Stock valuation formulas: DDM, DCF and P/E

Mixing an equity cash flow with a firm discount rate changes the answer before any forecast is tested. A stock valuation formula must match the claim being valued: use dividends or free cash flow to equity with the cost of equity, or free cash flow to the firm with the weighted average cost of capital before converting to equity.

For a direct per-share estimate, the constant-growth dividend formula is V₀ = D₁ ÷ (kₑ − g). A broader DCF discounts a forecast cash-flow stream plus its terminal value. A P/E estimate is EPS × a selected P/E multiple. Choose among them by the cash flows you can support, then check the rate, time period and units. The valuation research guide places these calculations within the wider disclosure-reading process.

Compare the formulas before entering numbers

The same algebra can price different claims. Label the cash flow and output before using a spreadsheet cell called “value.”

Here, Σ adds forecast years 1 through n, t identifies a year, and TVₙ is the value of later cash flows measured at the end of year n. DDM is itself a form of equity DCF. The firm/equity split follows Damodaran’s introduction; the terminal-value structure follows his public valuation lecture, both accessed October 15, 2026.

Keep an input log beside the formula. A reported dividend, a forecast dividend and an assumed growth rate have different evidential status, even when all three occupy adjacent cells. What a company valuation has to identify explains that distinction.

One hypothetical industrial company for every example

All amounts below are invented teaching assumptions for one mature industrial company. They are not disclosures, market prices or suggested valuation parameters. Cash flows arrive at year-end; the share count stays fixed. The company is assumed to sustain the stated growth after reinvestment and financing.

These inputs were deliberately selected to reconcile. Matching answers therefore demonstrate the arithmetic, not independent evidence that any real stock has that value. For a real issuer, the forecasts, capital structure and discount rates must also agree with one another.

DDM: use the next dividend and test the denominator

The constant-growth dividend discount model divides next year’s dividend by equity cost minus perpetual dividend growth. The CFA Institute’s public 2026 refresher gives this equation with kₑ > g and describes its use for a discernible dividend policy related to profitability.

For the hypothetical company:

V₀ = USD 2.10 per share ÷ (0.10 − 0.03) = USD 30.00 per share.

D₁ is the next dividend, not the last payment. If the starting input is the most recent annual dividend D₀, calculate D₁ = D₀ × (1+g) under the same growth assumption. A quarterly payment needs an explicit annual forecast; a quarterly amount cannot silently become the annual numerator.

This model assumes a continuing distribution stream. A company retaining cash for new capacity may need an explicit forecast of when distributions begin, or an FCFE model. Entering a zero current dividend into the constant-growth shortcut does not establish that the business has zero value.

What happens when growth reaches the discount rate?

The shortcut fails when kₑ ≤ g. At g = 10% and kₑ = 10%, its denominator is zero. At g = 11%, the mechanical result is USD 2.10 ÷ −0.01 = −USD 210 per share, but the assumed infinite dividend stream has no finite present value under this model. That negative number is an invalid model output, not an economic estimate.

Even valid inputs can be sensitive. Holding D₁ at USD 2.10 and kₑ at 10%, hypothetical growth assumptions of 2%, 3% and 4% produce USD 26.25, USD 30.00 and USD 35.00 per share. This is a controlled sensitivity calculation; the three growth rates are not forecasts.

DCF: distinguish equity cash flows from firm cash flows

An FCFE model values equity directly; an FCFF model first values operations. Damodaran’s equity-valuation framework pairs FCFE with equity cost and FCFF with WACC. Interest and debt repayment belong in the equity cash-flow calculation, while the firm calculation is before those financing payments.

For a stable FCFE stream, the hypothetical company’s total equity is:

E₀ = USD 4.20 million ÷ (0.10 − 0.03) = USD 60.00 million.

Dividing by 2.00 million shares gives USD 30.00 per share. DDM agrees here because all FCFE is paid as dividends. If payouts differ from cash available to equity, that equivalence needs investigation.

Calculate terminal value at its own date

A continuing-growth FCFF terminal value uses the first cash flow after the explicit forecast: TVₙ = FCFFₙ₊₁ ÷ (WACC − g), with WACC > g. Then discount TVₙ back n periods, alongside the explicit forecast cash flows.

Using the same company’s 3% growth and 8% WACC, split its continuing stream after two years. All amounts in this calculation are USD millions:

The equity result is again USD 30.00 per share. The operating value also equals 7 ÷ (0.08 − 0.03) = USD 140 million because this constructed example has the same growth and discount rate throughout. Splitting it into forecast and terminal periods simply exposes the dates.

Do not add USD 148.526 million directly to today’s forecast present values: it is a year-2 value. Do not count year-3 cash flow separately as well as inside the terminal value. And do not subtract debt again from an FCFE result, which already values the equity claim.

Deduct reinvestment before calling the cash flow free

For an ordinary nonfinancial operating business, a simplified FCFF construction is after-tax operating earnings + depreciation − capital expenditure − increase in noncash operating working capital. It assumes consistent definitions and a reconciled tax treatment. The firm’s forecast needs those investment outflows to support the growth it assumes.

For industrial research, investigate equipment upkeep and working-capital needs before treating earnings as distributable cash. For resource research, also ask whether asset life supports a perpetual terminal assumption. These are analytical checks, not accounting advice. The EBITDA valuation guide explains why an operating earnings subtotal can leave capital spending unresolved.

P/E: separate the observed ratio from the assumed multiple

P/E = share price ÷ EPS describes a price relative to earnings. Rearranging it gives an estimate only after selecting a multiple: estimated share value = EPS × selected P/E. OpenStax’s P/E explanation distinguishes trailing reported earnings from leading forecast earnings.

For the same hypothetical company, next-year EPS of USD 2.50 × an assumed leading P/E of 12 = USD 30.00 per share. Twelve is a teaching assumption, not an industry benchmark. Using an observed price to calculate P/E and multiplying that same P/E by the same EPS merely returns the starting price.

A loss or near-zero EPS can make the comparison unusable or unstable. A peak-cycle EPS also needs investigation before extrapolation. Use the valuation multiples guide for numerator/denominator selection and sample comparability; this page supplies no sector multiple table.

Check the inputs before interpreting the answer

The most useful final check is to trace each result back to a defined input and date. Leave a missing input blank until it can be supported.

For a cyclical industrial or resource business, record why the earnings year represents the cycle. If a single year’s profit dominates the estimate, return to the input log and test a different earnings assumption. A small spread between the discount rate and perpetual growth calls for more scrutiny, not extra decimal places.

Method and sources

This is a public-source explanation with original hypothetical arithmetic, updated October 15, 2026. The formulas follow the specific Damodaran, CFA Institute and OpenStax pages linked above and listed below, accessed on that date. No current issuer, market rate, commodity forecast or investment return was estimated. The photographs introduce research inputs, distributions and physical reinvestment; they are not source documents or evidence for the numerical example.

For the McKinsey reference, the bibliographic record is: Tim Koller, Marc Goedhart and David Wessels, Valuation: Measuring and Managing the Value of Companies, eighth edition, Wiley, May 2025. This is confirmed by McKinsey’s May 10, 2025 announcement, accessed October 15, 2026. Only that announcement was opened for the citation; no book chapter is summarized here.

To use these methods in research, begin with the input log, select the claim and model, and recalculate under alternative assumptions. The research disclaimer applies throughout: this page provides education, without a buy, sell or hold recommendation.