EI 6 Discounted Cash Flow (DCF) and Growth Models
The value of a financial asset is the present value of the future cash flows it is expected to deliver, each adjusted for when it arrives and how likely it is. Bond cash flows are finite and contractual, but the cash a shareholder receives is discretionary: management decides what to distribute, and it decides indefinitely. Some issuers pay steady cash dividends or buy back stock, while others distribute nothing. A discounted cash flow (DCF) model handles this by forecasting the cash available to investors and discounting it at their required rate of return.
The generalized present value model applies to any of these cash flow measures. Intrinsic value equals the discounted stream of expected periodic cash flows plus the discounted expected price at the end of the forecast horizon.
Here is intrinsic value, is periodic expected cash flow, and is the expected terminal price. Because the inputs come from financial statement measures, the approach can absorb changes in sales, costs, capital spending, working capital, leverage, and payout policy. That same flexibility makes the output very sensitive to which model is chosen and to the assumptions fed in, so the analysis should follow a disciplined process that starts with picking the right cash flow measure.
Analysts generally select from four measures introduced earlier in the curriculum: dividends, free cash flow to the firm (FCFF), free cash flow to equity (FCFE), and residual income (RI). Three of the four are cash flow measures drawn from the statement of cash flows. Residual income is the exception: it is built from net income, the book value of equity, and the cost of equity, so it is a return measure rather than a cash flow.
Dividends
Dividends are the narrowest measure, capturing only the portion of net income handed to shareholders as cash rather than retained or returned through buybacks. A dividend discount model (DDM) treats cash distributions as the shareholder’s only access to firm value, so it fits companies with positive, stable earnings that pay out a large and consistent share of income. It takes the perspective of a non-controlling investor who cannot steer payout policy. Regulated utilities and real estate investment trusts (REITs) are natural candidates: a REIT must distribute nearly all of its taxable income to avoid corporate tax, and utility returns come largely through dividends because regulated pricing caps growth. Enel SpA, an Italy-based utility, paid a semiannual dividend of EUR0.215 per share while its shares traded near EUR6.60, an annualized dividend yield of roughly 6.5 percent against a 20-year total return near 7.5 percent.
When a dividend is assumed to grow at a constant rate forever, the DDM collapses to a growing perpetuity. Analysts either grow the most recent dividend or forecast next period’s dividend directly.
The required return on equity, , is also called the cost of equity. When the numerator is stated per share, the answer is an intrinsic price per share.
Excelitate Corporation has a current dividend of USD1.33 per share and a required return on equity of 8.5 percent. One analyst treats the company as mature with a flat dividend; another expects 5 percent annual dividend growth.
Free cash flow to equity
FCFE broadens the dividend measure to all cash that could go to equity owners, distributed or not. Buybacks are a return to shareholders that dividends miss; a share sale raises equity capital, which lowers FCFE even though the dividend does not move; and cash retained beyond operating needs still counts as available to owners. Because issuance and other uses can dominate, FCFE can turn negative, whereas dividends can never fall below zero. One definition builds FCFE from operations, capital spending, and net borrowing.
An equivalent view expresses what is left for owners directly in terms of the change in cash, dividends, and the change in equity, where the change in equity is issuance net of repurchases.
Excelitate reports net income of USD4,800,000, depreciation of USD700,000, an inventory rise of USD2,000,000, an accounts receivable rise of USD1,000,000, an accounts payable fall of USD1,000,000, capital expenditures of USD2,000,000, and new debt issuance of USD600,000.
When FCFE is projected forward, analysts usually assume the firm finances new investment at a target debt ratio (DR), the share of total capital funded by debt.
Assuming depreciation is the only non-cash charge, FCFE equals net income less net investment plus new borrowing, where net investment covers growth in long-term assets beyond depreciation plus the working capital increase. If borrowing rises proportionally with investment at the target ratio, substituting leaves FCFE as net income minus the equity-financed portion of net investment.
Two forces drive FCFE higher, holding net income fixed: lower investment spending and a greater reliance on debt to fund it. The features that tend to accompany positive versus negative FCFE are summarized below.
| Feature | FCFE greater than 0 | FCFE less than 0 |
|---|---|---|
| Capital expenditures | Lower spending, or spending funded by debt | Large equity-funded spending relative to operating cash flow |
| Debt policy | Growing debt balance | Large debt drawdowns |
| Cash management | Growing cash balances | Large cash drawdowns |
| Payout policy | Positive dividends or buybacks | No dividends or buybacks |
| Share issuance | Little to no issuance | Large issuance |
In a revised scenario Excelitate has net income of USD4,800,000, depreciation of USD700,000, a working capital increase of USD2,000,000, and capital expenditures (the rise in gross long-term assets) of USD1,500,000.
Free cash flow to the firm
FCFF is broader still because it measures cash available to every capital provider, debtholders as well as shareholders, which is why it values the whole firm rather than only its equity. It adds after-tax interest back to operating cash flow and subtracts capital spending.
Comparing the two measures directly highlights the role of debt: FCFF equals FCFE plus after-tax interest less the net change in debt.
For an all-equity firm the two are identical. When debt is used and the balance is unchanged, FCFF exceeds FCFE; but a large rise in debt outstanding can pull FCFF below FCFE. Because it does not lean on a target debt ratio, FCFF is more stable across changing capital structures and suits controlling investors who can shape investment and financing.
Excelitate has cash flow from operations of USD3,500,000, capital expenditures of USD1,500,000, a 20 percent tax rate, and before-tax interest expense of USD840,000. Its FCFE in this scenario is USD3,120,000 under a 40 percent debt ratio.
EBITDA versus free cash flow
Earnings before interest, taxes, depreciation, and amortization (EBITDA) captures revenue less operating expenses but ignores payments to debtholders, non-cash charges, and taxes. It relates to FCFF through the tax shield on depreciation and the deductions for investment.
EBITDA is useful for comparing firms with different leverage, tax rates, and investment because it strips those effects out, and it can be positive even when a company reports a net loss. But it is not a GAAP or IFRS measure, and adjusted EBITDA has no agreed definition, which leaves room for flattering adjustments. It is also a before-tax figure, so any discount rate applied to it must be a before-tax rate.
WeWork’s 2017 statements showed revenue of USD866 million against a net loss of USD933.5 million. By adding back rent holidays, stock-based compensation, and a range of growth, marketing, and administrative costs it labelled as unrelated to running its office space, the company reported a positive community adjusted EBITDA of USD233 million. Value estimates reached as high as USD50 billion, but the anticipated 2019 IPO was postponed as investors questioned the inflated growth picture. WeWork eventually listed two years later at a far lower value near USD9 billion.
Excelitate has net income of USD4,800,000, depreciation of USD700,000, interest expense of USD840,000, and a 20 percent tax rate.
Residual income
Residual income measures profit rather than cash flow. It is the earnings a firm generates beyond a charge for the opportunity cost of its equity, also called economic profit. A company can post positive net income yet add no value for owners unless its return on equity clears the cost of equity. Per share, residual income is EPS less a capital charge on the opening book value of equity.
The measure assumes clean surplus accounting, in which book value moves only with income and shareholder flows; items such as translation gains that bypass the income statement require an adjustment. Because it relies on clean surplus and book value, an RI valuation should in theory match an FCFE valuation, and unlike the free cash flow models it can be applied to firms currently generating negative free cash flow.
Excelitate has net income of USD4,800,000, book value of equity of USD14,000,000, and 1,000,000 shares outstanding. The cost of equity is 8.5 percent.
| Metric | What it captures | Distinctive features |
|---|---|---|
| Dividends | Cash distributed to shareholders only | Easiest to observe; a single payout measure; never a negative figure |
| FCFE | Total cash available to shareholders | Includes buybacks, issuance, and cash changes; sensitive to debt; can be positive or negative |
| FCFF | Cash available to all capital providers | Most comprehensive; invariant to debt changes; suits controlling investors |
| EBITDA | Operating cash generation before investment and tax | Comparable across leverage and tax profiles; non-standardized, before-tax measure |
| Residual income | Earnings above the cost of equity | Not a cash flow; built on book value and the cost of equity |
A well-run valuation follows five steps, each of which shapes the intrinsic value estimate.
- Select a cash flow measure. This chooses the numerator of the present value model: dividends, FCFE, FCFF, EBITDA, or residual income.
- Forecast that measure over a horizon. The projection can use a constant growth rate, a changing (multistage) rate, or a detailed statement-driven forecast covered later.
- Choose a required return. Cash flows belonging to shareholders are discounted at the cost of equity, ; cash flows shared with debtholders are discounted at the weighted average cost of capital, WACC.
- Establish a terminal value. This captures all cash flows beyond the explicit horizon, here using a constant growth assumption.
- Produce an intrinsic value. A single set of assumptions gives a point estimate; varying the assumptions gives a range for comparison with the market price.
The numerator and the discount rate must be consistent: an equity cash flow paired with a cost of equity, or a whole-firm cash flow paired with WACC. Mixing them, for example discounting FCFE at WACC, breaks that link and produces a value estimate that is not meaningful even if the arithmetic is correct.
Steinschlager AG pays a stable annual dividend of EUR1.50, and analysts expect the share price to be EUR20 five years out. The required return on equity is 10.0 percent.
Once a cash flow measure is chosen, the next task is to project it into the indefinite future. The right growth pattern depends on where a firm sits in its life cycle: startups often have little revenue and frequent losses, growth firms expand as their markets open up, mature firms settle into steadier cash flows, and some eventually decline.
Constant growth
Mature firms with stable cash flows justify a single constant growth rate. They tend to carry near-average risk, an industry-typical debt ratio, a return on capital close to their cost of capital, lower capital spending, and higher payout ratios. For any metric, the constant growth model discounts next period’s cash flow by the required return less the growth rate.
Next period’s cash flow can be grown from the current figure, , or forecast directly. The model is appealing because it needs no explicit horizon, but the estimate is highly sensitive to . For the value to be positive and sensible, the growth rate must stay below the discount rate, and over the long run it should not exceed the growth rate of the economy, which the nominal risk-free rate can approximate. Firms in decline may even carry a negative growth rate.
Excelitate has a next-period FCFE forecast of USD4.2 million, a long-run growth rate of 4.3 percent, and its required return on equity is 8.5 percent. It has 1,500,000 shares outstanding.
Reversing the model gives an implied growth rate: substitute the market price for intrinsic value and solve for the steady growth the market must be assuming.
Reducing a market price to a single implied growth number makes it easy to compare companies within an industry, across industries, or against overall economic growth.
Multistage growth
Most firms do not grow at one steady rate. A multistage model lets an early phase grow at one rate before settling to a lower long-term rate, which better fits companies expanding into new markets. Starbucks is a familiar example: annual revenue growth ran above 20 percent before the 2008 to 2009 financial crisis, then fell to roughly half that pace over the following decade as the store base matured and the company began paying and growing dividends.
Using FCFE, the value equals the discounted high-growth cash flows plus the discounted terminal value, where the terminal value at period is the first stable-growth cash flow capitalized at the required return less the long-term rate.
Excelitate’s most recent FCFE is USD3,500,000. An analyst assumes 12 percent growth for three years, then 4 percent forever. The required return on equity is 8.5 percent, and there are 1,500,000 shares outstanding.
| Year 1 | Year 2 | Year 3 | Year 4 | |
|---|---|---|---|---|
| FCFE | 3,920,000 | 4,390,400 | 4,917,248 | 5,113,938 |
| PV at 8.5% | 3,612,900 | 3,729,448 | 3,849,753 |
Growth rate determinants
Growth forecasts come from historical rates or from fundamentals. Historical estimates depend on the base year chosen: a starting point distorted by an unusual year introduces a base effect that biases the result. For Starbucks, both free cash flow measures spiked in 2018 and reversed in 2019, so a compound growth rate anchored on 2018 would be biased downward.
| 2017 | 2018 | 2019 | 2020 | 2021 | 2022 | 2023 | |
|---|---|---|---|---|---|---|---|
| FCFF | 2,794.2 | 10,094.5 | 3,506.8 | 461.2 | 4,887.5 | 2,930.7 | 4,095.1 |
| FCFE | 3,082.6 | 15,545.5 | 4,886.4 | 5,280.7 | 2,837.9 | 3,229.1 | 4,143.7 |
The fundamental alternative is the sustainable growth rate (SGR), the product of the earnings retention rate and the return on equity. It suits firms whose payout and profitability ratios are expected to hold steady.
The framework extends to the other metrics. For FCFE, replace the dividend term with the ratio of FCFE to net income; for FCFF, use FCFF over net operating profit after tax (NOPAT) and the return on total capital, where . Because these ratios differ, the same firm can show different sustainable growth rates depending on the cash flow measure.
Bhardwaj Supply, a Mumbai-based distributor, pays out 70 percent of earnings and earns a 15 percent return on equity. Its most recent dividend per share is INR5.00 and its required return on equity is 10 percent.
The discount rate must match the investor claim in the numerator. Cash flows for all capital providers use WACC, the market-value-weighted average of the after-tax cost of debt and the cost of equity.
Because FCFF values the whole firm, its equity value is the discounted FCFF stream, at WACC, less the market value of debt. Cash flows belonging only to shareholders, such as dividends, FCFE, and residual income, are discounted at the cost of equity instead. Since debt bears less risk than equity, it carries the lower required return, so WACC is at most equal to the cost of equity and sits strictly below it whenever debt is present.
FCFE and FCFF should produce similar equity values when the assumptions behind them are kept consistent.
Belchamp Corporation, a Canadian firm, has a market value of equity four times its market value of debt. Its cost of equity is 12 percent, its cost of debt is 6 percent, and the tax rate is 20 percent. Base-year FCFE is CAD40 million with 2.0 percent expected growth, and base-year FCFF is CAD40.8 million. Debt is worth CAD104 million.
The terminal value is the expected price at the end of the horizon, and it looms largest when the horizon is short or when the forecast growth rate is close to the long-run rate. To limit bias, analysts standardize the stable rate: it usually sits between expected inflation and nominal economic growth, so it varies across countries and should reflect the markets where a firm actually operates, not just where it is headquartered. It can be near zero, or negative for a declining firm.
Swisserv AG has a base-year FCFE of CHF3,120,000 growing 12 percent for three years, and a required return on equity of 10 percent. With Swiss nominal GDP growth near 2 percent and inflation near 0.5 percent, the analyst uses a 1.25 percent stable rate.
Even a disciplined DCF carries drawbacks, from company-specific factors to broad macroeconomic ones. The choice of a single cash flow measure can bias the result if it misses part of the value story. Dividends, for instance, understate value for a firm that returns cash through buybacks, and dividend and free cash flow measures can diverge sharply when payout policy or share count shifts.
MacArthur Company, an Australian office supply retailer, faces digitization and low-cost rivals. Its most recent FCFE was AUD250 million, and shareholders require a 10 percent return.
Suppose a MacArthur analyst grows FCFE at 1 percent, giving a value of AUD250(1.01) divided by (0.10 minus 0.01), or AUD2.81 billion. A colleague instead grows total dividends of AUD150 million at 5 percent, giving AUD150(1.05) divided by (0.10 minus 0.05), or AUD3.15 billion. The AUD340 million gap can come from a rising dividend payout ratio or a falling share count through buybacks, since the dividend-per-share growth cited ignores any change in shares outstanding when total dividends are used as the metric.
Broader measures such as FCFE and FCFF face their own estimation problems: base-year effects when a constant debt ratio must be imposed, and the difficulty of pinning down margins and investment. Models that lean on a single base-year cash flow and a growth rate work best for mature firms. They struggle when a firm transforms itself. Amazon is a case in point: its shift into cloud services, physical grocery retail, and a vast fulfillment network, financed increasingly with debt while reinvesting earnings, changed leverage, profitability, and investment so profoundly that a single base-year cash flow and growth rate would badly mis-measure its value.
Decline poses a different problem. Present value models assume the firm survives the forecast horizon, but financial distress is often sudden rather than a smooth slide, so it is better handled with explicit scenario analysis than with a gently negative growth rate.
Top-down inputs matter as much as company factors, especially the cost of capital. The risk-free rate embedded in both debt and equity costs moves with macroeconomic conditions, and a shift in it can swing valuations sharply.
Because these distortions can compound, analysts typically apply more than one model and approach, recognizing that each involves simplification and uncertainty over its appropriateness, specification, and inputs.
Preferred stock pays periodic dividends set as a fixed percentage of par value. It is a small slice of total equity, concentrated among large issuers in regulated industries like banking, insurance, and utilities, along with private and venture-backed firms. Preferred dividends are not contractual, but preferred holders rank ahead of common holders both for dividends and for assets in liquidation. This lesson concentrates on non-callable, non-convertible shares paying a constant fixed dividend.
Because those cash flows resemble a dividend-paying common stock, a dividend discount model values them with three adjustments: the dividend is fixed rather than growing, a share with a finite maturity returns its face value FV instead of an expected terminal price, and the discount rate is below the cost of common equity to reflect the priority claim.
A perpetual preferred share with no maturity is simply a fixed perpetuity.
Monte Cabrio Bank has preferred shares with a EUR1,000 face value, a 6.75 percent annual dividend, and five years to maturity. Monte Corsa Bank has perpetual preferred shares with a EUR1,000 face value and an 8 percent dividend trading at EUR1,020.
Contingency features are rights, not obligations, and each shifts intrinsic value because it carries economic value to the issuer or the investor. A callable preferred share lets the issuer redeem early, typically at par or a declining premium, so the issuer must offer a higher dividend to compensate; the call reduces the share’s value to an investor relative to an otherwise identical non-callable share. A putable preferred share lets the investor sell back to the issuer, a right that supports a lower dividend. A convertible preferred share can be exchanged for common shares at a fixed ratio, blending a senior, fixed-income-like claim with equity-like upside, which also allows a lower dividend. From highest to lowest expected dividend, the ranking is callable, then plain non-callable and non-convertible, then putable, with convertible shares likewise paying below the plain preferred.