Valuing a Company: DCF, Terminal Value, EVA, and Multiples

A company is worth the cash it can generate for its capital providers. Valuation turns that idea into a disciplined set of forecasts: how much cash, when it arrives, what investment it requires, and how risky it is.

All numerical examples below are invented teaching examples. Amounts are in millions unless stated otherwise; cash flows arrive at year-end. Rates and cash flows are nominal, in the same currency. The main DCF assumes a stable capital structure and a constant, appropriate WACC.

1. First decide what you are valuing

There are two different questions:

1. What are the operating businesses worth to all their capital providers?
2. After settling other claims, how much belongs to common shareholders?

Discounting unlevered free cash flow, also called FCFF, at WACC answers the first question:

$$EV_0=\sum_{t=1}^{T}\frac{FCFF_t}{(1+WACC)^t}+\frac{TV_T}{(1+WACC)^T}.$$

Here, enterprise value (EV) means operating business value. FCFF is available to debt and equity providers together, so do not subtract interest in the forecast and then discount at WACC. That would count financing twice.

The basic operating cash flow calculation is:

$$FCFF=EBIT(1-\tau)+Depreciation-Capex-\Delta NWC.$$

Use operating working capital: receivables, inventory, and other operating current assets less operating current liabilities. Exclude financing debt and separately valued excess cash.

The enterprise-to-equity bridge

A more complete bridge than simply subtracting debt is:

$$\begin{aligned} Common\ equity\ value={}&EV+Excess\ cash+Nonoperating\ assets\\ &-Debt-Preferred\ claims-Noncontrolling\ interests\\ &-Other\ applicable\ claims. \end{aligned}$$

Every adjustment must match the scope of the cash flow forecast. For example, if consolidated FCFF includes 100% of a subsidiary, deduct the value attributable to outside owners. If the forecast includes only the parent’s share, do not deduct that interest again.

Use market values of claims where available. Debt’s face value is a reasonable shortcut only when it approximates market value. Required operating cash belongs in operating investment; excess cash can be added separately. An asset already generating cash included in FCFF cannot also be added as a separate nonoperating asset.

The familiar identity $V=D+E$ is a simplified capital-provider identity. Operating EV equals debt plus common equity only when excess assets and other claims do not require adjustments.

After obtaining common equity value, calculate value per share using a consistent treatment of options, convertibles, and dilution. Do not deduct an option claim and also count the same claim through a second dilution adjustment.

2. Forecast until the economics stabilize

The explicit forecast should describe the company’s operating story: sales, margins, taxes, working capital, and capital spending. A five-year forecast is not automatically better than a ten-year forecast. Choose the horizon at which a defensible steady state begins.

A young company may need time for margins to normalize. A cyclical business may need a forecast across the cycle. A declining business may never reach positive growth. The terminal year should reflect those economics rather than an arbitrary spreadsheet endpoint.

Terminal value is the value at date $T$ of cash flows after date $T$. The year-$T$ cash flow is already in the explicit forecast.

Today        Year 1        Year 2        Year T        Year T+1 ...
  0 ---------- 1 ------------ 2 ----------- T ------------>
             FCFF1         FCFF2        FCFFT       terminal stream
                                          |
                                         TVT

Bring both $FCFF_T$ and $TV_T$ back to today. Forgetting the second discounting step can dramatically overstate value.

3. Three terminal-value approaches

A. Liquidation

If operations end, value the cash actually recovered from selling assets and releasing working capital:

$$TV_T=S-\tau(S-B_{tax})+Recoverable\ NWC-Closure\ costs,$$

where $S$ is sale proceeds and $B_{tax}$ is the assets’ remaining tax basis. The tax expression assumes gains are taxable and losses produce usable tax benefits at rate $\tau$. Actual tax treatment can differ.

If sale proceeds are 200, tax basis is 120, the tax rate is 25%, recoverable NWC is 40, and after-tax closure costs are 10:

$$TV_T=200-0.25(200-120)+40-10=210.$$

The shorthand $S(1-\tau)+\tau PPE+NWC$ works only when PPE represents the relevant tax basis and working capital is recoverable at that value. Receivables may default, inventory may sell at a discount, and liquidation may create additional taxes or costs.

Do not add full liquidation proceeds to a going-concern terminal value for the same assets: the latter already assumes the assets keep generating cash.

B. No-growth perpetuity

For a sustainable constant annual cash flow beginning in year $T+1$:

$$TV_T=\frac{FCFF_{T+1}}{k}.$$

This becomes $NOPAT_{T+1}/k$, with $NOPAT=EBIT(1-\tau)$, only if net reinvestment is zero. A standard simplifying assumption is maintenance capex equal to depreciation and no increase in operating NWC.

No revenue growth does not mean no capital spending. Machines still wear out. Depreciation is an accounting estimate; it may differ materially from the economic cost of replacing assets.

C. Growing perpetuity

For sustainable constant growth with $k>g$:

$$TV_T=\frac{FCFF_{T+1}}{k-g}.$$

The numerator is next year’s cash flow, not the last forecast year’s cash flow. Growth must be financed. Let invested operating capital $IC$ equal net operating fixed assets plus operating NWC. Under a clean capital roll-forward:

$$FCFF_t=NOPAT_t-(IC_t-IC_{t-1}).$$

If profits and invested capital both grow at $g$ after year $T$:

$$FCFF_{T+1}=(1+g)NOPAT_T-gIC_T,$$

and therefore:

$$TV_T=\frac{(1+g)NOPAT_T-gIC_T}{k-g}.$$

The term $gIC_T$ is net new operating investment, not total replacement spending. The identity requires appropriate accounting adjustments if acquisitions, write-offs, currency movements, or revaluations change reported capital without corresponding operating cash investment.

For WACC, use $k=WACC$. For APV, value unlevered operating cash flows at $k_A$ and separately value financing effects, including their terminal continuation under the assumed debt policy.

4. Complete example: from operations to a share value

Suppose the explicit FCFF forecast is:

Year	1	2	3
FCFF	90	105	120

At the end of year 3, NOPAT is 150 and invested operating capital is 1,000. Thereafter both grow at 3%; WACC is 9%.

First calculate the first terminal cash flow:

$$FCFF_4=150(1.03)-1{,}000(0.03)=124.5.$$

Then value the terminal stream at year 3:

$$TV_3=\frac{124.5}{0.09-0.03}=2{,}075.$$

The operating enterprise value today is:

$$\begin{aligned} EV_0&=\frac{90}{1.09}+\frac{105}{1.09^2}+\frac{120}{1.09^3} +\frac{2{,}075}{1.09^3}\\ &=263.61+1{,}602.28=1{,}865.89. \end{aligned}$$

Now reconcile claims:

Item	Value
Operating enterprise value	1,865.89
Add excess cash	100.00
Add separately valued nonoperating assets	40.00
Subtract market value of debt	(500.00)
Subtract preferred claims	(30.00)
Subtract noncontrolling interests	(20.00)
Common equity value	1,455.89

With 100 million common shares and no additional dilution, the implied share value is 14.56. This is a model output conditional on the assumptions, not an observed market price.

Sensitivity is part of the answer

Hold the explicit forecasts, year-3 NOPAT, and year-3 invested capital fixed. Recalculate terminal reinvestment whenever $g$ changes:

Operating EV	$g=2\%$	$g=3\%$	$g=4\%$
WACC 8%	2,028.28	2,245.26	2,570.73
WACC 9%	1,730.76	1,865.89	2,055.07
WACC 10%	1,507.81	1,595.02	1,711.29

A higher growth assumption increases reinvestment as well as future profit. Keeping terminal FCFF fixed while changing growth would describe a different model.

Here, terminal value supplies about 86% of operating EV. That is a reason to investigate the steady-state assumptions carefully. Ask whether competitive returns, reinvestment, and growth can persist together; do not treat a large terminal contribution as automatic evidence of an error.

5. EVA: growth must earn its capital charge

Economic Value Added (EVA) subtracts a charge for the capital needed to generate operating profit:

$$EVA_t=NOPAT_t-kIC_{t-1}.$$

Using beginning-of-period capital makes the timing explicit. Define:

$$ROIC_t=\frac{NOPAT_t}{IC_{t-1}}, \qquad EVA_t=(ROIC_t-k)IC_{t-1}.$$

A company earning 120 on capital of 1,000 with a 10% capital cost has EVA of $120-100=20$. Accounting profit is positive, and the business also earns more than the required return on its capital.

But existing positive EVA does not guarantee that expansion creates value. Suppose a new investment costs 100 and produces sustainable additional annual NOPAT of only 8, with zero net reinvestment thereafter. Its incremental ROIC is 8%, below the 10% hurdle rate:

$$NPV_{expansion}=\frac{8}{0.10}-100=-20.$$

Sales and earnings rise, yet shareholder wealth falls. Evaluate incremental returns, not just historical average profitability.

Connecting EVA and DCF

Substitute $NOPAT_t=EVA_t+kIC_{t-1}$ into the FCFF identity. Discounting and summing causes the capital movements to telescope. With consistent capital accounting and an appropriate terminal condition:

$$Operating\ value_0=IC_0+PV(Future\ EVA).$$

This is another way to organize the same economic valuation. A single year’s EVA is a snapshot; the entire expected EVA stream is needed for value. Current negative EVA can coexist with a valuable young business if future economic profits justify its investment. Book capital also needs care when internally developed intangibles have been expensed.

EVA is distinct from the sustainable growth rate: one measures profit after a capital charge; the other concerns financing capacity under specified policies.

6. Multiples: match the claim to the denominator

A multiple transfers a market relationship from comparable businesses to the target. The critical first step is matching whose value appears in the numerator to whose income or cash flow appears in the denominator.

Multiple	What it values	Main interpretation
EV / EBITDA	Operations	Before interest, tax, depreciation, and amortization; omits reinvestment
EV / EBIT or EV / NOPAT	Operations	Operating profit before or after operating taxes
EV / FCFF	Operations	Cash available to all capital providers
Equity value / common net income, or P/E	Common equity	Earnings after financing costs and other senior claims
Equity value / FCFE	Common equity	Cash available to equity after debt cash flows
Equity value / common book equity	Common equity	Market value relative to recorded shareholder capital
EV / invested operating capital	Operations	Operating value relative to its capital base

FCFE means free cash flow to equity. A ratio labeled simply “price/free cash flow” is ambiguous until you inspect the cash flow definition. Do not apply an equity price multiple to FCFF, or treat net income after interest as an unlevered operating measure.

Enterprise multiples reduce some direct leverage effects, but they do not eliminate differences in tax treatment, leases, pension obligations, capital intensity, or accounting. P/E is particularly sensitive to financing because debt changes both equity risk and net income.

Subscribers, patents, or production capacity can be useful industry denominators. They are proxies for future cash generation: subscribers with high churn or low margins are not economically identical to profitable, loyal subscribers.

What assumptions hide inside a multiple?

For a stable growing FCFF stream:

$$\frac{EV_0}{FCFF_1}=\frac{1}{WACC-g}, \qquad \frac{EV_0}{FCFF_0}=\frac{1+g}{WACC-g}.$$

Forward and trailing multiples differ. At WACC 9% and growth 3%, the forward FCFF multiple is 16.67 times; the trailing multiple is 17.17 times.

For equity, the dividend growth model gives:

$$P_0=\frac{D_1}{k_E-g} \quad\Rightarrow\quad \frac{P_0}{EPS_1}=\frac{Payout\ ratio}{k_E-g}.$$

With a 60% payout, 10% equity cost, and 4% growth, the forward P/E is $0.60/(0.10-0.04)=10$ times. Omitting the payout ratio would incorrectly give 16.67 times. The payout, retention, growth, and investment-return assumptions must also be mutually consistent.

Similar multiples therefore require more than the same industry label. Compare business risk, sustainable growth, returns on new investment, margins, tax rates, cash conversion, and financing policy. Similar leverage alone does not guarantee similar WACC.

7. Worked comparable-company check

Suppose three genuinely comparable firms trade at forward EV/EBITDA ratios of 6, 8, and 10 times. Their median is 8 times. The target’s normalized forward EBITDA is 200:

$$Implied\ EV=8\times200=1{,}600.$$

Using the same net bridge adjustment of $-410$ as the DCF example:

$$Common\ equity=1{,}600-410=1{,}190, \qquad Value/share=11.90.$$

DCF gave 14.56 per share. Do not automatically average the two. Investigate the reason: does the target deserve better growth or reinvestment economics, or is the DCF too optimistic? Are the peers temporarily depressed? Is target EBITDA before a recurring expense that peers include?

The DCF implies EV/EBITDA of approximately $1{,}865.89/200=9.33$ times. That makes the disagreement concrete: the DCF places the target toward the upper end of the assumed peer range.

For practical comparables, use a common valuation date, consistent forward or trailing periods, and normalized recurring measures. Negative or near-zero denominators can make earnings multiples unusable. Transaction multiples also embed control, synergies, and deal conditions that public trading multiples may not include.

8. Use DCF and multiples to challenge each other

Approach	What it makes visible	What needs scrutiny
DCF	Explicit operating forecasts, reinvestment, risk, and strategic changes	Forecast quality, terminal economics, and discount rates
Multiples	How markets price similar businesses	Comparability, accounting definitions, and possible market mispricing

DCF is a structured statement about fundamentals. Multiples express a relative market judgment. A useful valuation reconciles the operating story behind both and reports a defensible range rather than hiding uncertainty behind a precise share price.

Before finishing, trace every value back to a cash flow or claim. Check the forecast-to-terminal transition, the growth investment requirement, the cash and debt bridge, the numerator/denominator match, and the treatment of financing effects.

9. Practice questions

1. Operating EV is 900, excess cash is 80, debt is 250, and preferred stock is worth 30. What is common equity value?
2. A company has FCFF of 60 in year 6. Year 5 is the forecast horizon, WACC is 8%, and perpetual growth is 2%. Find terminal value at year 5 and its present value.
3. NOPAT at year $T$ is 100, invested capital is 500, growth is 4%, and WACC is 10%. Calculate next year’s FCFF and terminal value.
4. Assets sell for 150 with a tax basis of 100. Recoverable NWC is 20 and the tax rate is 30%. Ignore closure costs. What liquidation cash flow results?
5. A business earns NOPAT of 45 on beginning capital of 400 with a 9% capital cost. Calculate EVA and ROIC.
6. A peer forward EV/EBITDA multiple is 7 times. Target forward EBITDA is 50, excess cash is 10, and debt is 100. Find EV and equity value.
7. Under constant growth, expected EPS is 5, payout is 40%, $k_E=12\%$, and $g=4\%$. Find forward P/E and price.
8. Explain two errors in: “Revenue grows 5%, so terminal FCFF can grow 5% without extra investment; then multiply that FCFF by an equity price multiple.”

Answers and reasoning

1. $900+80-250-30=700$. Add excess assets and deduct claims senior to common equity.
2. $TV_5=60/(0.08-0.02)=1{,}000$. Its present value is $1{,}000/1.08^5=680.58$. The first terminal cash flow arrives in year 6.
3. $FCFF_{T+1}=104-20=84$; $TV_T=84/(0.10-0.04)=1{,}400$. Growth consumes 20 of additional capital.
4. $150-0.30(150-100)+20=155$. Taxes apply to the gain over tax basis.
5. $EVA=45-0.09(400)=9$; $ROIC=45/400=11.25\%$. The return spread is 2.25 percentage points.
6. $EV=7(50)=350$; equity value is $350+10-100=260$.
7. $P/E_1=0.40/(0.12-0.04)=5$ times; price is $5(5)=25$. Expected dividends are 2, giving the same price through the dividend model.
8. Growth often requires capex and working capital, so its cash flow consequences must be modeled. FCFF belongs to all capital providers and requires an enterprise-value multiple; an equity multiple requires an equity denominator such as common net income or FCFE.

References and further study

These are original teaching explanations and illustrative calculations, organized around the supplied lecture outline. The following course materials provide the underlying lecture context; the qualifications about claim matching, timing, and reinvestment are made explicit throughout this lesson.

• MIT OpenCourseWare, Finance Theory II, Spring 2003: Valuing Companies, Lecture 21, Section A — Dirk Jenter. Covers terminal-value alternatives, EVA, and comparable valuation.
• MIT OpenCourseWare, Finance Theory II, Spring 2003: Valuing Companies, Lecture 21, Section B — Katharina Lewellen. Companion treatment of company valuation.
• Review the preceding lessons on FCF, WACC and APV, and real options when forecasts depend on financing policy or future managerial flexibility.

Feynman study lab

Explain it simply

Value operations first, then reconcile which claims and non-operating assets belong to equity holders.

Concrete example. Enterprise value of 100, debt of 30 and excess cash of 10 imply equity value 80 in a simplified bridge.

Teach it back without looking

Close the lesson and explain the idea aloud to a beginner in two minutes. Define each technical term you use, walk through the example, and state one assumption or limitation. Then answer:

Why should you not subtract the same debt twice?

Check your explanation after you try

Enterprise value and equity value refer to different claims. Align the cash flows, discount rate and bridge so each claim is counted once.

Find the gap and try again

If you hesitated, relied on a formula you could not explain, or missed the self-check, write down the exact gap. Revisit the relevant section of this lesson and work through its example. Close the notes, explain it again in simpler language, then change one number or assumption and predict what changes. Recalculate or check the lesson to test your prediction. Try once more tomorrow from memory.