# DCF Valuation Concept Card: [Company, course or case] > A concept card for discounted cash flow (DCF) valuation as it is taught in the MBA core corporate finance course and > used in banking, consulting, private equity and corporate development. It covers free cash flow to the firm (FCFF) > and to equity (FCFE), how to build a forecast from value drivers, the terminal value by the Gordon growth formula > and by an exit multiple with the consistency checks that link them, the mid-year convention, the bridge from > enterprise value to value per share, a computed sensitivity table, and a cross-check against trading multiples. It > is for MBA students in the core, candidates preparing for finance interviews and managers who must read a valuation > someone else built. Worked example A is fully solved, B is half solved and Exercise C is left to you; the self-test > answers sit in a separate key. > Source basis: Williams (1938), Gordon (1959), Miller and Modigliani (1961) on the equivalence of valuation methods, > Kaplan and Ruback (1995) on DCF accuracy, and standard valuation textbooks named as further reading; all wording, > notation and examples are original. Corvane Robotics and Northfield Outdoor Co. are fictional. > Replace every [bracketed] value and every row marked *Example*. ## Document control | Field | Value | |---|---| | Document ID | [MBA-CF-DCF-001] | | Course or project | [Core corporate finance / valuation elective / interview preparation] | | Learner | [Your name] | | Company or case | [Corvane Robotics (fictional) / your case] | | Valuation date | YYYY-MM-DD | | Currency and units | [USD m unless stated] | | Conventions used | [Mid-year discounting; FCFF at WACC; Gordon growth terminal value with value-driver check] | | Excel version used for checks | [Microsoft 365 / Excel 2021] | | Reviewed by | [Study group member, tutor or mentor] | | Last updated | YYYY-MM-DD | | Version | [0.1] | ## Contents 1. When to use it 2. The idea in plain language 3. Formulas and notation 4. Assumptions and limits 5. How managers use it in practice 6. The DCF process 7. Forecasting drivers 8. Terminal value and consistency checks 9. Worked example A (fully solved): Corvane Robotics 10. Worked example B (half solved): Northfield Outdoor Co. 11. Exercise C (unsolved) 12. Connections to other cards 13. Common mistakes and misconceptions 14. Self-test questions 15. My notes and next steps ## When to use it **One-sentence rule:** use a DCF when the value of a business or project comes from cash flows you can forecast from operating drivers, and you need a value that reflects this specific company's plan rather than the market's average view. | Use a DCF when | Be careful or add another method when | |---|---| | The business has, or will reach, positive and forecastable free cash flow | Cash flows are negative for many years and the value is almost all terminal value (early-stage ventures: see mba/mba-venture-finance-cap-table-card) | | You need to test a strategy, a plan or a synergy case driver by driver | You only need a quick market reference point (start with finance/comparable-companies-analysis) | | Management, a board or an investment committee asks what drives value | The firm is a bank or insurer, where debt is raw material, not financing (use an equity or dividend model) | | You must value a division or a private company with no market price | Value depends mostly on flexibility to expand, wait or abandon (add mba/mba-options-real-options-card) | | Interviews and case exams ask you to walk through a valuation | Leverage will change sharply over the forecast, for example in a buyout (use APV, see mba/mba-capital-structure-card) | A DCF is a disciplined way to state assumptions, not a machine that produces truth. Its main value in a meeting is that every number can be traced to a driver that someone can challenge. ## The idea in plain language A business is worth the cash it will generate for its investors, adjusted for when that cash arrives and how risky it is. Williams (1938) stated the idea for shares: the value of a stock is the present value of the cash it will pay out. A DCF applies it in three steps. 1. **Forecast free cash flow** for an explicit period, usually 5 to 10 years, until the business reaches a steady state in which growth, margins and reinvestment are stable. 2. **Estimate a terminal value** at the end of that period, which captures all cash flows after it, either with a perpetual growth formula or with a multiple of a metric such as EBITDA. 3. **Discount** both at a rate that matches the risk of the cash flows and the investors who receive them, then move from the value of the operations to the value of each share. Two families exist. The **enterprise (entity) approach** values the cash flows available to all capital providers (FCFF) at the weighted average cost of capital and then subtracts the claims of non-equity holders. The **equity approach** values the cash flows left for shareholders after debt service (FCFE) at the cost of equity. If the assumptions about financing are consistent, both give the same equity value; in practice the enterprise approach is more common because the forecast does not depend on a debt schedule. ## Formulas and notation **Free cash flow to the firm** (unlevered free cash flow): $$ FCFF_t = EBIT_t\,(1 - t_c) + DA_t - CapEx_t - \Delta NWC_t $$ **Free cash flow to equity:** $$ FCFE_t = FCFF_t - Int_t\,(1 - t_c) + \text{Net borrowing}_t $$ **Enterprise value with end-of-year discounting:** $$ EV_0 = \sum_{t=1}^{T}\frac{FCFF_t}{(1 + WACC)^t} + \frac{TV_T}{(1 + WACC)^T} $$ **Mid-year convention** (cash flows arrive on average in the middle of each year): $$ EV_0 = \sum_{t=1}^{T}\frac{FCFF_t}{(1 + WACC)^{t - 0.5}} + \frac{TV_T}{(1 + WACC)^{T - 0.5}} $$ When the terminal value comes from an exit multiple, it represents a sale at the end of year $T$, so it is discounted for $T$ full years even when the forecast years use the mid-year convention. **Terminal value, Gordon growth form** (Gordon 1959; Gordon and Shapiro 1956 for the capital budgeting version): $$ TV_T = \frac{FCFF_{T+1}}{WACC - g}, \qquad FCFF_{T+1} = NOPAT_{T+1}\left(1 - \frac{g}{RONIC}\right) $$ The second expression is the value-driver form: in a steady state, growth $g$ requires reinvesting the share $g/RONIC$ of NOPAT, where $RONIC$ is the return on new invested capital. **Terminal value, exit multiple form:** $TV_T = M \times EBITDA_T$ (or EBIT, revenue, earnings, as the sector uses). **Enterprise to equity bridge:** $$ \text{Equity value} = EV - \text{Debt} - \text{Lease liabilities} - \text{Preferred} - \text{NCI} + \text{Cash} + \text{Non-operating assets} $$ $$ \text{Value per share} = \frac{\text{Equity value}}{\text{Diluted shares}} $$ | Symbol | Meaning | |---|---| | $EBIT_t$, $NOPAT_t$ | Earnings before interest and taxes; net operating profit after tax, $EBIT(1 - t_c)$ | | $t_c$ | Marginal (or normalised cash) tax rate on operating profit | | $DA_t$, $CapEx_t$ | Depreciation and amortisation, capital expenditure | | $\Delta NWC_t$ | Increase in net (operating) working capital | | $Int_t$ | Interest expense | | $WACC$ | Weighted average cost of capital (see mba/mba-capm-wacc-card) | | $g$ | Perpetual nominal growth rate of FCFF after year $T$ | | $RONIC$ | Return on new invested capital in the steady state | | $M$ | Exit multiple, for example EV/EBITDA | | NCI | Non-controlling (minority) interests | | $T$ | Last year of the explicit forecast | ## Assumptions and limits - **Consistency of cash flow and rate.** FCFF goes with WACC, FCFE with the cost of equity; nominal cash flows with a nominal rate, real with real; the currency of the cash flows with the currency of the rate. - **Constant capital structure.** Discounting at one WACC assumes the firm keeps a constant target ratio of debt to value. If leverage changes a lot, use adjusted present value (APV, Myers 1974; see mba/mba-capital-structure-card). - **Steady state at year T.** The Gordon formula is valid only when growth, margins, reinvestment and risk are stable from year $T+1$ onward, and when $g < WACC$. If the business is still growing fast in year $T$, extend the forecast. - **Growth ceiling.** A perpetual nominal growth rate above the long-run nominal growth of the economy the firm sells into implies the firm eventually becomes larger than that economy. - **Going concern.** A DCF assumes the business continues. If liquidation or a sale is likely, value that path too. - **Market efficiency is not assumed, but checked.** A DCF can differ from market multiples. The gap is a hypothesis to explain (growth, returns on capital, risk), not proof that the market is wrong. - **Accuracy.** Kaplan and Ruback (1995) found that DCF values built from management forecasts for highly leveraged transactions were, on average, within about 10 percent of the transaction values and at least as accurate as multiples. Treat this as evidence that the method is sound when inputs are disciplined, not as a guarantee. ## How managers use it in practice - **Board and investment committee decisions:** acquisitions, divestitures, large capital projects. The DCF is shown with a sensitivity table and a football-field chart beside trading and transaction multiples (finance/valuation-report). - **Strategy and planning:** value-based management links the plan to value through the drivers (growth, margin, capital intensity, return on capital). A plan that grows revenue at a return on new capital below WACC destroys value even though revenue rises. - **Fairness opinions, impairment tests and purchase price allocation:** accountants and auditors read DCFs for impairment under IAS 36 and for fair value; see finance/impairment-test-memo. - **Banking and consulting interviews:** "walk me through a DCF" is a standard technical question; see mba/mba-banking-technical-prep. - **Survey evidence:** Graham and Harvey (2001) report that NPV and IRR are the capital budgeting methods most used by large US firms, with the CAPM the dominant way to set the cost of equity. Reporting note (dated fact): as of October 2026, IFRS 18 *Presentation and Disclosure in Financial Statements* replaces IAS 1 for annual periods beginning on or after 1 January 2027 and requires new subtotals, including operating profit (checked on ifrs.org, 2026-10-28). "Operating profit" under IFRS 18 is a defined subtotal and need not equal the EBIT in your model: reconcile the two before you take a margin from reported accounts. US GAAP is not affected. Check the current standard at https://www.ifrs.org before you rely on this; see finance/ifrs-18-transition-plan. ## The DCF process ```mermaid flowchart TD A["Understand the business: industry, model, history"] --> B["Choose approach: FCFF at WACC or FCFE at cost of equity"] B --> C["Forecast drivers: growth, margin, tax, capital intensity, working capital"] C --> D["Build FCFF for the explicit period"] D --> E["Estimate WACC (mba/mba-capm-wacc-card)"] E --> F["Terminal value: Gordon growth and exit multiple"] F --> G{"Consistency checks pass?"} G -->|"No"| C G -->|"Yes"| H["Discount with the chosen timing convention"] H --> I["Bridge: EV to equity to diluted value per share"] I --> J["Sensitivity table and scenarios"] J --> K["Cross-check with multiples and transactions"] K --> L["Write the valuation conclusion as a range"] ``` The loop back from the checks to the drivers is the most important arrow in the diagram. A model that fails a terminal value check is fixed by changing a driver you can defend, never by adjusting the discount rate until the answer looks right. Keep inputs, calculations and outputs in separate blocks of the workbook so that the sensitivity table, the checks and the bridge all point at the same input cells. ## Forecasting drivers Build the forecast from a short list of drivers, each with a source: | Driver | Typical anchor | Question to ask | |---|---|---| | Revenue growth | Market growth, share change, price and volume, capacity | Which customers, products and regions produce this growth, and is the market large enough? | | EBIT margin | History, peers at maturity, operating leverage | Which costs scale with revenue and which are fixed? | | Cash tax rate | Statutory rate, losses carried forward, incentives | When do tax losses run out? | | D&A as share of revenue or of PP&E | Asset lives, history | Is D&A consistent with the capex plan? | | CapEx as share of revenue | Capacity plan, maintenance needs | Does capex fall towards D&A plus growth capex as growth slows? | | Net working capital as share of revenue | Receivable, inventory and payable days | Do working capital days match the operating model and peers? | | Return on invested capital | Competitive advantage (see mba/mba-competitive-advantage-card) | Can returns stay above WACC, and for how long? | Three rules keep the forecast honest. First, **reinvestment must fund growth**: you cannot grow revenue 20 percent a year with capex below depreciation. Second, **margins converge**: above-peer margins need a source of advantage you can name. Third, **the last forecast year must be a steady state**, because the terminal value will extrapolate it forever. ## Terminal value and consistency checks The terminal value is usually the largest part of a DCF: in Worked example A it is 82.5 percent of enterprise value. Run these checks on every model. | ID | Check | Pass rule | Example A result | |---|---|---|---| | TV-01 *(Example)* | Growth below WACC and below long-run nominal growth of the economy | $g < WACC$ and $g$ at or below [your long-run nominal growth assumption] | $g$ = 3.0%, WACC = 9.5%: pass | | TV-02 *(Example)* | Reinvestment consistent with growth | Reinvestment rate in $FCFF_{T+1}$ equals $g/RONIC$ | 3% / 12% = 25%; year-5 rate is 14.9%, so year-5 FCFF is not grown naively | | TV-03 *(Example)* | Implied exit multiple from the Gordon value is plausible | Compare $TV_T / EBITDA_T$ with mature peers | 6.93x versus mature peers [your range] | | TV-04 *(Example)* | Implied perpetual growth from an exit multiple is plausible | Solve for $g$ that makes the Gordon value equal $M \times EBITDA_T$ | 10.0x implies $g$ of 6.80%: fail, too high | | TV-05 *(Example)* | Terminal value share of EV is understood | No fixed limit; above about 75% means the forecast period may be too short | 82.5%: review the explicit period | | TV-06 *(Example)* | RONIC at or modestly above WACC in perpetuity | Competition erodes excess returns over time | 12% versus 9.5%: defend with a durable advantage or lower it | The two terminal value methods answer different questions. The Gordon formula states what the business is worth if it grows at $g$ forever with the stated return on new capital. The exit multiple states what a buyer might pay at year $T$, which imports today's market pricing into a future year. Use the Gordon value as the base case and the exit multiple as a cross-check; if they differ greatly, one of the inputs is inconsistent. In Worked example A, a 10.0x exit multiple would require 6.8 percent perpetual growth, which is not credible for a company whose market grows at the rate of the economy. ## Worked example A (fully solved): Corvane Robotics **Situation (*Example*, fictional).** Corvane Robotics, a growth-stage warehouse-robotics company, is preparing for a possible sale. Revenue last year (year 0) was USD 400m with an EBIT margin of 6 percent. Value the company at the valuation date using FCFF, WACC 9.5 percent, a tax rate of 25 percent, the mid-year convention and a Gordon growth terminal value with $g$ = 3.0 percent and RONIC = 12 percent. **Drivers (*Example*).** | Driver | Year 1 | Year 2 | Year 3 | Year 4 | Year 5 | |---|---|---|---|---|---| | Revenue growth | 25% | 20% | 15% | 10% | 6% | | EBIT margin | 8% | 10% | 12% | 13% | 14% | | D&A, share of revenue | 4% | 4% | 4% | 4% | 4% | | CapEx, share of revenue | 7.0% | 6.5% | 6.0% | 5.5% | 5.0% | | NWC, share of revenue (year 0: 10% of 400) | 10% | 10% | 10% | 10% | 10% | **Step 1: forecast FCFF (USD m, computed at full precision, shown rounded).** Sheet layout assumed by the formulas: year numbers in row 1 (C1:G1 = 1 to 5), growth row 4, revenue row 5 (B5 = 400), margin row 6, EBIT row 7, NOPAT row 8, D&A share row 9, capex share row 10, D&A row 11, capex row 12, NWC increase row 13, FCFF row 14, EBITDA row 15; named cells Tax, WACC, g, RONIC and NWC_pct. | Line | Year 1 | Year 2 | Year 3 | Year 4 | Year 5 | Excel (year 1, column C) | |---|---|---|---|---|---|---| | Revenue | 500.00 | 600.00 | 690.00 | 759.00 | 804.54 | `=B5*(1+C4)` | | EBIT | 40.00 | 60.00 | 82.80 | 98.67 | 112.64 | `=C5*C6` | | NOPAT | 30.00 | 45.00 | 62.10 | 74.00 | 84.48 | `=C7*(1-Tax)` | | D&A | 20.00 | 24.00 | 27.60 | 30.36 | 32.18 | `=C5*C9` | | CapEx | 35.00 | 39.00 | 41.40 | 41.74 | 40.23 | `=C5*C10` | | Increase in NWC | 10.00 | 10.00 | 9.00 | 6.90 | 4.55 | `=(C5-B5)*NWC_pct` | | **FCFF** | **5.00** | **20.00** | **39.30** | **55.72** | **71.88** | `=C8+C11-C12-C13` | | EBITDA | 60.00 | 84.00 | 110.40 | 129.03 | 144.82 | `=C7+C11` | Year-4 capex is 41.745 before rounding; the FCFF of 55.72 is computed from unrounded values. **Step 2: discount the explicit period.** | Item | Value | Excel | |---|---|---| | Discount factors, mid-year (years 1 to 5) | 0.9556, 0.8727, 0.7970, 0.7279, 0.6647 | `=1/(1+WACC)^(C1-0.5)` | | PV of FCFF, mid-year | 141.89 | `=SUMPRODUCT(C14:G14,1/(1+WACC)^(C1:G1-0.5))` | | PV of FCFF, end-year (for comparison) | 135.59 | `=NPV(WACC,C14:G14)` | **Step 3: terminal value (value-driver Gordon form).** | Item | Value | Excel | |---|---|---| | NOPAT year 6 = 84.48 × 1.03 | 87.01 | `=G8*(1+g)` | | Reinvestment rate = g / RONIC | 25.0% | `=g/RONIC` | | FCFF year 6 | 65.26 | `=G8*(1+g)*(1-g/RONIC)` | | $TV_5$ = 65.26 / (0.095 - 0.03) | 1,003.97 | `=G8*(1+g)*(1-g/RONIC)/(WACC-g)` | | PV of TV, mid-year (4.5 years) | 667.36 | `=TV/(1+WACC)^4.5` | Growing year-5 FCFF by 3 percent instead would give 74.03 for year 6: it carries year-5 reinvestment of only 14.9 percent of NOPAT into a perpetuity that needs 25 percent, and overstates the terminal value. **Step 4: enterprise value.** | Item | Mid-year | End-year | Excel | |---|---|---|---| | PV of FCFF | 141.89 | 135.59 | see step 2 | | PV of TV | 667.36 | 637.75 | `=TV/(1+WACC)^5` for end-year | | **Enterprise value** | **809.25** | **773.35** | `=PV_FCFF+PV_TV` | | TV share of EV | 82.5% | 82.5% | `=PV_TV/EV` | The mid-year value is 4.64 percent higher, which is exactly $(1.095)^{0.5} - 1$: every cash flow, including the perpetuity, arrives half a year earlier. **Step 5: bridge to value per share (balance sheet at the valuation date, *Example*).** | Item | USD m | Note | |---|---|---| | Enterprise value | 809.25 | mid-year | | less Debt (market value) | (180.00) | bank loan and notes | | less Lease liabilities | (45.00) | include only if lease payments were excluded from FCFF (IFRS 16 practice) | | plus Cash and equivalents | 95.00 | assume all excess cash; deduct operating cash if needed | | less Non-controlling interests | (15.00) | share of a consolidated subsidiary owned by others | | plus Investments in associates | 25.00 | not in EBIT, so added separately | | **Equity value** | **689.25** | | **Diluted shares with the treasury stock method.** Basic shares 60.0m, restricted stock units 1.5m, options 5.0m with a strike of USD 6.00. The price depends on the share count and the share count on the price, so iterate (or use Excel's iterative calculation): incremental shares = $1.5 + 5.0\,(1 - 6.00/P)$. | Item | Value | Excel | |---|---|---| | Incremental shares at convergence | 3.726m | `=RSU+Options*(1-Strike/Price)` (iterative) | | Diluted shares | 63.726m | `=Basic+Incremental` | | **Value per share** | **USD 10.82** | `=Equity/Diluted` | **Step 6: sensitivity of value per share (USD) to WACC and g** (mid-year, value-driver TV, RONIC 12%, computed). | g \ WACC | 8.5% | 9.0% | 9.5% | 10.0% | 10.5% | |---|---|---|---|---|---| | 2.0% | 12.35 | 11.28 | 10.35 | 9.54 | 8.82 | | 2.5% | 12.75 | 11.57 | 10.57 | 9.70 | 8.94 | | 3.0% | 13.21 | 11.91 | **10.82** | 9.88 | 9.07 | | 3.5% | 13.75 | 12.30 | 11.10 | 10.08 | 9.21 | | 4.0% | 14.40 | 12.77 | 11.42 | 10.31 | 9.36 | Build it in Excel with a two-variable data table (Data, What-If Analysis, Data Table) pointing the row input at the WACC cell and the column input at the $g$ cell. The value moves more with WACC than with $g$ here because the value-driver formula raises reinvestment as $g$ rises, which partly offsets the higher growth. ```vega-lite { "$schema": "https://vega.github.io/schema/vega-lite/v5.json", "description": "Corvane Robotics (fictional): DCF value per share against WACC for three perpetual growth rates", "width": 380, "height": 220, "data": {"values": [ {"WACC": 8.5, "g": "g = 2%", "Value per share": 12.35}, {"WACC": 9.0, "g": "g = 2%", "Value per share": 11.28}, {"WACC": 9.5, "g": "g = 2%", "Value per share": 10.35}, {"WACC": 10.0, "g": "g = 2%", "Value per share": 9.54}, {"WACC": 10.5, "g": "g = 2%", "Value per share": 8.82}, {"WACC": 8.5, "g": "g = 3%", "Value per share": 13.21}, {"WACC": 9.0, "g": "g = 3%", "Value per share": 11.91}, {"WACC": 9.5, "g": "g = 3%", "Value per share": 10.82}, {"WACC": 10.0, "g": "g = 3%", "Value per share": 9.88}, {"WACC": 10.5, "g": "g = 3%", "Value per share": 9.07}, {"WACC": 8.5, "g": "g = 4%", "Value per share": 14.4}, {"WACC": 9.0, "g": "g = 4%", "Value per share": 12.77}, {"WACC": 9.5, "g": "g = 4%", "Value per share": 11.42}, {"WACC": 10.0, "g": "g = 4%", "Value per share": 10.31}, {"WACC": 10.5, "g": "g = 4%", "Value per share": 9.36} ]}, "mark": {"type": "line", "point": true}, "encoding": { "x": {"field": "WACC", "type": "quantitative", "title": "WACC (%)", "scale": {"domain": [8.4, 10.6]}}, "y": {"field": "Value per share", "type": "quantitative", "title": "Value per share (USD)", "scale": {"zero": false}}, "color": {"field": "g", "type": "nominal", "title": "Perpetual growth"} } } ``` **Step 7: terminal value cross-check with an exit multiple.** | Item | Value | Excel | |---|---|---| | Implied EV/EBITDA from the Gordon TV (TV / EBITDA year 5) | 6.93x | `=TV/G15` | | TV at a 10.0x exit multiple | 1,448.17 | `=10*G15` | | PV of exit TV (5 full years) | 919.92 | `=TV_exit/(1+WACC)^5` | | EV with exit TV (mid-year flows) | 1,061.81 | `=PV_FCFF_mid+PV_TV_exit` | | Perpetual growth implied by 10.0x (value-driver, RONIC 12%) | 6.80% | Goal Seek on $g$ | | Perpetual growth implied by 10.0x (naive growth of year-5 FCFF) | 4.32% | Goal Seek on $g$ | **Step 8: cross-check with trading multiples** (finance/comparable-companies-analysis). Five listed warehouse automation peers (*Example*) trade at next-twelve-months EV/EBITDA of 8.5x, 9.0x, 10.5x, 11.5x and 12.5x; median 10.5x. Applied to Corvane's year-1 EBITDA of 60.00, the multiple gives EV of 630.00. The DCF value of 809.25 implies 13.49x year-1 EBITDA. The gap is explained if Corvane grows faster and expands margins more than the peers (EBITDA grows from 60.00 to 144.82 in five years); if it does not, the DCF is too optimistic. Present both in a football-field chart in finance/valuation-report. **Step 9: FCFE check for year 1.** With debt of 180 at 6 percent (interest 10.80, after tax 8.10) and net new borrowing of 20, $FCFE_1 = 5.00 - 8.10 + 20.00 = 16.90$ (`=FCFF-Int*(1-Tax)+NetBorrowing`). FCFE is higher than FCFF in year 1 only because of new borrowing; it is not a better cash flow, it is a different claim discounted at a different rate. **Conclusion (*Example*).** On the base case, Corvane is worth about USD 809m as an enterprise and USD 10.82 a share, with a range of USD 9.07 to 13.21 for WACC of 8.5 to 10.5 percent at 3 percent growth. The value rests on margin expansion to 14 percent and a durable 12 percent return on new capital; the 10x exit multiple sometimes quoted for the sector is not consistent with these drivers. ## Worked example B (half solved): Northfield Outdoor Co. **Situation (*Example*, fictional).** Northfield Outdoor Co., a mature outdoor-gear retailer and brand, forecasts FCFF of USD 42m, 45m and 47m for years 1 to 3, after which it expects steady 2 percent growth. WACC is 8 percent. Debt is USD 210m, cash USD 30m, 40m diluted shares. Year-3 EBITDA is USD 95m. | Step | Item | Value | Excel | |---|---|---|---| | 1 | Discount factors years 1 to 3 | 0.9259, 0.8573, [ ] | `=1/(1+0.08)^3` | | 2 | PV of FCFF years 1 to 3 | [ ] | `=NPV(0.08,42,45,47)` | | 3 | $TV_3$ = 47 × 1.02 / (0.08 - 0.02) | [ ] | `=47*1.02/(0.08-0.02)` | | 4 | PV of TV | 634.27 | `=TV/1.08^3` | | 5 | Enterprise value | [ ] | `=PV_FCFF+PV_TV` | | 6 | TV share of EV | [ ] | `=PV_TV/EV` | | 7 | Equity value | [ ] | `=EV-210+30` | | 8 | Value per share | [ ] | `=Equity/40` | | 9 | Implied EV/EBITDA at year 3 (TV / 95) | [ ] | `=TV/95` | | 10 | Is the TV share a warning sign here? Why or why not? | [ ] | | ## Exercise C (unsolved) Use the Corvane Robotics forecast from Worked example A, with three changes: WACC 10.0 percent, $g$ = 2.5 percent and RONIC = 15 percent, and use **end-of-year** discounting throughout. 1. Compute the PV of FCFF for years 1 to 5. 2. Compute $FCFF_6$ with the value-driver formula and the terminal value at year 5. 3. Compute enterprise value, equity value (same bridge) and value per share (same treasury stock method). 4. What share of EV is the terminal value, and what EV/EBITDA does the terminal value imply? 5. In two sentences, explain to a non-finance manager why value fell compared with Example A even though RONIC rose. ## Connections to other cards | Card or template | What it gives the DCF | |---|---| | mba/mba-npv-irr-card | Discounting, NPV and IRR logic, Excel `NPV` and `XNPV` conventions | | mba/mba-capm-wacc-card | Cost of equity, cost of debt, target weights, WACC | | mba/mba-capital-structure-card | When WACC fails and APV is better; tax shields; distress costs | | mba/mba-three-statements-card and mba/mba-cash-flow-statement-card | Where EBIT, D&A, capex and working capital come from | | mba/mba-ratio-analysis-card | Historical margins, turnover and return on invested capital for the drivers | | mba/mba-options-real-options-card | Value of flexibility that a static DCF misses | | mba/mba-competitive-advantage-card | Whether RONIC above WACC can persist | | finance/comparable-companies-analysis | Trading multiples for the cross-check | | finance/valuation-report | How to present the range and the football field | | mba/mba-paper-lbo | The buyer's view of the same company with high leverage | ## Common mistakes and misconceptions - **Mixing cash flow and rate.** Discounting FCFF at the cost of equity, or FCFE at WACC, mis-states value. Match the claim to the rate. - **Subtracting interest in FCFF.** FCFF is before financing. The tax benefit of debt is already in the after-tax cost of debt inside WACC; subtracting interest counts financing twice. - **Growing the last year's FCFF naively.** If the last forecast year still carries high-growth reinvestment, or too little, the perpetuity inherits it. Normalise with $NOPAT_{T+1}(1 - g/RONIC)$. - **Perpetual growth too high.** A $g$ close to WACC makes the denominator tiny and the value explode. A $g$ above long-run nominal growth of the economy is not credible forever. - **Exit multiple from today's peers applied mechanically.** A high multiple paid today for fast-growing peers is not the multiple a mature business earns in year $T$. Back out the implied growth (check TV-04). - **Mid-year convention applied to an exit-multiple TV.** A sale at the end of year $T$ is discounted for $T$ years. - **Bridge errors.** Forgetting lease liabilities when lease payments are excluded from FCFF; deducting all cash when some is needed to operate; ignoring non-controlling interests, preferred shares, pension deficits or associates. - **Basic instead of diluted shares.** In-the-money options and RSUs dilute value per share; use the treasury stock method at the DCF price, not at the current market price. - **Double counting working capital or tax losses.** Tax losses carried forward are valued either in the cash tax line or as a separate asset in the bridge, not both. - **Treating the point estimate as the answer.** A DCF output is a range driven by a few inputs. Always show the sensitivity table. - **Believing the DCF is "intrinsic" and multiples are "relative".** Both depend on assumptions; the DCF makes them explicit, and the two should reconcile. ## Self-test questions 1. Write FCFF from EBIT. Which three common items does it exclude, and why? 2. A model discounts FCFF at 9.5 percent and grows the terminal year at 9 percent. What happens, and what does it say about the inputs? 3. Why does the mid-year convention raise EV by about $(1 + WACC)^{0.5} - 1$, and when should you not apply it to the terminal value? 4. In Example A, why is $FCFF_6$ equal to 65.26 and not 74.03? 5. An analyst sets an exit multiple of 10x EBITDA. How do you test whether it is consistent with the rest of the model? 6. Name five items between enterprise value and equity value, and say whether each is added or subtracted. 7. Why can the treasury stock method not use today's market price when the DCF price differs from it? 8. Explain in two sentences when FCFE at the cost of equity and FCFF at WACC give the same equity value. 9. The terminal value is 85 percent of EV. Is the DCF wrong? What would you do? 10. A DCF gives 13.5x next-year EBITDA while peers trade at 10.5x. List three explanations that could justify the gap and one that would not. ## My notes and next steps | Item | My entry | |---|---| | Confidence with DCF (1 = lost, 5 = could teach it) | [ ] | | Model rebuilt from scratch in Excel (date) | YYYY-MM-DD | | Drivers I find hardest to justify | [ ] | | Questions for my professor, tutor or study group | [ ] | | Mistakes logged in mba/mba-error-log | [Date and short description] | | Flashcards made in mba/mba-concept-flashcards | [Card IDs] | | Next review date (spacing: +2 days, +1 week, +1 month) | YYYY-MM-DD | | Next card to study | [mba/mba-capital-structure-card / mba/mba-options-real-options-card] | ## Sources and further reading - Williams, J. B. (1938). *The Theory of Investment Value*. Harvard University Press. - Gordon, M. J., and Shapiro, E. (1956). Capital equipment analysis: the required rate of profit. *Management Science*, 3(1), 102–110. - Gordon, M. J. (1959). Dividends, earnings, and stock prices. *Review of Economics and Statistics*, 41(2), 99–105. - Miller, M. H., and Modigliani, F. (1961). Dividend policy, growth, and the valuation of shares. *Journal of Business*, 34(4), 411–433. - Myers, S. C. (1974). Interactions of corporate financing and investment decisions: implications for capital budgeting. *Journal of Finance*, 29(1), 1–25. - Kaplan, S. N., and Ruback, R. S. (1995). The valuation of cash flow forecasts: an empirical analysis. *Journal of Finance*, 50(4), 1059–1093. - Graham, J. R., and Harvey, C. R. (2001). The theory and practice of corporate finance: evidence from the field. *Journal of Financial Economics*, 60(2–3), 187–243. - Liu, J., Nissim, D., and Thomas, J. (2002). Equity valuation using multiples. *Journal of Accounting Research*, 40(1), 135–172. - IFRS Foundation. IFRS 18 *Presentation and Disclosure in Financial Statements*, https://www.ifrs.org (checked 2026-10-28). - Textbooks (further reading, by name only): Koller, Goedhart and Wessels, *Valuation: Measuring and Managing the Value of Companies* (McKinsey); Berk and DeMarzo, *Corporate Finance*; Brealey, Myers and Allen, *Principles of Corporate Finance*; Damodaran, *Investment Valuation*. - Open resources: OpenStax, *Principles of Finance* (2022), free online at https://openstax.org (check the licence on the book page); Aswath Damodaran's public data pages on industry multiples and costs of capital, NYU Stern. ## Answer key **Worked example B.** (1) 0.7938. (2) PV of FCFF = 114.78. (3) $TV_3$ = 799.00. (5) EV = 114.78 + 634.27 = 749.05. (6) 84.7 percent. (7) Equity = 749.05 - 210 + 30 = 569.05. (8) USD 14.23 a share. (9) 799.00 / 95 = 8.41x. (10) Not by itself: with only three explicit years and a mature business already in steady state, most value is naturally in the perpetuity. The warning is about whether 2 percent growth and the year-3 FCFF are steady state, not about the share. **Exercise C.** (1) PV of FCFF = 133.29. (2) $FCFF_6 = 84.48 \times 1.025 \times (1 - 0.025/0.15)$ and $TV_5$ = 962.10. (3) PV of TV = 597.39, EV = 730.67, equity = 610.67, value per share = USD 9.63. (4) 81.8 percent; implied EV/EBITDA 6.64x. (5) The higher discount rate and lower growth cut the value of every future cash flow, and the end-of-year timing delays them by half a year. A higher RONIC lowers the reinvestment needed for growth, but at 2.5 percent growth that saving is smaller than the effect of the higher rate. **Self-test.** 1. $FCFF = EBIT(1 - t_c) + DA - CapEx - \Delta NWC$. It excludes interest, dividends and debt flows (issues and repayments) because it measures cash available to all capital providers before financing; financing enters through WACC. 2. The denominator is 0.5 percent, so the terminal value becomes huge and extremely sensitive. A growth rate that close to WACC implies the company grows almost as fast as its required return forever, which is not credible. 3. Cash arrives on average mid-year, so each flow is discounted half a year less, which multiplies every PV by $(1 + WACC)^{0.5}$. Do not apply it to an exit-multiple terminal value, which represents a sale at the end of year $T$. 4. Because steady-state growth of 3 percent at RONIC 12 percent requires reinvesting 25 percent of NOPAT: $87.01 \times 0.75 = 65.26$. Growing year-5 FCFF assumes only 14.9 percent reinvestment. 5. Solve for the perpetual growth rate that makes the Gordon value equal $M \times EBITDA_T$ and judge it; compare the multiple with mature, not high-growth, peers; compare it with the multiple implied by the Gordon value. 6. Subtract debt, lease liabilities (when lease payments are excluded from FCFF), preferred shares, non-controlling interests, pension deficits; add excess cash, investments in associates and other non-operating assets. 7. Because the number of in-the-money options and their dilution depends on the share price; using the market price when the DCF price is different gives an inconsistent share count. Iterate to the DCF price. 8. When the debt policy used to forecast net borrowing and interest in FCFE is the same one assumed in the WACC weights, and the cost of equity reflects that leverage. Then both describe the same firm with the same financing. 9. Not necessarily: high shares are common for growth companies. Check that year $T$ is a steady state, test the TV with both methods, and consider lengthening the explicit period until growth and reinvestment stabilise. 10. Justifiable: faster growth, higher expected margins or return on capital, lower risk than peers. Not justifiable: a perpetual growth rate or RONIC that cannot be defended, or a bridge error that inflates value. ## Revision history | Version | Date | Author | Change summary | |---|---|---|---| | 0.1 | YYYY-MM-DD | [Your name] | First version from the template | | 0.2 | YYYY-MM-DD | [Your name] | *Example:* Replaced Corvane data with case data, switched to end-of-year convention as the course requires | ## Standard and licence note Based on the discounted cash flow method as developed in the works cited above (Williams 1938, Gordon 1959, Miller and Modigliani 1961) and as taught across MBA core corporate finance courses; no single standard governs DCF valuation. The explanations, notation, worked examples, checks and layout are original; no textbook text, published case or exam question is reproduced. Every number was computed in Python and is shown with the matching Excel formula. The template is not affiliated with or endorsed by any business school, publisher or standard setter. Check your course materials for the conventions they require and the current IFRS text on ifrs.org. Template licence: MIT.