Discounted Cash Flow Model
When to use
Use this when you need an intrinsic valuation of a business by projecting unlevered free cash flow, discounting it at the weighted average cost of capital, and bridging enterprise value to equity value and a per-share price. It consumes the operating forecast and produces a value range plus sensitivities.
Not for: building the underlying integrated forecast and schedules — use fina-3-statement-model; a leveraged buyout with tranche-level debt and IRR/MOIC returns — use fina-lbo-model; market-based valuation off trading or deal multiples — use fina-comps-analysis; verifying an existing model's links and formulas — use fina-audit-xls; or formatting the output workbook — use fina-xlsx-author.
Method
- Pull unlevered free cash flow from the operating model. You start from EBIT, tax it at the marginal rate, add back D&A, subtract capex, and subtract the change in net working capital — deliberately excluding interest so the cash flow is capital-structure-neutral. UFCF = EBIT × (1 − tax) + D&A − Capex − ΔNWC.
- Set the explicit forecast horizon. You forecast UFCF for 5 to 10 years, long enough that the business reaches a steady state (stable margins, capex ≈ D&A, normalized reinvestment) before terminal value begins.
- Build WACC from its components. You compute cost of equity via CAPM (risk-free + beta × equity risk premium), the after-tax cost of debt (pretax rate × (1 − tax)), and weight them by target market-value capital weights. Decision point: use a target/optimal capital structure rather than the current one if the current mix is temporary or clearly off-peer, because WACC should reflect the long-run financing of the assets, not a transient snapshot.
- Discount with the mid-year convention. You apply discount factors assuming cash flows arrive mid-period (period 0.5, 1.5, 2.5, …) rather than at year-end, since cash is generated throughout the year. Factor = 1 / (1 + WACC)^(t − 0.5).
- Compute terminal value two ways and reconcile them. You calculate a Gordon growth (perpetuity) TV and an exit-multiple TV, then cross-check. Decision point: if the exit-multiple TV implies a perpetuity growth rate above long-run GDP (roughly 2–3%), your exit multiple is too aggressive; if the perpetuity-growth TV implies an exit EV/EBITDA far off trading comps, your growth or WACC is off — reconcile before trusting the number.
- Discount the terminal value to present. You apply the terminal-year discount factor (using the same mid-year or year-end convention consistently) to the undiscounted TV.
- Sum to enterprise value. You add the PV of explicit UFCF and the PV of terminal value to get enterprise value.
- Bridge enterprise value to equity value and per share. You subtract net debt (total debt − cash), subtract preferred and minority interest, add non-operating assets, to reach equity value; divide by diluted shares (treasury-stock method) for per-share value.
- Build the sensitivity table. You lay out a two-way data table of per-share value across WACC (rows) and perpetuity growth or exit multiple (columns), so the reader sees the value range rather than a false-precision point estimate.
Example
A company's steady-state UFCF grows to 120 in the terminal year. WACC is built as: risk-free 4.0%, beta 1.2, ERP 5.5% → cost of equity 10.6%; pretax cost of debt 6.0% × (1 − 25%) = 4.5% after-tax; weights 80% equity / 20% debt → WACC ≈ 9.4%. With perpetuity growth of 2.5%, Gordon TV = 120 × (1.025) / (0.094 − 0.025) = 123 / 0.069 ≈ 1,783. Discounting at the year-5 mid-year factor 1 / 1.094^4.5 ≈ 0.665 gives a PV of TV ≈ 1,186. Adding PV of explicit UFCF of ~360 gives EV ≈ 1,546. Less net debt of 300 gives equity value 1,246; over 100 diluted shares that is 12.46 per share. The exit-multiple cross-check: 1,783 / terminal EBITDA of ~200 implies an 8.9x exit — in line with comps, so the two methods reconcile.
Pitfalls
- Mismatched cash flow and discount rate. Discounting unlevered FCF at cost of equity (instead of WACC) double-charges for leverage. Unlevered FCF pairs with WACC; levered FCF pairs with cost of equity — never cross them.
- Terminal value tail wagging the dog. When TV is 80%+ of EV (common), a 25-basis-point WACC or growth tweak swings the value massively. Always show the TV-as-percent-of-EV and the sensitivity grid.
- Perpetuity growth above GDP. A terminal growth rate that exceeds long-run nominal GDP implies the company eventually becomes the whole economy. Cap g at 2–3% and cross-check the implied exit multiple.
- Inconsistent mid-year convention. Applying mid-year to explicit flows but year-end to the terminal value (or vice versa) mis-times the largest cash flow. Pick one convention and apply it to both.
- Nominal-versus-real mismatch. Discounting nominal cash flows at a real rate (or the reverse) systematically distorts value. Keep cash flows and WACC both nominal.
- Stale net debt and share count. Using book debt instead of market net debt, or basic instead of diluted shares, corrupts the equity bridge. Use latest net debt and the treasury-stock diluted count.
Output format
UNLEVERED DCF ($ in 000s)
Yr1 Yr2 Yr3 Yr4 Yr5
UFCF 80 92 103 112 120
Mid-year factor (WACC 9.4%)
0.955 0.873 0.798 0.729 0.667
PV of UFCF 76 80 82 82 80 -> Sum 400
TERMINAL VALUE
Perpetuity (g=2.5%) 1,783 | Exit multiple (8.5x) 1,700
PV of TV 1,186
Implied exit multiple (perp method) 8.9x
Implied perp growth (exit method) 2.3% [cross-check OK]
VALUE BRIDGE
Enterprise value 1,586
(-) Net debt (300)
(-) Preferred / minority (0)
Equity value 1,286
/ Diluted shares 100
Value per share 12.86
SENSITIVITY: per share (WACC x g)
2.0% 2.5% 3.0%
8.9% 12.10 12.86 13.75
9.4% 11.30 12.00 12.80
9.9% 10.60 11.24 11.96
Reference
WACC formula table
| Component |
Formula |
| Cost of equity (Ke) |
Rf + β × ERP (CAPM) |
| Levered beta |
βu × [1 + (1 − tax) × D/E] (relever peer unlevered beta to target structure) |
| Pretax cost of debt (Kd) |
Yield to maturity on comparable debt, or risk-free + credit spread |
| After-tax cost of debt |
Kd × (1 − tax) |
| Equity weight (We) |
E / (D + E) at market values |
| Debt weight (Wd) |
D / (D + E) at market values |
| WACC |
We × Ke + Wd × Kd × (1 − tax) |
Terminal value formulas
| Method |
Formula |
Notes |
| Gordon growth (perpetuity) |
TV = UFCF_final × (1 + g) / (WACC − g) |
g must be < WACC and ≤ long-run GDP |
| Exit multiple |
TV = terminal EBITDA × exit EV/EBITDA |
multiple from fina-comps-analysis |
| Implied exit multiple |
Gordon TV / terminal EBITDA |
sanity vs comps |
| Implied perpetuity growth |
g = WACC − (UFCF_final × (1+g)) / exit-multiple TV (solve) |
sanity vs GDP |
Enterprise value to equity bridge
| Line |
Sign |
| PV of explicit UFCF |
+ |
| PV of terminal value |
+ |
| = Enterprise value |
= |
| Total debt |
− |
| Cash and equivalents |
+ |
| Preferred stock |
− |
| Minority (non-controlling) interest |
− |
| Non-operating / investment assets |
+ |
| = Equity value |
= |
| ÷ Diluted shares (treasury method) |
÷ |
| = Value per share |
= |
Mid-year convention factor
| Period t |
Year-end factor |
Mid-year factor |
| 1 |
1/(1+WACC)^1 |
1/(1+WACC)^0.5 |
| 2 |
1/(1+WACC)^2 |
1/(1+WACC)^1.5 |
| t |
1/(1+WACC)^t |
1/(1+WACC)^(t−0.5) |
| Terminal |
discounted at year-t factor consistent with explicit flows |
|
Sanity checks
| Check |
Passes when |
| Cash flow / rate consistency |
Unlevered FCF discounted at WACC (not Ke) |
| TV method reconciliation |
Implied exit multiple ≈ comps AND implied g ≤ GDP |
| TV concentration |
TV % of EV disclosed; sensitivity shown if > ~75% |
| Nominal consistency |
Both cash flows and WACC nominal (or both real) |
| Steady state reached |
Terminal year: capex ≈ D&A, margins stable, ΔNWC normalized |
| Net debt currency |
Market net debt and diluted shares as of valuation date |
Feed the exit multiple from fina-comps-analysis, take UFCF drivers from fina-3-statement-model, and finalize the workbook with fina-xlsx-author.
1---2name: fina-dcf-model3description: Value a business by discounting unlevered free cash flow at WACC with mid-year convention, a dual-method terminal value, and a full enterprise-to-equity-to-per-share bridge plus WACC-versus-growth sensitivity.4---56# Discounted Cash Flow Model78## When to use9Use this when you need an intrinsic valuation of a business by projecting unlevered free cash flow, discounting it at the weighted average cost of capital, and bridging enterprise value to equity value and a per-share price. It consumes the operating forecast and produces a value range plus sensitivities.1011**Not for:** building the underlying integrated forecast and schedules — use `fina-3-statement-model`; a leveraged buyout with tranche-level debt and IRR/MOIC returns — use `fina-lbo-model`; market-based valuation off trading or deal multiples — use `fina-comps-analysis`; verifying an existing model's links and formulas — use `fina-audit-xls`; or formatting the output workbook — use `fina-xlsx-author`.1213## Method141. **Pull unlevered free cash flow from the operating model.** You start from EBIT, tax it at the marginal rate, add back D&A, subtract capex, and subtract the change in net working capital — deliberately excluding interest so the cash flow is capital-structure-neutral. UFCF = EBIT × (1 − tax) + D&A − Capex − ΔNWC.152. **Set the explicit forecast horizon.** You forecast UFCF for 5 to 10 years, long enough that the business reaches a steady state (stable margins, capex ≈ D&A, normalized reinvestment) before terminal value begins.163. **Build WACC from its components.** You compute cost of equity via CAPM (risk-free + beta × equity risk premium), the after-tax cost of debt (pretax rate × (1 − tax)), and weight them by target market-value capital weights. Decision point: use a target/optimal capital structure rather than the current one if the current mix is temporary or clearly off-peer, because WACC should reflect the long-run financing of the assets, not a transient snapshot.174. **Discount with the mid-year convention.** You apply discount factors assuming cash flows arrive mid-period (period 0.5, 1.5, 2.5, …) rather than at year-end, since cash is generated throughout the year. Factor = 1 / (1 + WACC)^(t − 0.5).185. **Compute terminal value two ways and reconcile them.** You calculate a Gordon growth (perpetuity) TV and an exit-multiple TV, then cross-check. Decision point: if the exit-multiple TV implies a perpetuity growth rate above long-run GDP (roughly 2–3%), your exit multiple is too aggressive; if the perpetuity-growth TV implies an exit EV/EBITDA far off trading comps, your growth or WACC is off — reconcile before trusting the number.196. **Discount the terminal value to present.** You apply the terminal-year discount factor (using the same mid-year or year-end convention consistently) to the undiscounted TV.207. **Sum to enterprise value.** You add the PV of explicit UFCF and the PV of terminal value to get enterprise value.218. **Bridge enterprise value to equity value and per share.** You subtract net debt (total debt − cash), subtract preferred and minority interest, add non-operating assets, to reach equity value; divide by diluted shares (treasury-stock method) for per-share value.229. **Build the sensitivity table.** You lay out a two-way data table of per-share value across WACC (rows) and perpetuity growth or exit multiple (columns), so the reader sees the value range rather than a false-precision point estimate.2324## Example25A company's steady-state UFCF grows to 120 in the terminal year. WACC is built as: risk-free 4.0%, beta 1.2, ERP 5.5% → cost of equity 10.6%; pretax cost of debt 6.0% × (1 − 25%) = 4.5% after-tax; weights 80% equity / 20% debt → WACC ≈ 9.4%. With perpetuity growth of 2.5%, Gordon TV = 120 × (1.025) / (0.094 − 0.025) = 123 / 0.069 ≈ 1,783. Discounting at the year-5 mid-year factor 1 / 1.094^4.5 ≈ 0.665 gives a PV of TV ≈ 1,186. Adding PV of explicit UFCF of ~360 gives EV ≈ 1,546. Less net debt of 300 gives equity value 1,246; over 100 diluted shares that is 12.46 per share. The exit-multiple cross-check: 1,783 / terminal EBITDA of ~200 implies an 8.9x exit — in line with comps, so the two methods reconcile.2627## Pitfalls28- **Mismatched cash flow and discount rate.** Discounting unlevered FCF at cost of equity (instead of WACC) double-charges for leverage. Unlevered FCF pairs with WACC; levered FCF pairs with cost of equity — never cross them.29- **Terminal value tail wagging the dog.** When TV is 80%+ of EV (common), a 25-basis-point WACC or growth tweak swings the value massively. Always show the TV-as-percent-of-EV and the sensitivity grid.30- **Perpetuity growth above GDP.** A terminal growth rate that exceeds long-run nominal GDP implies the company eventually becomes the whole economy. Cap g at 2–3% and cross-check the implied exit multiple.31- **Inconsistent mid-year convention.** Applying mid-year to explicit flows but year-end to the terminal value (or vice versa) mis-times the largest cash flow. Pick one convention and apply it to both.32- **Nominal-versus-real mismatch.** Discounting nominal cash flows at a real rate (or the reverse) systematically distorts value. Keep cash flows and WACC both nominal.33- **Stale net debt and share count.** Using book debt instead of market net debt, or basic instead of diluted shares, corrupts the equity bridge. Use latest net debt and the treasury-stock diluted count.3435## Output format36```37UNLEVERED DCF ($ in 000s)38 Yr1 Yr2 Yr3 Yr4 Yr539UFCF 80 92 103 112 12040Mid-year factor (WACC 9.4%)41 0.955 0.873 0.798 0.729 0.66742PV of UFCF 76 80 82 82 80 -> Sum 4004344TERMINAL VALUE45 Perpetuity (g=2.5%) 1,783 | Exit multiple (8.5x) 1,70046 PV of TV 1,18647 Implied exit multiple (perp method) 8.9x48 Implied perp growth (exit method) 2.3% [cross-check OK]4950VALUE BRIDGE51 Enterprise value 1,58652 (-) Net debt (300)53 (-) Preferred / minority (0)54 Equity value 1,28655 / Diluted shares 10056 Value per share 12.865758SENSITIVITY: per share (WACC x g)59 2.0% 2.5% 3.0%60 8.9% 12.10 12.86 13.7561 9.4% 11.30 12.00 12.8062 9.9% 10.60 11.24 11.9663```6465## Reference6667### WACC formula table68| Component | Formula |69|---|---|70| Cost of equity (Ke) | Rf + β × ERP (CAPM) |71| Levered beta | βu × [1 + (1 − tax) × D/E] (relever peer unlevered beta to target structure) |72| Pretax cost of debt (Kd) | Yield to maturity on comparable debt, or risk-free + credit spread |73| After-tax cost of debt | Kd × (1 − tax) |74| Equity weight (We) | E / (D + E) at market values |75| Debt weight (Wd) | D / (D + E) at market values |76| WACC | We × Ke + Wd × Kd × (1 − tax) |7778### Terminal value formulas79| Method | Formula | Notes |80|---|---|---|81| Gordon growth (perpetuity) | TV = UFCF_final × (1 + g) / (WACC − g) | g must be < WACC and ≤ long-run GDP |82| Exit multiple | TV = terminal EBITDA × exit EV/EBITDA | multiple from `fina-comps-analysis` |83| Implied exit multiple | Gordon TV / terminal EBITDA | sanity vs comps |84| Implied perpetuity growth | g = WACC − (UFCF_final × (1+g)) / exit-multiple TV (solve) | sanity vs GDP |8586### Enterprise value to equity bridge87| Line | Sign |88|---|---|89| PV of explicit UFCF | + |90| PV of terminal value | + |91| = Enterprise value | = |92| Total debt | − |93| Cash and equivalents | + |94| Preferred stock | − |95| Minority (non-controlling) interest | − |96| Non-operating / investment assets | + |97| = Equity value | = |98| ÷ Diluted shares (treasury method) | ÷ |99| = Value per share | = |100101### Mid-year convention factor102| Period t | Year-end factor | Mid-year factor |103|---|---|---|104| 1 | 1/(1+WACC)^1 | 1/(1+WACC)^0.5 |105| 2 | 1/(1+WACC)^2 | 1/(1+WACC)^1.5 |106| t | 1/(1+WACC)^t | 1/(1+WACC)^(t−0.5) |107| Terminal | discounted at year-t factor consistent with explicit flows |108109### Sanity checks110| Check | Passes when |111|---|---|112| Cash flow / rate consistency | Unlevered FCF discounted at WACC (not Ke) |113| TV method reconciliation | Implied exit multiple ≈ comps AND implied g ≤ GDP |114| TV concentration | TV % of EV disclosed; sensitivity shown if > ~75% |115| Nominal consistency | Both cash flows and WACC nominal (or both real) |116| Steady state reached | Terminal year: capex ≈ D&A, margins stable, ΔNWC normalized |117| Net debt currency | Market net debt and diluted shares as of valuation date |118119Feed the exit multiple from `fina-comps-analysis`, take UFCF drivers from `fina-3-statement-model`, and finalize the workbook with `fina-xlsx-author`.
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