Daily study of economics, management, and finance

Written as of September 30, 2026, 7:03 AM (KST)
September 30, 2026 (KST) · Day 10
Today's topic: Turning future cash flows into today's value — The basics of DCF and enterprise valuation

1. Review of the previous lesson

Day 9 covered WACC, the average return required by shareholders and creditors, and how a company may create economic value when ROIC > WACC. Today, we use WACC to discount future free cash flows to present value through DCF valuation in this lesson.

2. Today's key concept

DCF (Discounted Cash Flow) values a business by discounting its future cash flows at a rate that reflects risk and the time value of money.

\[ \text{Enterprise value} = \text{Present value of future FCFF} + \text{Present value of terminal value} \]

When using FCFF, the free cash flow available to the entire firm, discount it at WACC.

\[ EV = \sum_{t=1}^{n} \frac{FCFF_t}{(1+WACC)^t} + \frac{Terminal\ Value_n}{(1+WACC)^n} \]

• FCFF: Free cash flow available to both shareholders and creditors
• WACC: Required return of all capital providers to the company
• Terminal Value: Continuing value beyond the explicit forecast period
• EV: Enterprise Value: The operating value of the entire business

DCF is fundamentally about answering the following question, rather than complicated formulas:

How much cash will this company generate, when, and with what degree of risk?

3. Concept explained

3-1. Why is KRW 100 hundred million in the future worth less than KRW 100 hundred million today?

KRW 100 hundred million today can be invested immediately to earn returns, while in 5 years, KRW 100 hundred million cannot be used during the intervening period. There is also uncertainty about whether it will actually be received in 5 years.

Future cash flows must therefore be discounted for time and risk.

\[ \text{Present value} = \frac{\text{Future cash flow}}{(1+\text{Discount rate})^{\text{Periods}}} \]

For example, discounting KRW 100 hundred million received in 1 year at 10% gives:

\[ \text{Present value} = 100\div1.10 = 90.9\text{ hundred million KRW} \]

The present value of KRW 100 hundred million received in 5 years is:

\[ \text{Present value} = 100\div(1.10)^5 \approx62.1\text{ hundred million KRW} \]

Present value falls when cash is received later or greater risk requires a higher discount rate.

3-2. The overall DCF calculation

DCF generally proceeds as follows:

1. Forecast future revenue.
2. Forecast operating profit and after-tax operating profit, or NOPAT.
3. Calculate FCFF incorporating depreciation, CapEx, and changes in working capital.
4. Discount FCFF over an explicit forecast period, such as 5–10 years, at WACC.
5. Calculate Terminal Value beyond the forecast period.
6. Add the present values of explicit-period FCFF and terminal value to obtain EV.
7. Adjust EV for net debt and other items to derive equity value.
8. Divide by diluted shares outstanding to obtain value per share.

The key sequence is:

\[ \text{Revenue}\rightarrow\text{Operating profit}\rightarrow NOPAT\rightarrow FCFF\rightarrow EV\rightarrow\text{Equity value}\rightarrow\text{Value per share} \]

3-3. What is FCFF in DCF?

FCFF (Free Cash Flow to Firm) is the free cash flow available to both shareholders and creditors across the entire firm.

The basic formula is:

\[ FCFF = NOPAT +\text{Depreciation and amortization} -CapEx -\Delta NWC \]

• NOPAT: After-tax operating profit
• Depreciation and amortization: An expense deducted from profit that is not a current-period cash outflow
• CapEx: Investment in tangible and intangible assets
• \(\Delta NWC\): Increase in operating working capital

NOPAT can be calculated as:

\[ NOPAT = \text{Operating profit}\times(1-\text{Normalized tax rate}) \]

Operating working capital varies with the analytical purpose, but a simplified definition is:

\[ \text{Operating working capital} = \text{Accounts receivable}+\text{Inventory}-\text{Accounts payable} \]

\[ \Delta NWC = \text{Ending operating working capital}-\text{Beginning operating working capital} \]

An increase in operating working capital ties up more cash in receivables, inventory, and similar items, so it is deducted from FCFF.

A simple FCFF example

• Operating profit: KRW 200 hundred million
• Normalized tax rate: 25%
• Depreciation and amortization: KRW 50 hundred million
• CapEx: KRW 70 hundred million
• Increase in operating working capital: KRW 20 hundred million

\[ NOPAT = 200\times(1-25\%) = 150\text{ hundred million KRW} \]

\[ FCFF = 150+50-70-20 = 110\text{ hundred million KRW} \]

This KRW 110 hundred million is cash flow available to the whole firm before financing-related payments such as interest, principal repayments, dividends, and buybacks.

3-4. OCF－CapEx and FCFF: Are they the same?

In Days 5–6, simple FCF was calculated as:

\[ \text{Simple FCF} = OCF-CapEx \]

This formula is useful for quickly assessing actual cash-generation trends. However, it is not necessarily identical to FCFF discounted at WACC in a DCF.

Under US GAAP in particular, interest paid is generally included in operating cash flow. In that case, OCF－CapEx can partially reflect financing choices and differ from strict FCFF.

Under IFRS, accounting-policy choices can affect the cash-flow classification of interest paid and received. Standardize interest, tax, and lease classifications when comparing companies or constructing a DCF.

For basic analysis, use OCF－CapEx to assess cash flows; for a full DCF, it is safer to reconstruct FCFF starting with operating profit.

3-5. What is the explicit forecast period?

The period during which revenue, margins, investment, and working capital can be forecast in detail is called the explicit forecast period in a DCF.

A period of 5–10 years is common, but it depends on the business.

• Mature, stable company: About 5 years
• High-growth company: 7–10 years or longer, until growth and margins stabilize
• Cyclical company: Until normalized conditions, rather than a cyclical peak or trough
• New factory or data-center investor: Until expansion is complete and utilization normalizes
• Patent-based company: A period capturing major patent expirations and product transitions

The company need not become a low-growth business at the end of the explicit period. However, terminal value requires growth, margins, reinvestment rates, and capital returns to approach sustainable long-term levels.

3-6. What is Terminal Value?

A company does not disappear after 5 years, so value beyond the explicit forecast period must also be included. This is called continuing value or Terminal Value.

Two common calculation methods are:

Method 1: Perpetual growth model

\[ Terminal\ Value_n = \frac{FCFF_{n+1}}{WACC-g} \]

• \(FCFF_{n+1}\): FCFF in the year following the explicit forecast period
• \(g\): Long-term perpetual growth rate
• \(WACC\): Discount rate

Next year's FCFF is calculated from the final forecast year's FCFF.

\[ FCFF_{n+1} = FCFF_n\times(1+g) \]

This model requires the following condition:

\[ WACC>g \]

If long-term growth equals or exceeds WACC, the denominator becomes 0 or negative, producing an economically meaningless result.

Because perpetual growth is assumed to last forever, a rate far above long-term nominal economic growth is difficult to justify.

Method 2: Exit multiple

Apply an appropriate multiple to final-year EBITDA or a similar measure.

\[ Terminal\ Value = \text{Final-year EBITDA}\times Exit\ Multiple \]

This method uses familiar market multiples, but effectively inserts relative valuation into a DCF. Multiples from overheated industry or stock-market conditions can overstate terminal value.

This lesson uses the perpetual growth model to explain the relationship between cash flow and WACC.

3-7. Terminal Value must also be discounted to present value

Terminal Value is measured at the end of the final forecast year and must therefore be discounted back to today.

\[ \text{Present value of Terminal Value} = \frac{Terminal\ Value_n}{(1+WACC)^n} \]

Adding this to the present value of explicit-period FCFF gives enterprise value, or EV.

\[ EV = \text{Present value of explicit-period FCFF} + \text{Present value of Terminal Value} \]

Terminal Value commonly accounts for 60–80% or more of total DCF EV. An excessively high share can make valuation overly dependent on small changes in distant-future assumptions.

3-8. How do you move from EV to equity value?

Discounting FCFF produces EV, the value belonging to both shareholders and creditors. Deriving equity value requires adjusting for creditors' claims and non-operating items.

In simplified form:

\[ \text{Equity value} = EV-\text{Net debt} \]

\[ \text{Net debt} = \text{Interest-bearing debt}-\text{Cash and cash equivalents} \]

A more detailed calculation is:

\[ \text{Equity value} = EV -\text{Interest-bearing debt} +\text{Excess cash} +\text{Non-operating assets} -\text{Non-controlling interests} -\text{Other claims} \]

Then divide by diluted shares outstanding to obtain value per share.

\[ \text{Value per share} = \frac{\text{Equity value}}{\text{Diluted shares outstanding}} \]

Diluted shares may reflect stock options, restricted stock, convertible securities, and other instruments.

3-9. DCF structures assumptions; it is not an exact-answer calculator

DCF results are highly sensitive to assumptions about:

• Revenue growth
• Operating margin
• Normalized tax rate
• Depreciation and amortization
• CapEx
• Working capital
• ROIC
• WACC
• Long-term growth
• Net debt
• Diluted shares outstanding

Understanding which assumptions drive the result matters more than presenting one price target precise to the decimal.

A good DCF does not claim “fair value is exactly KRW 15,992.” It shows:

• What growth rate does the current share price imply?
• How much does value decline if margins disappoint?
• How does prolonged CapEx affect FCF?
• How much does value decline if WACC rises by 1 percentage point?
• How long must the company sustain high ROIC to justify today's price?

4. A simple numerical example

The following are nonfinancial company A's hypothetical DCF teaching example. Amounts are in KRW hundred million, with figures simplified to explain the calculations.

① Forecast future FCFF

Assume the following:

• WACC: 9%
• Perpetual growth rate \(g\): 3%
• Net debt: KRW 400 hundred million
• Diluted shares outstanding: 1,000 ten-thousand shares
• Non-operating assets, non-controlling interests, and other adjustments: None

② Present value of explicit-period FCFF

\[ \text{Year 1 PV} = 100\div1.09 \approx91.7 \]

\[ \text{Year 2 PV} = 110\div(1.09)^2 \approx92.6 \]

\[ \text{Year 3 PV} = 121\div(1.09)^3 \approx93.4 \]

\[ \text{Year 4 PV} = 130\div(1.09)^4 \approx92.1 \]

\[ \text{Year 5 PV} = 138\div(1.09)^5 \approx89.7 \]

③ Calculate Terminal Value

Year 6 FCFF is:

\[ FCFF_6 = 138\times(1+3\%) = 142.14 \]

Terminal Value at the end of year 5 is:

\[ Terminal\ Value_5 = 142.14\div(9\%-3\%) \]

\[ Terminal\ Value_5 = 142.14\div6\% = 2,369.0 \]

Discount this to present value.

\[ \text{Present value of Terminal Value} = 2,369.0\div(1.09)^5 \approx1,539.7 \]

④ Calculate EV

\[ EV = \text{PV of explicit-period FCFF} + \text{PV of Terminal Value} \]

\[ EV = 459.5+1,539.7 = 1,999.2\text{ hundred million KRW} \]

⑤ Calculate equity value

\[ \text{Equity value} = EV-\text{Net debt} \]

\[ \text{Equity value} = 1,999.2-400 = 1,599.2\text{ hundred million KRW} \]

⑥ Calculate value per share

KRW 1,599.2 hundred million equals KRW 159,920,000,000.

\[ \text{Value per share} = 159,920,000,000\text{ KRW} \div10,000,000\text{ shares} \]

\[ \text{Value per share} \approx15,992\text{ KRW} \]

In this hypothetical calculation, A's value per share is approximately KRW 1 ten-thousand plus 6,000.

⑦ Check reliance on Terminal Value

\[ \text{Terminal Value share} = 1,539.7\div1,999.2 \approx77.0\% \]

Approximately 77% of total EV comes from Terminal Value. Small changes in WACC and perpetual growth can therefore substantially change the result.

⑧ Sensitivity to WACC and perpetual growth

With the same FCFF forecasts, changing only WACC and perpetual growth produces the following EVs:

Base EV is KRW 1,999 hundred million, but different assumptions produce approximately KRW 1,540–2,914 hundred million. This is why sensitivity analysis is essential in DCF.

5. Practical use in stock and company analysis

① Do not enter revenue growth arbitrarily

Break future revenue into actual business drivers wherever possible.

\[ \text{Revenue} = \text{Sales volume}\times\text{Average selling price} \]

Depending on the business, use the following measures:

Connect market size, competition, capacity, and customer contracts rather than simply extrapolating historical growth.

② Build a path toward normalized operating margins

Current margins may be temporarily high or low.

• Prices surge because of supply shortages
• New plants initially operate at low utilization
• Depreciation rises with AI and data-center investment
• Large restructuring expenses occur
• High-margin products gain a larger share of sales
• Recession increases promotions and price discounts

In a DCF, estimate normalized margins reflecting future competition and economies of scale rather than simply maintaining current margins.

③ Link growth to reinvestment

Revenue and NOPAT growth usually require additional investment.

• Factories, equipment, and data centers
• Research and development
• Inventory
• Accounts receivable
• Sales personnel
• Customer acquisition costs
• Acquisitions

Assuming sustained high growth without cash investment can overstate FCF.

Over the long term, growth and reinvestment can be related as follows:

\[ \text{Growth rate} \approx \text{Reinvestment rate}\times\text{Incremental ROIC} \]

For example, with long-term ROIC of 12% and perpetual growth of 3%, the simple reinvestment rate required is:

\[ \text{Reinvestment rate} = 3\%\div12\% = 25\% \]

This means reinvesting approximately 25% of NOPAT to sustain 3% growth. A high perpetual-growth assumption without the required CapEx and working-capital investment makes the model internally inconsistent.

④ Build three scenarios

Bear, Base, and Bull scenarios are more useful than a single forecast.

Scenarios can be assigned probabilities, but those probabilities are also estimates, so do not trust the results mechanically.

⑤ Do not confuse EV with market capitalization

Do not directly compare EV obtained by discounting FCFF with current market capitalization.

\[ \text{Equity value} = EV-\text{Net debt}+\text{Other adjustments} \]

A heavily indebted company can have high EV but little value left for shareholders. For a net-cash company, net cash is added to operating value.

Pay particular attention to:

• Borrowings and corporate bonds
• excess cash
• Lease liabilities
• Non-controlling interests
• Preferred shares
• Pension deficits
• Stakes in associates
• Non-operating real estate
• Holdings of listed shares
• Stock options and convertible securities

⑥ Reverse-engineer expectations embedded in the share price

DCF can calculate price targets and also work backward to infer the future performance required by today's price. This is called Reverse DCF.

For example, calculate backward to identify which assumptions justify the current share price:

• Revenue CAGR of 20% over the next 5 years
• Operating margin rising from 15% to 25%
• Normalized CapEx
• WACC remaining at 8%
• High ROIC lasting more than 10 years

Assessing whether those assumptions are realistic makes judgments of cheapness or expensiveness more concrete.

⑦ Cross-check with other valuation methods

Compare DCF results with:

• PER
• EV/EBITDA
• EV/EBIT
• PBR
• FCF Yield
• Historical valuation ranges
• Peer valuations
• Transaction precedents and acquisition multiples

If DCF suggests undervaluation while all relative measures suggest extreme overvaluation, revisit growth, margins, WACC, and Terminal Value assumptions.

⑧ Allow a margin of safety

If DCF fair value is KRW 16,000 and the share price is KRW 15,500, the 3% difference is likely within estimation error.

DCF inevitably contains errors, so investment decisions require a sufficient discount to fair value—a margin of safety to allow for uncertainty.

The required margin of safety depends on:

• Earnings predictability
• Debt levels
• Cyclicality
• Business-model stability
• Customer concentration
• Technological change
• Management's capital-allocation ability
• DCF reliance on Terminal Value

Greater business uncertainty requires a larger margin of safety.

6. What to look for in filings

Because DCF includes forecasts, clearly separate disclosed historical figures from analysts' future estimates.

Korean companies: DART

The Financial Supervisory Service's DART annual, half-year, and quarterly reports should be reviewed for the following items.

DART figures represent historical or current disclosed facts. Future revenue, margins, and FCFF remain forecasts, even with company guidance; they are not confirmed results.

US companies: SEC 10-K and 10-Q

SEC EDGAR for the following items.

• 10-K: Item 8. Financial Statements and Supplementary Data
• 10-Q: Part I, Item 1. Financial Statements
• Consolidated Statements of Operations
• Consolidated Statements of Cash Flows
• Consolidated Balance Sheets
• Segment Information
• Revenue Recognition
• Property, Plant and Equipment
• Debt
• Leases
• Income Taxes
• Commitments and Contingencies
• Earnings per Share
• Stock-Based Compensation
• Business Combinations
• MD&A – Results of Operations
• MD&A – Liquidity and Capital Resources

DCF forecasts can also use the following from earnings releases and conference calls:

• Revenue growth guidance
• Operating margin or cost outlook
• CapEx guidance
• Capacity expansion schedules
• Customer demand and backlog
• Conversion of RPO or backlog into revenue
• Pricing and product mix
• Regulatory, tariff, and exchange-rate effects

Company guidance represents management estimates, not audited financial statement figures.

Additional information needed outside filings

It is safer to distinguish the following in analysis tables:

• R(Reported): Figures directly stated in filings
• G(Guidance): Company guidance
• M(Market): Market data on the valuation date
• C(Calculated): Values calculated directly from disclosed figures
• E(Estimated): Analyst forecasts

7. Key takeaways

• DCF values a company by discounting future cash flows at a rate reflecting risk and the time value of money.
• FCFF available to the entire firm should be discounted at WACC.
• FCFF is fundamentally NOPAT + Depreciation and amortization − CapEx − Increase in working capital using this formula.
• Simple OCF－CapEx is useful for assessing cash generation but is not always equal to FCFF for DCF.
• DCF enterprise value is the sum of the present values of explicit-period FCFF and Terminal Value.
• The perpetual growth model is Next year's FCFF ÷ (WACC − Long-term growth rate) and requires WACC > Long-term growth rate for validity.
• Discounting FCFF produces EV, so net debt and other claims must be adjusted to obtain equity value.
• Divide equity value by diluted shares outstanding to obtain value per share.
• Link growth to required reinvestment, including CapEx, working capital, and incremental ROIC.
• Because Terminal Value can account for most of EV, WACC and perpetual-growth sensitivity analysis is essential.
• DCF is not an exact-answer calculator; it systematically tests future expectations and risks reflected in the current share price.
• Actual investment decisions should consider DCF, relative valuation, financial soundness, competitive advantages, and a margin of safety together.

8. 3 review questions

Question 1

A company has NOPAT of KRW 300 hundred million, depreciation of KRW 80 hundred million, CapEx of KRW 120 hundred million, and an operating working-capital increase of KRW 30 hundred million. Calculate FCFF.

Question 2

Year 5 FCFF is KRW 200 hundred million, perpetual growth is 2%, and WACC is 8%. Use the perpetual growth model to calculate Terminal Value at the end of year 5.

Question 3

DCF EV is KRW 5,000 hundred million, with the following information:

• Interest-bearing debt: KRW 1,500 hundred million
• Excess cash: KRW 500 hundred million
• Non-controlling interests: KRW 200 hundred million
• Other non-operating assets: KRW 100 hundred million
• Diluted shares outstanding: 2,000 ten-thousand shares

Calculate equity value and value per share.

Answers and explanations

Answer 1

\[ FCFF = NOPAT+\text{Depreciation and amortization}-CapEx-\Delta NWC \]

\[ FCFF = 300+80-120-30 = 230\text{ hundred million KRW} \]

Add back depreciation as a noncash expense, and subtract CapEx and working-capital increases as uses of cash.

Answer 2

First calculate year 6 FCFF.

\[ FCFF_6 = 200\times(1+2\%) = 204\text{ hundred million KRW} \]

Terminal Value is:

\[ Terminal\ Value_5 = 204\div(8\%-2\%) \]

\[ Terminal\ Value_5 = 204\div6\% = 3,400\text{ hundred million KRW} \]

KRW 3,400 hundred million is the value at the end of year 5. Discount it at WACC for another 5 years to obtain present value.

Answer 3

Equity value is:

\[ \text{Equity value} = EV -\text{Interest-bearing debt} +\text{Excess cash} -\text{Non-controlling interests} +\text{Non-operating assets} \]

\[ \text{Equity value} = 5,000-1,500+500-200+100 = 3,900\text{ hundred million KRW} \]

KRW 3,900 hundred million equals KRW 390,000,000,000.

\[ \text{Value per share} = 390,000,000,000\text{ KRW} \div20,000,000\text{ shares} \]

\[ \text{Value per share} = 19,500\text{ KRW} \]

In this hypothetical calculation, equity value is KRW 3,900 hundred million and value per share is KRW 1 ten-thousand plus 9,500. Real analysis must also check lease liabilities, preferred shares, pension deficits, stock options, and other adjustments.

Next lesson — Day 11:
“From enterprise value to a target share price — Adjusting for EV, net debt, non-controlling interests, and diluted shares”