Valuation

How to put a number on a business: intrinsic (DCF) valuation step by step with a complete worked model, the bridge from enterprise value to a price per share, dividend and FCFE models, multiples and comparables, sector metrics, young and unprofitable companies, startup methods, and the biases that make most valuations wrong in predictable directions. Discount rates, CAPM and WACC are derived in corporate finance; free cash flow definitions and statement analysis in financial statements; cap tables, SAFEs and 409A mechanics in startup finance.

Value versus price

Value is what an asset is worth given its expected cash flows and their risk. Price is what someone pays today, set by supply, demand, mood, liquidity and narrative. They converge only if the market eventually agrees with your cash-flow view, and nothing guarantees when.

Damodaran's framing: most "valuations" in practice are pricing exercises. That is fine if you know which one you are doing. A DCF that is reverse-engineered to hit a comparable's multiple is pricing dressed as valuation.

Approaches

Use at least two approaches and reconcile the difference; the gap usually tells you which assumption to investigate.

DCF step by step

1. Understand the business and write the narrative

   What does it sell, to whom, why does it win, how big can it get, what does it cost to grow? Every number below should trace back to a sentence here.

2. Normalize the base year

   Start from financial statements: strip one-offs, capitalize R&D if it behaves like investment, treat leases as debt consistently, separate non-operating assets.

3. Forecast free cash flow to the firm

   Revenue growth → operating margin → taxes → reinvestment (capex − D&A + ΔNWC). Explicit period of 5–10 years, long enough to reach a steady state where growth, margins and returns on capital are stable.

4. Discount at WACC

   Market-value weights, bottom-up beta, risk-free rate and equity risk premium from the same date (see corporate finance). Use the mid-year convention if cash arrives through the year (multiply by $(1+WACC)^{0.5}$).

5. Terminal value

   Gordon growth with a growth rate at or below long-run nominal GDP and reinvestment consistent with that growth; cross-check against an exit multiple.

6. Bridge to equity and per share

   Add non-operating assets, subtract debt and other claims, divide by diluted shares (treasury stock method).

7. Stress and reconcile

   Sensitivity table (WACC × g), scenarios, compare to multiples and to the current price; explain the gap.

Terminal value

Gordon growth (perpetuity) method:

The second form is Koller et al.'s value-driver formula: growth needs reinvestment, and the reinvestment rate is $g/RONIC$ (return on new invested capital). If $RONIC = WACC$, growth adds no value and $TV = NOPAT_{n+1}/WACC$ whatever $g$ is. Plugging a growth rate in without the matching reinvestment is the most common way DCFs overstate value.

Exit multiple method: $TV_n = \text{multiple} \times EBITDA_n$. Simple and market-consistent, but it is a relative valuation inserted into a DCF: the multiple embeds someone else's growth and return assumptions. Always back out the implied perpetual growth rate and ask if it is plausible.

From enterprise value to equity value

Treasury stock method (TSM): in-the-money options add $N \times (1 - K/P)$ shares, because the exercise cash buys back shares at price $P$. In a DCF, $P$ is the value you are solving for, so iterate (or value options with Black–Scholes and subtract their value from equity before dividing by basic shares, the more rigorous route).

Worked five-year DCF

An invented company, Quillmark Sensors: industrial sensors, $500m revenue last year, growing fast but slowing. USD millions except per share.

Year                    1       2       3       4       5
Revenue             600.0   696.0   779.5   849.7   900.7
EBIT                 72.0    94.0   116.9   135.9   153.1
Tax at 21%          -15.1   -19.7   -24.6   -28.5   -32.2
NOPAT                56.9    74.2    92.4   107.4   121.0
+ D&A                24.0    27.8    31.2    34.0    36.0
- Capex             -36.0   -41.8   -46.8   -51.0   -54.0
- Change in NWC     -10.0    -9.6    -8.4    -7.0    -5.1
FCFF                 34.9    50.7    68.4    83.4    97.8
Discount factor    0.9174  0.8417  0.7722  0.7084  0.6499
PV of FCFF           32.0    42.7    52.8    59.1    63.6
 
Sum of PV (years 1-5)                        250.2
NOPAT year 6 = 121.0 x 1.03                  124.6
Reinvestment rate = g / RONIC = 3% / 15%       20%
FCFF year 6 = 124.6 x (1 - 0.20)              99.7
Terminal value = 99.7 / (9.0% - 3.0%)       1,661.2
PV of terminal value = 1,661.2 x 0.6499     1,079.6
Enterprise value                            1,329.8
Terminal value share of EV                    81.2%
 
+ Cash                                         60.0
+ Non-operating investments                    25.0
- Debt                                       -220.0
- Minority interest                           -15.0
Equity value                                1,179.8
 
Basic shares 40.0m; RSUs 0.8m
Options 3.0m at strike 12 (in the money)
Options 1.5m at strike 30 (out of the money)
TSM, iterated: diluted shares 42.50m
Value per share                              27.76

• The iteration converges at $27.76: the $12 options add $3.0 \times (1 - 12/27.76) = 1.70$m shares; the $30 options are out of the money and add nothing.
• The terminal value is 81% of enterprise value. The five forecast years, where all the modeling effort went, contribute less than a fifth.
• Exit-multiple cross-check. The Gordon terminal value is 8.8× year-5 EBITDA (189.1). An "industry" exit multiple of 11× gives TV 2,080.5 and EV 1,602.4 (+20%), but at 15% RONIC that multiple implies perpetual growth of about 4.9%, above what most forecasters expect for long-run US nominal GDP. The multiple is smuggling in growth.
• A naive $FCF_5 \times (1+g)$ terminal cash flow gives EV 1,341.9: close here only because year-5 reinvestment (19.1% of NOPAT) happens to be near the 20% that 3% growth requires. With heavier year-5 capex, the naive method would be badly off.

Sensitivity: value per share (WACC × terminal growth)

Enterprise value across the same grid runs from $1,073m (10%, 2%) to $1,828m (8%, 4%). A ±1 point range on WACC, which is roughly the honest uncertainty in any cost of capital, moves value per share from $23.12 to $34.12 (−17% to +23%). Report a range, not a point.

Common DCF mistakes

FCFE and dividend discount models

Free cash flow to equity is what is left for shareholders after reinvestment and debt flows:

Worked: net income 120, capex 60, D&A 40, ΔNWC 10, net borrowing 15 → $FCFE = 120 - 20 - 10 + 15 = 105$. Discount FCFE at the cost of equity to get equity value directly. Use FCFE when leverage is stable or when debt is operating raw material (banks, insurers).

Dividend discount model (Gordon 1959):

$D_1$ = $2.00, $k_E$ = 8%, $g$ = 4% → $50.00. Two-stage: $D_0$ = $1.50 growing 12% for 5 years ($1.680, $1.882, $2.107, $2.360, $2.644), then 4%, at $k_E$ = 9%. PV of dividends $8.14, terminal value $2.644 \times 1.04 / 0.05 = 54.99$, PV $35.74, value $43.88, 81% of it from the terminal value.

DDMs suit stable dividend payers (utilities, banks, consumer staples) and fail for firms that pay little and buy back a lot; use FCFE or FCFF there.

Multiples

Rules: equity multiples (P/E, P/B) pair equity value with equity-holder earnings; enterprise multiples (EV/…) pair EV with pre-interest measures. Mixing them (price / EBITDA) is wrong. Prefer forward multiples for growing firms and be consistent across peers.

Multiples are compressed DCFs. From the Gordon model:

A peer "trading at a discount" may simply have lower ROIC or higher risk. Before calling it cheap, check that the fundamentals match.

Picking comparables

• Same economics: business model, growth, margins, ROIC, risk, size, geography. Industry code is a starting point, not a test.
• 5–10 peers beats 30 loosely related ones. Remove outliers with a stated reason, not because they are inconvenient.
• Use the median (robust to outliers) and the interquartile range; show both.
• Adjust for accounting differences (leases, SBC, one-offs) before computing multiples.
• Regress the multiple on its driver (EV/Revenue on operating margin or growth) across peers when the set is large enough.

Worked example

Target: EBITDA $120m, net income $45m, net debt $300m, 50m shares.

The P/E answer is lower: either the target has higher interest costs or tax than peers, or its EBITDA converts to earnings less efficiently. Find out which before averaging the two.

Sector-specific metrics

Rule of 40. Revenue growth % + profit margin % ≥ 40 for a healthy software company at scale. Brad Feld popularised it in "The Rule of 40% For a Healthy SaaS Company" (3 February 2015), saying he heard it from a late-stage investor at a board meeting; he preferred EBITDA as the profit measure and applied it to companies with at least about $50m of revenue. Many now use free-cash-flow margin instead. Worked: 35% growth and 5% FCF margin scores 40. It is a heuristic for the growth-versus-profit trade-off, not a valuation model; at illustrative EV/ARR multiples of 6–10×, $50m ARR spans $300–500m of EV, a range that shows how much the multiple, not the company, drives the answer.

FFO (Nareit definition): GAAP net income excluding gains or losses on sales of property, impairments of depreciable real estate, and real-estate depreciation and amortization.

Young, high-growth and unprofitable companies

No earnings, short history, few comparables and a real chance of failure. Damodaran's approach (The Dark Side of Valuation; his paper on young and start-up companies) keeps the DCF structure but changes what drives it:

Worked (invented, USD millions). Revenue 20, operating margin −30%, NOL 5, cash 30. Growth 60% decaying to 3% by year 10; margin converging linearly to 20%; sales-to-capital 2.0; tax 21%; cost of capital 11% for years 1–5, falling to 8.5% by year 10.

Yr  Growth  Revenue  Margin   EBIT    Tax  Reinvest   FCFF    WACC  PV
 1   60.0%    32.0   -25%     -8.0    0.0     6.0    -14.0   11.0%  -12.6
 2   50.0%    48.0   -20%     -9.6    0.0     8.0    -17.6   11.0%  -14.3
 3   40.0%    67.2   -15%    -10.1    0.0     9.6    -19.7   11.0%  -14.4
 4   35.0%    90.7   -10%     -9.1    0.0    11.8    -20.8   11.0%  -13.7
 5   30.0%   117.9    -5%     -5.9    0.0    13.6    -19.5   11.0%  -11.6
 6   24.6%   146.9     0%      0.0    0.0    14.5    -14.5   10.5%   -7.8
 7   19.2%   175.2     5%      8.8    0.0    14.1     -5.3   10.0%   -2.6
 8   13.8%   199.3    10%     19.9    0.0    12.1      7.8    9.5%    3.5
 9    8.4%   216.1    15%     32.4    2.8     8.4     21.2    9.0%    8.7
10    3.0%   222.6    20%     44.5    9.3     3.2     31.9    8.5%   12.0
 
Sum of PV, years 1-10                                  -52.8
Terminal: NOPAT 36.2 x (1 - 3%/15%) / (8.5% - 3%)        526.8
PV of terminal value                                    198.6
Value of operating assets (going concern)               145.8
Failure probability 25%, distress proceeds 5.0
Adjusted: 145.8 x 0.75 + 5.0 x 0.25                     110.6
+ Cash                                                   30.0
Equity value (before option and preference claims)      140.6

Seven of the ten years have negative cash flows and their combined PV is negative, so all of the value is in the terminal value; the failure probability alone removes about a quarter. The model's use is not the point estimate but showing which story assumptions (TAM, target margin, capital efficiency) the price requires.

Startup valuation

At seed and Series A there is little to discount, so investors price the round. Details of cap tables, SAFEs, option pools and dilution are in startup finance.

Pre-money vs post-money. $\text{post} = \text{pre} + \text{new money}$; investor ownership = $\text{investment} / \text{post}$. A $2m investment at $8m pre is $10m post and 20%. Watch whether the option pool is created before the round (reducing the effective pre-money for founders) and whether SAFEs convert on a pre- or post-money basis.

VC method

Worked: a VC invests $8m. If the company succeeds, year-6 revenue of $60m at 5× EV/Revenue gives an exit value of $300m. Target multiple 10× (≈ 46.8% IRR over 6 years).

The high target multiple is not greed alone: it bundles the probability of failure (most portfolio companies return little), illiquidity and the VC's own fees into one number, applied to a success-case exit value. That makes the method a pricing convention, not an expected-value calculation.

Scorecard and Berkus

Both are negotiation anchors for angels, not valuations: neither looks at cash flows, and both inherit whatever the local market is paying.

Headline valuations overstate common stock

The headline post-money = latest preferred price × all fully diluted shares. It assumes every share is worth what the newest preferred paid, but preferred shares carry liquidation preferences, seniority and other rights common shares do not.

Worked: 100m fully diluted shares; Series B buys 10m at $10 ($100m) with a 1× non-participating preference. Headline post-money: $1bn.

Common is only worth the headline price if the exit is at least $1bn. With a participating preference, at $400m Series B takes $100m + 10% of the remaining $300m = $130m, and common falls to $3.00. Gornall and Strebulaev (2020) modeled 135 US unicorns and found reported post-money valuations averaged 48% above fair value, with common shares overvalued by 56%; 65 lost unicorn status after adjustment.

409A valuations

US private companies granting options need a fair-market-value estimate of common stock under IRC §409A; an independent appraisal is presumed reasonable (a safe harbor) for up to 12 months unless a material event occurs. It is usually well below the preferred price because of preferences and illiquidity. Mechanics and timing are in startup finance.

Real options valuation

Some assets are worth more than their DCF because they carry rights to act later: undeveloped oil reserves, a drug patent, a pilot that could scale, the equity of a distressed firm (a call on the firm's assets struck at the face value of its debt).

Intuition: a project with negative NPV today can still be worth something if it can be deferred and is highly uncertain, because you only exercise in the good states. Keep option value separate from the DCF and show it explicitly; do not add "strategic value" to a DCF without a named decision, trigger and payoff. Decision trees are usually more honest than Black–Scholes for non-traded assets. Details in corporate finance.

Biases, narrative and numbers

Valuations are biased before they are wrong: the analyst usually knows the answer the client wants.

More on these in cognitive biases and decision-making.

Narrative and numbers (Damodaran, 2017). Every valuation is a story told in numbers. Write the story first (what the company will be), check it is possible, plausible and probable, convert it into drivers (market size, share, margins, reinvestment, risk), value it, then keep a feedback loop: when events change the story (a regulatory ruling, a new competitor, a management change) the value changes; noise that does not change the story should not. Storytellers learn where their narrative is implausible; number-crunchers learn when their spreadsheet tells a story no one would believe.

Famous valuation lessons

Common threads: the price was set by a narrative that was never converted into cash-flow assumptions, or by a comparable set that was itself mispriced, and the people setting it had incentives to agree.

Templates and checklists

DCF template

COMPANY: __________   Valuation date: ______   Currency: ___
 
NARRATIVE (3-5 sentences): what it is, why it wins, how big,
how profitable, what it costs to grow, what could break it.
 
INPUTS                          Value     Source / date
Base-year revenue, EBIT         ______    ______________
Revenue growth yrs 1..n         ______    TAM x share logic
Target operating margin         ______    mature peer median
Sales-to-capital / reinvest.    ______    industry benchmark
Tax rate (effective -> marg.)   ______    ______________
Risk-free rate                  ______    10y yield, date
Equity risk premium             ______    implied ERP, date
Beta (bottom-up, relevered)     ______    peer set listed
Cost of debt (pre-tax)          ______    rating / yield
Target D/(D+E)                  ______    ______________
WACC                            ______
Terminal g / RONIC              ______    <= risk-free rate
Probability of failure          ______    (young firms)
 
OUTPUT
Sum PV FCFF ____  PV TV ____  EV ____  TV % of EV ____
+ cash ____ + non-op ____ - debt ____ - leases ____
- minority ____ - preferred ____ - other claims ____
Equity ____  Diluted shares (TSM) ____  Per share ____
 
CROSS-CHECKS
Implied EV/EBITDA and P/E vs peers: ____
Implied g from exit multiple: ____
Sensitivity grid WACC x g attached: [ ]
Bear / base / bull and weights: ____
Current price ____  Gap ____  Which assumption explains it?

Valuation checklist

[ ] Am I valuing (cash flows) or pricing (multiples)? Say so.
[ ] Narrative written before the spreadsheet was opened?
[ ] Base year normalized (one-offs, R&D, leases, SBC)?
[ ] FCFF with WACC, or FCFE with cost of equity, never mixed?
[ ] Nominal/real and currency consistent with the discount rate?
[ ] Rf and ERP from the same stated date?
[ ] Growth backed by reinvestment (g / RONIC, sales-to-capital)?
[ ] Terminal g at or below long-run nominal GDP / risk-free?
[ ] Terminal-year margins and ROIC plausible vs mature peers?
[ ] TV share of EV reported and examined?
[ ] Implied exit multiple and implied growth sanity-checked?
[ ] Bridge: cash, non-operating assets, debt, leases, minority,
    preferred, pensions, options (TSM or option value)?
[ ] Failure probability for young or distressed firms?
[ ] Comparables chosen on economics; median and IQR shown?
[ ] Equity vs enterprise multiples matched correctly?
[ ] For startups: preferred terms modeled, not headline post?
[ ] Sensitivity grid and scenarios shown; answer is a range?
[ ] Who wants which answer, and have I corrected for it?

References

• Tim Koller, Marc Goedhart and David Wessels (McKinsey & Company), Valuation: Measuring and Managing the Value of Companies, 8th ed. (Wiley, 2025): DCF practice, the value-driver terminal value formula, the EV-to-equity bridge
• Aswath Damodaran, Investment Valuation, 3rd ed. (Wiley, 2012): DCF, relative valuation and option-based valuation in depth
• Aswath Damodaran, The Dark Side of Valuation, 3rd ed. (Pearson FT Press, 2018): young, distressed, cyclical and hard-to-value companies
• Aswath Damodaran, Narrative and Numbers: The Value of Stories in Business (Columbia Business School Publishing, 2017): connecting story to valuation inputs
• Damodaran (2009), Valuing Young, Start-up and Growth Companies: Estimation Issues and Valuation Challenges (opens in a new tab): the revenue → margin → reinvestment → failure-probability approach
• Aswath Damodaran: Historical implied equity risk premiums, January 2026 (opens in a new tab): implied ERP 4.23% and T-bond rate 4.18% at the start of 2026
• Aswath Damodaran: Cost of capital by industry (US), January 2026 (opens in a new tab): industry betas and WACCs for bottom-up estimates
• Damodaran, A Disruptive Cab Ride to Riches: The Uber Payoff (June 2014) (opens in a new tab): the $5.9bn Uber valuation
• Bill Gurley, How to Miss By a Mile: An Alternative Look at Uber's Potential Market Size (July 2014) (opens in a new tab): the rebuttal on TAM
• Richard A. Brealey, Stewart C. Myers, Franklin Allen and Alex Edmans, Principles of Corporate Finance, 14th ed. (McGraw Hill, 2023): valuation of bonds, stocks and businesses; real options
• Myron J. Gordon, "Dividends, Earnings, and Stock Prices", Review of Economics and Statistics 41(2), 1959: the constant-growth dividend model
• Gornall and Strebulaev (2020), Squaring Venture Capital Valuations with Reality (opens in a new tab), Journal of Financial Economics 135(1): unicorn post-money valuations average 48% above fair value
• Brad Feld, The Rule of 40% For a Healthy SaaS Company (3 February 2015) (opens in a new tab): the post that popularised the Rule of 40
• Dave Berkus, The Berkus Method: Valuing an Early-Stage Investment (opens in a new tab): the method's author on its five elements
• Bill Payne, Scorecard Valuation Methodology: Establishing the Valuation of Pre-revenue, Start-up Companies (white paper for angel investors): the scorecard factor weights
• Nareit Funds From Operations White Paper, 2018 Restatement (opens in a new tab): the standard FFO definition for REITs
• Moeller, Schlingemann and Stulz (2005), Wealth Destruction on a Massive Scale? (opens in a new tab), Journal of Finance 60(2): acquirer losses in the 1998–2001 merger wave
• AOL Time Warner Form 10-K for 2002 (SEC EDGAR) (opens in a new tab): the goodwill write-downs behind the 2002 loss
• TechCrunch: WeWork, once valued at $47B, files for bankruptcy (6 November 2023) (opens in a new tab): WeWork's valuation history and Chapter 11 filing
• CNBC: WeWork shares jump in public markets debut after SPAC merger (21 October 2021) (opens in a new tab): the roughly $9bn SPAC listing
• CNBC: Uber prices IPO at $45 per share (9 May 2019) (opens in a new tab): Uber's IPO price and valuation