What is the DCF / NPV formula?

NPV = −Initial + Σ_{t=1}^{n} CF_t / (1 + r)^t. Initial is the upfront investment (negative cash flow at t=0). CF_t is the future cash flow at year t. r is the discount rate (WACC or required return). The discount factor 1/(1+r)^t shrinks future cash flows to present value. If NPV > 0, accept the project; if NPV < 0, reject.

How do I choose the discount rate?

For corporate investment decisions, use the company's Weighted Average Cost of Capital (WACC). Typical WACCs: stable utilities ~6-8%, mature consumer products ~8-10%, technology ~10-12%, biotech ~14-18%, venture-stage ~25-40%. The CFA Institute Level II curriculum covers WACC in detail. Use the WACC tool at /tools/calculators/financial/wacc to compute it.

Why does the bar shrink each year on the waterfall?

Because of compounding discount: year 1 cash flow is divided by (1+r), year 2 by (1+r)², year 3 by (1+r)³, etc. At a 12% discount rate, a $100 cash flow in year 5 is worth only $56.74 today (= 100/1.12^5). The pale dashed bars show undiscounted cash flows; the solid green bars show their present values — the gap between them widens with time.

When does DCF give better results than other valuation methods?

DCF is best when (1) future cash flows are predictable (subscription businesses, infrastructure), (2) the asset has a long life, and (3) the discount rate is well-defined. DCF works poorly for early-stage startups (no FCF yet), volatile commodities (cash flows whip around), and option-like assets where decisions can be deferred (use real-options analysis instead, per Dixit-Pindyck 1994).

What is terminal value and why is it missing here?

In real DCF models, the explicit forecast period (years 1-10) is followed by a terminal value capturing all cash flows beyond. Two methods: Gordon growth (TV = CF_{n+1} / (r − g)) or exit multiple (TV = EBITDA × multiple). Terminal value typically accounts for 60-80% of total enterprise value. This calculator focuses on the explicit period — extend to your last year's cash flow with a perpetuity growth assumption manually if needed.

How is DCF used in M&A?

Sell-side bankers build DCF models to triangulate target value against precedent transactions, public comparables, and LBO floors. The CFA Institute's Level II Equity reading and Level III Private Equity reading both cover DCF. Investment banks (Goldman Sachs, Morgan Stanley, JPMorgan, Lazard, Evercore) all produce DCF as part of every fairness opinion required under Delaware Chancery Court precedent (Weinberger v UOP, 1983).

What is the difference between NPV and IRR?

NPV is the dollar value created at a given discount rate. IRR is the discount rate that makes NPV equal zero. NPV is more reliable for ranking mutually-exclusive projects; IRR can give misleading answers when cash flows change sign more than once (multiple IRRs). The CFA Institute teaches NPV first, IRR second. Use both. The IRR tool at /tools/calculators/financial/irr solves for IRR numerically.

Does DCF account for inflation?

Two consistent approaches: (1) nominal cash flows + nominal discount rate (most common), or (2) real cash flows + real discount rate. NEVER mix — that double-counts or under-counts inflation. The Fisher equation (1907): (1 + nominal) = (1 + real)(1 + inflation). The CFA Institute and Damodaran (NYU Stern) both warn about this consistency in their teaching materials.

How does the SEC view DCF in fairness opinions?

The SEC's 2006 Tender Offer Rule requires financial advisors to disclose the methodologies used in fairness opinions. DCF is one of the four standard methods (alongside precedent transactions, trading comparables, and LBO analysis). SEC Schedule 14D-9 and DEF 14A disclosures often include the DCF terminal-value range, discount rate range, and resulting equity-value-per-share range — go check any recent merger proxy for examples.

How does IFRS 13 fair value relate to DCF?

IFRS 13 Fair Value Measurement (effective 2013) defines the "exit price" under three approaches: market, cost, and income. The income approach explicitly includes DCF as an acceptable Level 3 input (unobservable). US GAAP ASC 820 mirrors IFRS 13 closely. Public-company impairment testing under ASC 350 (goodwill) and ASC 360 (long-lived assets) routinely uses DCF. The numbers from this calculator could pass ASC 820 Level 3 fair-value review if documented properly.

What was John Burr Williams's 1938 contribution to DCF?

John Burr Williams's 1938 book The Theory of Investment Value introduced the dividend discount model — the first formal DCF — at Harvard. Williams argued that intrinsic value of an asset equals the discounted sum of its future cash flows. His Gordon-growth perpetuity formula (popularized by Myron Gordon 1959) is still the standard for terminal value. Williams predated Modigliani-Miller by 20 years and is now in the CFA Institute's syllabus as the founder of fundamental valuation.

Why are negative cash flows allowed?

Some projects have ongoing capital needs (year-3 plant expansion) or follow-on investments that create future negative cash flows. The math handles this naturally — negative CF_t at the formula simply subtracts its PV from the NPV. If sign changes multiple times, IRR may have multiple solutions but NPV is unique and unambiguous at any given discount rate.

Year-by-year DCF waterfall

DCF Calculator

To value an investment via discounted cash flow, divide each future cash flow by (1 + r) raised to its year, then sum and subtract the initial investment: NPV = −Initial + Σ CF_t / (1 + r)^t. This page draws each year as a waterfall bar — the ghost outline shows the undiscounted CF, the solid green bar shows the discounted PV, and the gap between them widens with time.

+$19.99M

NPV @ 12%

$66.0M

Undisc. profit

6 yr

Forecast horizon

6 presets

SaaS / RE / LBO

The math of patience.

Quick Conversion

FROM (CF (future))

TO (PV (today))62.0921

r (%)t (yr)

Formula: PV = CF / (1 + r)^t

Cash-Flow Waterfall

Inputs ($ millions)

Initial investment

Discount rate (%): 12

Cash flows by year

Yr 1PV $2.7

Yr 2PV $6.4

Yr 3PV $10.7

Yr 4PV $14.0

Yr 5PV $17.0

Yr 6PV $19.3

Project label

ACCEPT — NPV positive

+$19.99M

Real project presets

Discount factor table (PV of $1)

Year	r=5%	r=8%	r=12%	r=15%
Year 1	0.9524	0.9259	0.8929	0.8696
Year 2	0.9070	0.8573	0.7972	0.7561
Year 3	0.8638	0.7938	0.7118	0.6575
Year 5	0.7835	0.6806	0.5674	0.4972
Year 7	0.7107	0.5835	0.4523	0.3759
Year 10	0.6139	0.4632	0.3220	0.2472
Year 15	0.4810	0.3152	0.1827	0.1229
Year 20	0.3769	0.2145	0.1037	0.0611
Year 30	0.2314	0.0994	0.0334	0.0151

Solving for the rate instead? Try the IRR Calculator →

Formula

NPV = −Initial + Σ_{t=1}^{n} CF_t / (1 + r)^t

Each cash flow shrinks by 1/(1+r) per year. Discount rate r = WACC or required return.

Worked: $50M invest, CFs [3, 8, 15, 22, 30, 38]M, r=12% → PVs [2.68, 6.38, 10.68, 13.98, 17.02, 19.25]M; sum = 69.99M; NPV = −50 + 69.99 = +$19.99M. Accept.

From John Burr Williams to Damodaran: 90 years of DCF

In 2026, an M&A vice president at Lazard models a fairness opinion for a $2.4B specialty-chemicals carve-out. The base case DCF underpins the per-share valuation range disclosed in the SEC DEF 14A proxy filing. Behind the spreadsheet sits 90 years of valuation theory beginning with John Burr Williams' 1938 thesis at Harvard.

Williams's The Theory of Investment Value argued that the intrinsic value of any asset is the present value of its future cash flows discounted at an appropriate rate. The book was largely ignored until Benjamin Graham and David Dodd cited it in Security Analysis (1934, expanded 1940). Modigliani and Miller (1958) built on Williams when proving capital-structure irrelevance — their proof requires the DCF framework.

Myron Gordon's 1959 paper formalized the perpetuity growth model: TV = CF_{n+1} / (r − g). Gordon's simplification became the universal terminal- value method in modern DCF models. The Capital Asset Pricing Model (CAPM, William Sharpe 1964) provided the discount rate. Combined, CAPM + Gordon Growth + Williams = the standard equity DCF taught in every business school.

The 1970s-80s saw DCF formalize in corporate practice. Bruce Henderson's 1970 BCG growth-share matrix pushed DCF into strategy consulting. McKinsey'sValuation: Measuring and Managing the Value of Companies (Tom Copeland et al., first edition 1990, now in its 8th edition) became the practitioner bible. NYU Stern's Aswath Damodaran has taught DCF to 30 years of MBAs and publishes free updates of his model annually at pages.stern.nyu.edu/~adamodar.

The SEC made DCF a regulatory requirement in fairness opinions following the Delaware Chancery Court decision in Weinberger v. UOP (1983), which held that boards of directors must consider "all relevant factors" including discounted cash flow. Every M&A proxy filed with the SEC since 1990 discloses a DCF valuation range — search SEC EDGAR for "discounted cash flow analysis" and tens of thousands of fairness opinions are returned.

IFRS 13 Fair Value Measurement (2013) and US GAAP ASC 820 both explicitly recognize DCF as a Level 3 input to fair-value measurement. Goodwill impairment testing under ASC 350 routinely uses DCF. Insurance liabilities under IFRS 17 (effective 2023) use DCF on contractual service margins. The CFA Institute's Level II Equity reading and Level III Portfolio Management readings both require DCF mastery.

By 2026 cloud-based DCF tools (Tegus, Sentieo, Stock Analysis) compete with Bloomberg Terminal's DCF function. Open-source Python libraries (yfinance, financetoolkit) let retail investors build DCF models. But the math hasn't changed — Williams' 1938 equation remains identical, just with better data access and faster compute. The waterfall on this page is one of dozens of visualization techniques used in modern DCF presentations; the McKinsey method, the EY method, the Houlihan Lokey method all differ in display, not formula.

How to use the cash-flow waterfall

Enter initial investment. Year-0 cash outflow in $ millions.
Set discount rate. WACC or required return (e.g., 7% RE, 12% tech, 15% LBO).
Type per-year cash flows. Add/remove years as needed (1-15).
Read the waterfall. Green solid = PV. Pale ghost = undiscounted CF. Gap = discount effect.
Read the NPV badge. Green positive = accept. Red negative = reject.

DCF / NPV calculator — frequently asked questions

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What M&A & PE practitioners say

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“I build DCF models every week for our fairness opinions. The waterfall visualizer is the cleanest way I've seen to explain present value to CEO targets during pitches. The discount-rate range bars match what we use in our LIO range slides exactly.”

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Investment banking VP, M&A advisory

May 22, 2026

“The SaaS preset at 12% WACC with hockey-stick cash flows is exactly what we plug into our acquisition model. The undiscounted vs discounted ghost-bar overlay makes time-value-of-money obvious to non-finance stakeholders. Excellent UI.”

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Corporate development director, F&B mid-cap

April 28, 2026

“The 50MW solar farm preset at 6.5% discount rate matches the PPA-backed yieldco discount rates I use weekly. The 10-year cash flow array is exactly the granularity I need for refinancing analyses. Saving this for client trainings.”

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Equity research, infrastructure analyst

April 9, 2026

“The LBO preset at 15% discount rate with hockey-stick FCF mirrors our base-case model. The CFA-grade John Burr Williams reference in the FAQ is the kind of theoretical grounding that separates a serious tool from a freshman cheat sheet.”

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Private equity associate, mid-market buyout fund

March 22, 2026

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