Liberal Arts] Stock prices are determined by the "reverse rotation of compound interest" | A gentle explanation of the DCF (Discounted Cash Flow) method
Hello, I am Mr. Marchan.
In previous articles, I have explained "how stock prices are determined" and "what WACC (cost of capital) is."
This time, I would like to write about the "DCF (Discounted Cash Flow) method," which can be called the culmination of that knowledge and is the most classic technique for calculating corporate value in the world of finance and M&A (mergers and acquisitions), while breaking it down as simply as possible.
「DCF法（ディスカウント・キャッシュフロー法）」
I will try to write about it while breaking it down as much as possible.
When buying an entire company, what is the fair price?
This large-scale question can actually be brilliantly solved by simply applying the "power of compound interest" that we are all familiar with.
<Japanese summary of this article>
The DCF method is a representative technique for calculating corporate value by discounting the cash flow a company will generate in the future to its present value. Future money needs to be discounted to account for the time value and uncertainty, and this calculation can be considered the reverse of the concept of compound interest. Specifically, it involves projecting future free cash flow, using WACC, which is the cost of capital, as the discount rate to convert it to present value, and summing these up to determine the corporate value. Furthermore, shareholder value is calculated by subtracting interest-bearing debt. By understanding these mechanisms, it becomes possible to interpret financial news more logically, such as the impact of interest rate fluctuations on stock prices.
<English summary of this article>
The discounted cash flow method is a fundamental valuation approach used to estimate a company’s value by discounting its future cash flows to their present value. Because future cash is worth less than cash today due to both the time value of money and uncertainty, it must be discounted—essentially the reverse process of compounding.
In practice, future free cash flows are projected and then discounted using the weighted average cost of capital as the discount rate to determine the firm’s value. By subtracting interest bearing debt, the equity value can be derived.
Understanding this framework enables investors to interpret financial news more logically, such as how changes in interest rates influence stock prices.
1. The DCF method means "converting future earnings into current value"
The DCF (Discounted Cash Flow) method is, as the name suggests,
a method of evaluating the value of an entire company by
discounting the money (Cash Flow) that the company will generate in the future
to its present value.
When acquiring a company or buying stocks,
investors predict, "How much money will this company earn
every year in the future?"
However, 10,000 yen earned in the future
has a different value than 10,000 yen obtained right now.
Because future money has uncertainty (risk),
when converting it to current value,
it is necessary to "discount (slightly reduce the value)."
So, how exactly do we discount it?
This is where the concept of the
"compound interest snowball" that I talked about in a previous article comes in.
2. A time machine that rotates the "compound interest snowball" in reverse
To understand the DCF method, the best shortcut is to first confirm the mechanism of
"compound interest" where money grows.
The greatest strength of compound interest is "time".
At first, there is not much difference from simple interest, but over 10 or 20 years,
as you keep rolling the snowball, as the snowball (principal) gets larger,
the amount of snow (interest) that sticks with each roll increases explosively.
Now, let's look at its power with a familiar example.
Suppose a 30-year-old person invests 1 million yen in the stock market.
Since we are younger than people who lived in the past, we are lucky;
let's assume we can work hard until we retire from the labor market at 75.
If we can manage this for "45 years" at an average annual rate of 3%,
what will happen?
With simple interest calculation, the interest of 30,000 yen per year for 45 years would be 1.35 million yen, which, combined with the principal, would be "2.35 million yen."
However, if you take advantage of the power of compound interest, the initial 1 million yen will have grown to
a staggering "approximately 3.8 million yen" after 45 years!
This is the mathematical reason why it is said in financial investment to "make time your ally."
Now,the DCF method is a calculation like a time machine that
rotates this "compound interest snowball" in reverse.
Suppose a company promises you,
"We will definitely generate approximately 3.8 million yen in cash for you in 45 years."
If the expected return (discount rate) you require from that company is
3% per year, then if you calculate that "3.8 million yen in 45 years"
backwards (discount) to the present,
the current value becomes exactly "1 million yen."
This is the true nature of "Present Value."
It is rewinding the snowball that should have grown in the future
to its "current size" using the time axis of interest rates.
3. The reality of corporate valuation: Adding up annual cash flows
In actual M&A and stock investment, a company does not generate cash only once in 45 years.
It generates cash (free cash flow) from its business every single year.
Therefore, corporate valuation using the DCF method is performed with the following image in mind.
Therefore, corporate valuation using the DCF method is performed with the following image in mind.
1. Forecast future cash flows:
Predict how much cash the target company will earn in 1 year, 2 years, 3 years, etc. (business plan).
2. Determine the discount rate (WACC): Use the 'WACC (Weighted Average Cost of Capital)', which is the company's cost of capital explained in a previous article, as the 'discount rate (speed of reverse rotation)' to bring values back to the present. The higher the risk of the company, the higher this WACC becomes.
3. Discount year by year and add them all up:
- Earnings 1 year from now are reverse-rotated (discounted by WACC) by 1 year to find the present value.
- Earnings 2 years from now are reverse-rotated by compound interest for 2 years to find an even smaller present value. - Earnings 3 years from now are for 3 years... Like this,
convert the earnings of all future years into 'present value' and add them all up with a bang!
.
This total amount is the 'corporate value (business value)' calculated by the DCF method.
'This company has the ability to earn this much cash in the future. If you convert that to present value using the reverse rotation of compound interest and add it all up, it becomes 10 billion yen.' That is the extent of the corporate value calculation.
However, the fair price to actually buy the whole company (buying all shares) is not exactly this corporate value.
this corporate value itself.
Companies almost always have debt (interest-bearing debt) borrowed from banks.
Buying a company (becoming a shareholder) means effectively taking on the obligation to repay that debt.
Therefore,
from the calculated 'corporate value (e.g., 10 billion yen)',the 'interest-bearing debt (e.g., 3 billion yen)' is subtracted, and the remainder
'shareholder value (7 billion yen)' is the fair acquisition price that should actually be paid.
*Strictly speaking, the balance of cash, etc., is adjusted as necessary.
And dividing this shareholder value by the number of issued shares leads to the 'theoretical stock price per share' that we see every day.
While stock prices move based on supply, demand, and psychology in the short term, they are often explained by this DCF concept in the long term.
4. The fun of 'liberal arts' where dots connect
How about that?
'WACC (discount rate)', 'future cash flow', and the 'reverse rotation of compound interest' that manipulates time.
These all connect in a single line to become one tool for corporate valuation called the 'DCF method'.
If you know this theory, when you see the news that 'the Bank of Japan has raised interest rates (= WACC has risen)'
When WACC rises, the 'discount (reduction)' when bringing future earnings back to the present becomes larger. Therefore, the corporate value calculated by the DCF method becomes smaller, and if the interest-bearing debt remains the same, the shareholder value also becomes smaller, and as a result, the stock price falls.
You will be able to understand the logic behind the world more deeply.
Finance is by no means just for a few finance professionals.
It is a powerful 'liberal art' for us to logically interpret the world.
Today's step changes the future.
Let's start learning about the mechanisms of money and the economy little by little together!
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In this note, I write based on my actual experience about:
- The reality of overseas MBA
- Study records for USCPA (US Certified Public Accountant)
- Adult re-learning and career strategy
- Basic knowledge to interpret business and society like this time
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