Valuation

A DCF values a company as the present value of its future free cash flows.

You take the cash flows of a company like SAP over 5–10 years and discount them at the WACC (around 8%). The sum gives the Enterprise Value.

The valuation comes from fundamentals (growth, margins, capex, taxes) — not from the market prices of comps.

Independent of market sentiment (good), but dependent on many assumptions (risky).

```
UFCF = EBIT × (1 − t) + D&A − Capex − ΔNWC
= NOPAT + D&A − Capex − ΔNWC
```

Inputs:

• EBIT: $100m
• Tax rate t: 30%
• D&A: $20m
• Capex: $25m
• ΔNWC: $5m

Calculation:
```
NOPAT = EBIT × (1 − t) = $100 × 0.70 = $70m
UFCF = NOPAT + D&A − Capex − ΔNWC
= $70 + $20 − $25 − $5 = $60m
```

UFCF is measured before interest payments and belongs to all capital providers — it is discounted at the WACC, not the cost of equity.

Tax on EBIT, not on (EBIT − interest) — otherwise you double-count the tax shield.

1. Project the FCFs: typically 5–10 years.
2. Terminal Value: Gordon Growth or exit multiple.
3. Discount at the WACC back to t=0; the sum gives the Enterprise Value.

```
EqV = EV − Net Debt − Minorities + Associates + Excess Cash
```

Inputs:

• EV: $500m
• Net Debt: $100m
• Minorities, Associates, Excess Cash: 0

Calculation:
```
EqV = EV − Net Debt = $500 − $100 = $400m
```

Cash flows arise evenly across the year and, on average, fall at mid-year. Discount factor: `1 / (1+WACC)^(t−0.5)` instead of `^t`.

A higher present value per cash flow, because the period is 0.5 years shorter.

Inputs:

• Year-1 FCF: $100m
• WACC: 8%

Calculation:
```
End-of-Year: $100 / (1.08)^1 = $92.6m
Mid-Year: $100 / (1.08)^0.5 = $96.2m
```

• Industrial companies with an even cash-flow profile: a good fit.
• Seasonal businesses (retail with a Q4 peak): end-of-year is more honest.

5–10 years.

long enough to reach a steady state in the terminal year.

• Mature middle-market companies: 5 years is enough
• Growth companies: 7–10 years (margins and capex normalize later)

Terminal Value makes up 60–80% of the EV — no matter how long the explicit period is.

Inputs:

• Revenue: $800m
• EBIT margin: 12%
• Tax rate t: 30%
• D&A: $35m
• Capex: $45m
• ΔNWC: $8m

Calculation:
```
EBIT = $800 × 12% = $96m
NOPAT = $96 × (1 − 0.30) = $67.2m
UFCF = NOPAT + D&A − Capex − ΔNWC
= $67.2 + $35 − $45 − $8 = $49.2m
```

Capex > D&A means net investment is positive — the company is still growing. The NWC increase is a use of cash (more working capital tied up).

FCF margin $49.2 / $800 = around 6% — typical for a mid-market machinery business in its growth phase.

UFCF is 'unlevered' — it values the operating business independently of the capital structure. Interest is a financing item, so it does not belong in operating cash flow. If you calculated taxes on EBT (i.e. EBIT − interest), you would build in the tax shield on interest — but the WACC already captures that through (1 − t) × cost of debt. Double-counting.

Net working capital = operating current assets − operating current liabilities, typically: trade receivables + inventories − trade payables. The change ΔNWC = NWC(t) − NWC(t−1) gives the cash effect:

• NWC rises: a use of cash, subtract from FCF.
• NWC falls: a source of cash, add to FCF.

NWC is often set as a % of revenue, e.g. 18%. With 5% growth p.a. and a stable NWC %, NWC also rises by 5% — the resulting ΔNWC helps fund the growth.

Operating NWC covers the balance-sheet items of day-to-day business, not financing or capital-structure positions.

trade receivables, inventories, trade payables, other operating receivables/payables.

cash (a financing item), tax liabilities (often separate), debt (capital structure), accrued interest, pension provisions (net-debt-like).

family-owned companies often have large 'other assets' — check critically whether they are operating or a hidden investment.

right-of-use assets are NOT NWC but fixed assets.

In the steady state a company invests exactly as much as it depreciates — 'maintenance capex'. If capex is permanently > D&A: the company is still growing, but growth does not belong in the terminal phase (by definition a steady state). If capex is permanently < D&A: the company is shrinking (its asset base is being run down). In the terminal year the two should be roughly equal, or capex slightly higher to offset inflation and modest growth (capex ≈ D&A × (1+g)). Important for a clean terminal-value calculation.

Two approaches to SBC in a DCF:

• Cash-based: SBC is non-cash, so add it back like D&A — but shares are issued later, diluting the share count at the end. Reflect SBC × forecast years as an equity-value deduction, or via the treasury-stock method in the share count.
• Run-rate cost: treat SBC as a real expense (do not add it back), because it costs real economic value.

approach 2 is the standard today at US tech (Apple, Adobe). Rarely relevant for middle-market companies — most have no SBC programs.

Since IFRS 16 (2019), operating leases are capitalized as right-of-use assets and lease liabilities are recognized on the balance sheet.

Pension provisions are debt-like and are deducted from EV to reach equity value. The calculation runs in two steps:

• Net pension obligation (unfunded): defined benefit obligation (DBO) less plan assets.
• Tax adjustment: net value × (1 − t), because the tax shield applies on unwind — the after-tax item is deducted from EV.

Often significant at middle-market companies, because direct pension promises are frequently run without external funding (no plan assets).

Consolidated EBITDA and FCF include 100% of the subsidiary, but the equity holders own only the majority stake. Two routes:

• Top-down: EV (on a 100% basis) minus net debt minus minority interests gives the group equity value.
• Bottom-up: reduce the cash flows by the minority share, then discount.

The standard is the top-down method with minorities at market value (or book value as a proxy).

```
NCI mark-to-market = NCI book value × (sector EV/EBITDA) / NCI valuation EBITDA
```

Relevant at groups with historically complex holding structures — often a position that moves the valuation.

Book taxes (P&L) are the tax expense under IFRS including deferred taxes. Cash taxes are the actual payments to the tax authority. Three sources drive the difference:

• D&A: book and tax depreciation differ (e.g. declining-balance vs. straight-line).
• Loss carryforwards: temporarily reduce cash tax.
• Tax rates: a book rate around 30%, an effective cash rate closer to 25% in practice (varies by jurisdiction).

In UFCF you want the real cash effect, so use cash taxes. Formula: NOPAT × cash tax rate. In the steady state the cash tax rate converges on the book rate, because temporary differences even out.

In the terminal year the FCF must be sustainably repeatable — otherwise it destroys the terminal value. Normalization points:

• D&A ≈ capex (no more growth capex).
• ΔNWC = NWC × g (only inflation/growth needs).
• Margins at a sustainable level (no one-off effects, no cyclical peak).
• Taxes at the long-run tax rate (no more NOL benefit).

Inputs:

• WACC: 9%
• Mid-year convention: on
• FCFs: Year 1 $10m, Year 2 $15m, Year 3 $22m, Year 4 $30m, Year 5 $38m

Calculation:
```
Year 1: DF = 1/(1.09)^0.5 = 0.9578 PV = $10 × 0.9578 = $9.58m
Year 2: DF = 1/(1.09)^1.5 = 0.8788 PV = $15 × 0.8788 = $13.18m
Year 3: DF = 1/(1.09)^2.5 = 0.8062 PV = $22 × 0.8062 = $17.74m
Year 4: DF = 1/(1.09)^3.5 = 0.7397 PV = $30 × 0.7397 = $22.19m
Year 5: DF = 1/(1.09)^4.5 = 0.6786 PV = $38 × 0.6786 = $25.79m
Sum of PVs = $88.48m
```

The PV of the explicit period is smaller here than the expected terminal-value contribution — typical for growth companies.

An 85% TV share is high — it means your model is very dependent on TV assumptions (g, exit multiple, normalized FCF). The usual range: 60–80% TV. At 85%+:

• The forecast may be too short — extend it to 10 years.
• The growth assumption in the forecast is too conservative.
• Normalized FCF in the terminal year is too high (capex underestimated).

From June 30 (the valuation date) to the end of forecast Year 1 is 6 months. The first cash flow is generated at the midpoint of the stub period (September) → discount factor 1/(1+WACC)^0.25 for Year 1 (mid-stub). Later years: offset by +0.5 from the stub end (0.5) — Year 2 (mid-year) = 1.0, Year 3 = 2.0, Year 4 = 3.0, Year 5 = 4.0. Terminal Value at Year 5 = 4.5 years (end-of-year) or 4.0 years (mid-year) after the valuation date.

The Year 1 stub FCF must be reduced pro rata (FCF × 6/12). A classic trap: forgetting to scale the stub FCF.

Implicitly, you assume that every FCF generated can be reinvested at the WACC. In reality that is rarely the case — excess cash is often parked in money-market accounts (1–3% return), not reinvested at a 9% WACC. Implication: DCF values are a theoretical 'top-of-range' value. Ignored in practice, because the correction is complex and the assumption about reinvestment opportunities is speculative. A similar problem arises with MIRR (modified IRR) for PE returns.

NOLs reduce future cash taxes. Two methods:

• In the FCF: set a lower cash tax rate until the NOLs are used up, then the long-run rate.
• Separate NOL value: loss carryforward × tax rate × discount factor → add to EV. Method (2) is cleaner, because NOLs are an 'asset'. Watch out: minimum-taxation rules (many jurisdictions let carryforwards offset only part of the annual profit above a de-minimis threshold, capping the shelter) and change-of-ownership rules (loss forfeiture when >50% of the shares change hands) — in LBOs/M&A often a complete loss of the NOLs. In a PE context, check loss carryforwards before structuring the LBO — it can tip the valuation.

A standard DCF often projects off the most recent figures — which, for cyclical companies, represent either a cyclical peak or trough. Two failures:

• If you start at the trough: the forecast extrapolates the weakness, the terminal year is 'normalized' too low — valuation too low.
• If you start at the peak: the forecast extrapolates for too long, the terminal year is not normalized enough — valuation too high. Fix: use mid-cycle earnings (a 10-year average of margins) in the terminal year, NOT trailing twelve months.

Negative FCFs are discounted at the WACC and make a negative contribution to EV. Three points are decisive:

• A long enough horizon: the company must reach BOTH profitability AND a steady state, often Year 8–12 rather than 5 for pre-profitability targets.
• Margin trajectory: model an S-curve path, e.g. −10% today, +5% in Year 5, +20% in Year 10. Capex intensity falls with maturity.
• Funding gap: can the company finance the negative FCFs? If not, you need dilution assumptions or a debt burnout.

Many software companies have historically gone through exactly this shift from negative FCFs to high profitability — the DCF needs a long horizon to capture it.

Negative NWC arises when customers pay in advance (subscriptions) and suppliers are paid only later — this creates an operating source of cash. In the DCF, an even more negative NWC means a negative ΔNWC, which becomes a cash inflow. With growth this advantage compounds: the faster the company grows, the more 'interest-free working capital' it gets.

```
Valuation date September 30 = the last October 1 is 9 months ago, Year-1 forecast ends December 31, stub = 3 months (0.25 years)
FCF Year 1 is scaled to 3/12 (stub FCF = full-year × 0.25)
```

Mid-stub discount: 1/(1+WACC)^0.125.

```
Year 2 (mid-year) = 0.75 years after the valuation date
TV at the end of Year 5 = 4.25 years after the valuation date
```

Complexity at highly seasonal companies: the stub FCF is not linear — e.g. a Q4-heavy business generates 50% of annual FCF in those 3 months.

The WACC should reflect the risks of where the cash flows are actually generated (e.g. a euro-area risk-free rate and ERP for the European share), not blindly the home-market WACC. Genuinely relevant for groups with a large foreign revenue share (software, pharma, industrials).

Two variants of the DCF, depending on how inflation is handled:

• Nominal DCF: FCFs and WACC include inflation. The IB standard — cash flows grow with around 2% inflation plus real growth.
• Real DCF: FCFs and WACC are inflation-adjusted. Convert via the Fisher formula:

```
WACC_real = (1 + WACC_nom) / (1 + Inflation) − 1
```

Theoretically identical; in practice the nominal method is simpler — forecasts (revenue, margins, capex) are typically set in nominal terms.

• Hyperinflationary markets (Argentina, Turkey in the 2020s) — otherwise nominal forecasts get absurdly high.
• Long-term infrastructure (50+ year concessions).

nominal.

Maintenance capex keeps the existing asset base — and thus output — constant. Growth capex expands capacity for future growth.

• D&A as a rule of thumb: D&A roughly equals maintenance capex (really a lower bound, because book values don't reflect replacement cost).
• Capex-to-revenue ratio: from zero-growth comparable companies (mid-cycle).
• Management disclosure: some companies report maintenance separately.

```
Forecast: Total Capex = Maintenance + Growth
Terminal: Capex = Maintenance × (1 + g)
```

Growth capex has an NPV ≥ 0 (otherwise growth would destroy value), but in a DCF that value contribution already sits in the growth FCF.

The value of all cash flows beyond the forecast horizon, capitalized at the end of the forecast, then discounted back to t=0.

TV typically accounts for 60–80% of total EV → the DCF becomes highly sensitive to the TV assumptions.

• Gordon Growth: perpetual growth
• Exit Multiple: a multiple applied to terminal EBITDA

run both, cross-check the implied values.

```
TV = FCF_terminal × (1+g) / (WACC − g)
```

• FCF_terminal: normalized FCF in the last forecast year
• g: perpetual growth rate (developed markets: 1.5–2.5%, capped at the nominal GDP rate)
• WACC: the discount rate

WACC > g (otherwise the denominator turns negative).

a g above inflation + real GDP implies perpetual market-share gains — unrealistic.

```
TV = Terminal Year EBITDA × Exit Multiple
```

the current trading-comps range (median/mean), often slightly conservative.

comps show 8x → assume 7.5x (pricing in multiple compression).

market-anchored, intuitive.
Disadvantage: mixes intrinsic with relative valuation — exactly what a DCF is meant to avoid.

show both methods, take the range.

60–80% of EV. The share depends on:

• Forecast length (5 yrs → ~75% TV; 10 yrs → ~60% TV).
• Growth phase (a growth company → higher TV share, because the large FCFs arrive only late).
• Discount rate (higher WACC → lower TV share, because future CFs are discounted harder). Above an 85% TV share: red flag → extend the forecast, the terminal assumptions are too dominant. Below 50%: possibly too long a forecast period for a mature business, or the terminal assumptions are too conservative.

the nominal long-run GDP growth rate. Developed markets: ~2.0–2.5% (1.5% real + 1.5–2% inflation). Rationale: a company cannot grow faster than the economy forever (otherwise it would eventually exceed 100% of GDP). Lower bound: inflation, about 1.5%. Sector differentiation: growth sectors (tech, healthcare) at the upper bound; mature/declining sectors (print, coal) at or below inflation. IB standard: discipline — a 1.5–2.5% range, don't get 'creative'. A g of 3.0%+ immediately draws critical senior questions in the pitch.

TV = FCF × (1+g) / (WACC − g). At g = WACC → denominator = 0, TV = infinite. At g > WACC → denominator negative, TV negative — absurd. Economically: g > WACC would mean the business earns a higher return than its cost of financing — forever. That would be a money-printing machine, would attract competition, and margins would collapse. Consequence: in steady state g cannot stay above WACC permanently. Practical rule of thumb: g should not exceed half of WACC.

Inputs:

• Terminal year FCF: $60m
• g (steady state): 2%
• WACC: 8.5%
• Terminal year: Year 5 (end-of-year discounting)
• Terminal year EBITDA: $100m (for the sanity check)

Calculation:
```
TV = $60 × (1 + 0.02) / (0.085 − 0.02)
= $61.2 / 0.065 = $941.5m
DF Year 5 = 1 / (1.085)^5 = 0.6650
PV(TV) = $941.5 × 0.6650 = $626m
Sanity check: Implied Exit Multiple = $941.5 / $100 = 9.4x
```

If EBITDA is, say, $100m → implied multiple 9.4x — plausible for specialty chemicals (trading comps often 8–10x EBITDA).

If the implied multiple is unrealistically high or low → revisit the assumptions.

Inputs:

• Year 5 EBITDA: $80m
• Exit multiple: 12x EV/EBITDA
• WACC: 9%
• Discounting: end-of-year, Year 5

Calculation:
```
TV (at end of Year 5) = $80 × 12 = $960m
DF Year 5 = 1 / (1.09)^5 = 0.6499
PV(TV) = $960 × 0.6499 = $624m
```

if the forecast period is discounted mid-year, the TV usually stays on year-end discounting — it represents the value at the end of Year 5, not at the midpoint.

a software multiple of 12x EBITDA is on the higher side — consistent with a growth profile of high gross margin and customer retention. Implied Gordon g (at WACC 9% and FCF/EBITDA 50%): g about 4.6% — defensible for a mature software company, otherwise a red flag.

the implied exit multiple is the EBITDA multiple that a Gordon Growth terminal value implicitly assumes:

```
Implied Exit Multiple = Gordon TV / Terminal Year EBITDA
```

Inputs:

• WACC: 8.5%
• Terminal Year EBITDA: $100m
• FCF/EBITDA ratio: 60%
• Exit multiple: 8x EV/EBITDA

Calculation:
```
FCF = $100 × 60% = $60m
TV (Exit) = $100 × 8 = $800m
Implied g = WACC − FCF/TV
= 0.085 − $60/$800
= 0.085 − 0.075 = 1.0%
```

an 8x multiple implies a steady-state growth rate of about 1%. Realistic for mature industrial targets; for software/tech, 8x would often be too conservative.

in the terminal year you assume a steady state. Four normalization steps:

```
Capex = D&A × (1 + g) — no more growth capex
ΔNWC = NWC × g — only inflation-driven NWC increase
Taxes = Long-Run Tax Rate — no NOL effect
```

• Margins: for cyclical targets the forecast-end margin deviates from the long-run average — use the mid-cycle margin.

an explicit growth phase (Years 1–5: 8% growth) + steady state (Year 6+: 2% growth). The transition is abrupt. Three-stage: a growth phase + a fade phase (Years 6–10: linear reduction from 8% to 2%) + steady state (Year 11+: 2%). More realistic for growth companies, because growth does not collapse overnight.

tech / pharma / biotech with a clear maturity path. Example: SAP's cloud transition (2018–2025) — without a fade model the valuation becomes inaccurate. Standard IB: two-stage; equity research on growth companies often three-stage.

the fade period lets the growth rate converge from the forecast-start value to the terminal value. Linear fade formula:

```
g(t) = g_start − (g_start − g_terminal) × (t − t_start) / (t_end − t_start)
```

TV = FCF × (1+g) / (WACC − g). Implied: to grow at g% per year, the company must reinvest. Reinvestment rate = g / ROIC. If ROIC = WACC: reinvestment is value-neutral. If ROIC > WACC: reinvestment creates value.

a 7–10-year average of EBIT margins that covers at least one full economic cycle.

```
Year: 2018 2019 2020 2021 2022 2023 2024 2025e
Margin: −2% 4% −5% 12% 18% 8% 5% 4%
7-year average: 5.7%
```

A trailing-twelve-month margin (5%) would also be acceptable. Don't use forecast Year 5 directly if the forecast hits the next upswing — otherwise a pro-cyclical bias. Normalize capex analogously via mid-cycle capex / revenue.

g can be negative (typically −1% to −3%) in Gordon. The formula TV = FCF × (1+g) / (WACC − g) still works mathematically (positive denominator, numerator positive but shrinking).

The return required by equity investors — their opportunity cost for comparable risk.

• Discount rate for equity cash flows (LFCF approach)
• Component of WACC (UFCF approach)

CAPM.

• Mature industrials: 8–11%
• Growth / restructuring companies: 12–15%+

Higher business risk → higher CoE → lower equity value.

```
Cost of Equity = Rf + β × ERP
```

• Rf: risk-free rate (10-year government bond)
• β: beta (volatility relative to the market)
• ERP: equity risk premium

+ country risk premium (CRP) + size premium (SP) for smaller / EM targets.

A single-factor model — only market risk matters (unsystematic risk is diversifiable). The practical IB standard, even if the theory is debatable.

The 10-year government bond in the currency of the cash flows (e.g. the 10-year US Treasury for USD).

A highly rated sovereign issuer servicing debt in its own currency — the closest thing to a default-free rate.

Always pull the yield on the valuation date; it moves. For orientation, during 2025 the 10-year US Treasury traded roughly 4.0–4.8%, the 10-year UK gilt roughly 4.4–4.9%, and the 10-year German Bund roughly 2.4–2.9%.

always match the sovereign to the cash-flow currency — US Treasuries for USD, gilts for GBP, and for EUR usually the German Bund as the euro-area benchmark.

never discount USD and EUR cash flows with a single-currency risk-free rate.

The excess return equities must deliver over bonds in the long run to compensate for equity risk.

• Historical: average excess return over 50–100 years
• Implied: backed out from current market prices

5.0–6.5%.

Damodaran's implied ERP for a developed market: typically around ~5.5% (5–6%).

5.5–6.0% is the usual IB range — don't get 'creative', or it signals bias.

Two methods for estimating the ERP:

• Historical ERP: realized excess return of equities vs. bonds over long periods (Dimson-Marsh-Staunton: 1900–today, one major developed market ~5.1%). Advantage: empirically measurable; drawback: backward-looking, survivorship bias, sensitive to the start point.
• Implied ERP: backed out from current equity prices + consensus EPS (Damodaran). Advantage: forward-looking; drawback: assumption-dependent, fluctuates month to month.

Reference both; in a pitch typically 5.5–6.0% — a middle path that extrapolates neither hype nor crisis.

Beta measures the systematic volatility of a stock relative to the market:

• β = 1: moves with the market.
• β > 1: swings more (tech, cyclical).
• β < 1: swings less (utilities, defensive).

Linear regression of the stock's returns against market returns. Standard window: 5 years of weekly data or 2 years of daily data. The market index is typically a broad benchmark — the S&P 500, a mid-cap index, or the STOXX Europe 600.

raw beta plus 'adjusted beta' (Blume: 0.67 × raw + 0.33 × 1) — the adjustment is standard in IB.

beta includes both business risk and financing risk (leverage). This is what Bloomberg reports. Unlevered beta (asset beta): beta after stripping out the leverage effect → pure business risk.

If you use comps betas for a target with a different capital structure, you must delever → average the asset betas → relever to the target capital structure. Otherwise you are directly comparing companies with different debt levels. With comps of similar capital structure this is sometimes skipped, but it is best practice.

β_U = β_L / (1 + (1−t) × D/E).

β_relevered = β_U × (1 + (1−t) × D/E_target).

Two choices for beta.

Raw beta of the company: target publicly traded with 5+ years of trading history and a stable business model.

Industry beta for:

• Private targets (no market observation).
• Pre-IPO valuations.
• Thinly traded or recently listed stocks (<2 years of data).
• Raw beta implausibly low (<0.5) or high (>2.0) — often data artifacts.

Pick 8–12 comps, unlever each beta, take the median or mean, relever to the target capital structure. For middle-market PE targets, this is almost always the way.

The CRP is the additional return investors demand for country risk beyond the developed-market ERP.

• Targets in emerging markets (Brazil, Turkey, India).
• Developed-market targets with high EM exposure (e.g. a European manufacturer with 60% of revenue in Turkey).

Sovereign CDS spread or Damodaran's CRP tables.

the empirical observation that smaller firms have historically earned higher returns than CAPM predicts.

Three plausible drivers — smaller firms are less liquid, have greater information asymmetry (less analyst coverage), and carry concentration risk in their business models.

Ibbotson / Duff & Phelps — typically 1–4% on top of the CAPM CoE, depending on market cap.

For middle-market targets under $500m EV, often add +1–2%. Formula: CoE = Rf + β × ERP + SP. Academically contested (Fama-French), but the practical IB standard.

Inputs:

• Rf: 2.3%
• β_relevered: 1.15
• ERP: 6.0%
• Size premium SP: 1.5%

Calculation:
```
CoE = Rf + β × ERP + SP
= 2.3% + 1.15 × 6.0% + 1.5%
= 2.3% + 6.9% + 1.5%
= 10.7%
```

10.7% is plausible for a mid-cap specialty-chemicals name — a little above the pure CAPM CoE because of the size premium. For a family-owned company you would add a +0.5–1% illiquidity premium, so 11.2–11.7%. A strategic (public) target would be more like 9–10%.

The Hamada formula links levered and unlevered beta:

```
β_L = β_U × (1 + (1 − t) × D/E)
```

Inputs:

• β_U (asset beta): 0.8
• Tax rate t: 30%

Calculation:
```
D/E 0.5: β_L = 0.8 × (1 + 0.7 × 0.5) = 0.8 × 1.35 = 1.08
D/E 1.0: β_L = 0.8 × (1 + 0.7 × 1.0) = 0.8 × 1.70 = 1.36
D/E 2.0 (typical LBO): β_L = 0.8 × (1 + 0.7 × 2.0) = 0.8 × 2.40 = 1.92
```

Higher leverage raises equity risk more than proportionally — in an LBO setup, β_L is typically 1.5–2.0+.

Six steps:

• Identify a peer group — 8–12 public comps with a similar business model.
• Pull each peer's levered beta from Bloomberg (5Y weekly, adjusted).
• Unlever each beta with Hamada (peer-specific D/E).
• Take the median or mean of the asset betas.
• Relever to the target capital structure (target D/E from the industry average).
• Plug into CAPM, plus a size premium and illiquidity premium if applicable.

typically a 3–5% spread over public comps because of illiquidity and size.

For thinly traded or illiquid stocks (small mid- and small-cap names, illiquid small caps), beta tends to be underestimated — the stock reacts to market moves with a lag.

Fama-French extends CAPM with two factors: SMB (Small Minus Big — the size effect) and HML (High Minus Low — the value effect, B/M ratio). CoE = Rf + β_M × ERP + β_SMB × SMB + β_HML × HML. Empirically it explains 90%+ of cross-sectional returns vs. ~70% for CAPM. The five-factor model adds profitability (RMW) and investment (CMA). Rarely used directly in IB — but the model explains why the Ibbotson size premium is consistently positive (it compensates the SMB factor).

The middle-market discount is an add-on to the CoE for mid-cap family-owned companies — driven by:

• Illiquidity: no public market.
• Information density: lower than for public comps.
• Concentration risk: often single-family ownership.
• Governance: family conflicts, succession questions.

typically a 2–4% add-on.

```
WACC = (E/(D+E)) × Re + (D/(D+E)) × Rd × (1 − t)
```

• E (EqV), D (Debt): Market values of equity value and debt
• Re: Cost of equity (CAPM)
• Rd: Pretax cost of debt (YTM of outstanding bonds)
• t: marginal tax rate

Inputs:

• EqV: $600m
• Debt: $400m
• Re: 10%
• Rd: 5%
• t: 30%

Calculation:
```
EqV share = $600 / $1,000 = 60%
Debt share = $400 / $1,000 = 40%
WACC = 0.6 × 10% + 0.4 × 5% × 0.7
= 6.0% + 1.4%
= 7.4%
```

Weighted average of the cost of capital — weighted by share. (1−t) on Rd delivers the tax shield.

WACC is the discount rate for UFCF.

• UFCF + WACC: UFCF belongs to all capital providers (equity + debt) → weighted discount rate
• LFCF + cost of equity: LFCF after interest → belongs only to equity providers

Both approaches lead to the same equity value.

• UFCF is easier to project (no debt schedule needed)
• Allows capital-structure changes without rebuilding the model
• Market standard, comparable

```
After-Tax Rd = Pretax Rd × (1 − t)
```

Pretax 5%, t = 30% → after-tax = 3.5%.

typically the yield-to-maturity of outstanding bonds.

The tax rate should be marginal, not average. In most jurisdictions the marginal corporate tax rate is ~25–30%.

the tax shield doesn't apply fully → a higher effective cost of debt.

Three methods in descending priority:

• Yield-to-maturity (market standard): the YTM of outstanding bonds reflects current market conditions. The coupon rate is wrong because it is fixed historically.
• Credit-spread method: Rf + credit spread from rating and sector — practical when there is no tradable bond.
• Bank loan pricing: the company's current loan terms — an alternative when there is no bond and no rating.

Private targets often have no bonds. Estimate a rating from leverage ratios (Debt/EBITDA, interest coverage), then apply a sector-typical credit spread. Private-placement terms are often publicly available and give a good indication.

Marginal — i.e. "what tax applies to each additional dollar earned?" In most jurisdictions the marginal corporate rate is roughly 25–30%.

The effective tax rate from the annual report is often lower because of NOLs, tax planning, and international subsidiaries — but that reflects past conditions. In the DCF you need a forward-looking assumption.

If the effective rate today is 22% (NOLs) but the long-run marginal rate is 30%, you compute WACC with 30%. In the FCF use 22% short-term, then step up to 30%.

The target capital structure is standard. WACC reflects long-run financing costs — the current structure could deviate temporarily (e.g. after a recent M&A deal). The target is typically derived from: (1) the sector's optimal structure, (2) the median of the comp group, (3) management guidance.

D/V = 0.5 / 1.5 = 33.3%. E/V = 1 / 1.5 = 66.7%. After-tax cost of debt = 5% × (1 − 0.25) = 3.75%. WACC = 0.333 × 3.75% + 0.667 × 11% = 1.25% + 7.33% = 8.58%. Sanity check: ~8.6% is plausible for a mid-cap industrial business. At higher leverage (D/E 1.0): WACC drops slightly to ~8.2% due to a larger tax-shield share — until distress risk drives CoE and cost of debt up (U-curve).

Three methods:

• Industry median: compute the D/E of 8–12 public comps and take the median. Liquid market prices give realistic market values.
• Optimal capital structure: the theoretical minimum WACC across different D/E levels (U-curve). Academic, too complex in practice.
• Management plan: for PE targets, often the post-LBO structure.

industrials 0.4–0.7, software/tech 0.1–0.3 (cash-rich), real estate 1.5–3.0 (asset-financed).

Family-owned businesses are often more conservative than public comps (D/E 0.2–0.3) — but the target should reflect the industry norm, not the family's conservatism.

Two variants:

• Post-tax WACC (standard): cost of debt multiplied by the (1−t) factor. Standard in IB, combined with after-tax UFCF.
• Pretax WACC: cost of debt before the tax shield, without the (1−t) factor. Used when UFCF is modeled on a pretax basis — extremely rare.

If UFCF accounts for cash taxes, then use WACC with (1−t) on debt — otherwise the tax shield is double-counted or missed entirely.

If the company is in an NOL position and cash taxes are 0%, the (1−t) adjustment in WACC is premature. For the NOL period you should actually use the pretax cost of debt.

Project finance has higher leverage (D/E 3.0–5.0 typical) and lower equity risk (cash flows from long-term contracts, regulated tariffs).

WACC vs. leverage has a U-shape: high at low leverage (too little tax shield), falls as leverage rises (the tax shield dominates), reaches a minimum at the 'optimal D/E', then rises again (distress costs exceed the tax-shield benefit). Optimal point: typically 30–50% debt-to-total-capital for industrial companies. Theory: a trade-off between the tax shield (linearly positive) and distress risk (convexly rising). In practice: bankers rarely estimate the 'optimum' exactly — they anchor on the industry median or management guidance.

The cost of debt for HY is high — typically 7–10% pretax at a B rating, 10%+ at CCC. After tax, the tax-shield benefit remains as long as the company is profitable.

Inputs:

• Pretax cost of debt: 7%
• Tax rate t: 30%

Calculation:
```
After-tax cost of debt = 7% × (1 − 30%) = 7% × 0.7 = 4.9%
```

CoE is also higher: a higher beta due to distress risk, often a +2% distress premium. WACC for an HY issuer is typically 9–12% — so not dramatically lower than pure equity financing.

For distressed targets (yield-to-maturity > 12%), the 'cost of debt' is really the cost of distressed equity — the Modigliani-Miller setup breaks down.

At very high leverage and distress risk, replace WACC with the APV method (adjusted present value): a standalone valuation plus a separate tax-shield value.

Excess cash is the cash balance not needed for operations — typically assume 2–5% of revenue as 'operating cash', and the rest is excess.

• Capital structure with net debt: D/(D+E) becomes net debt / (net debt + E). When cash > debt, net debt turns negative — the structure behaves like pure equity financing, and WACC approaches CoE.
• Treat cash separately: apply WACC to operating assets and add cash separately to EV as 'excess cash value'.

Approach 1 is the IB standard. For cash-rich tech companies, net debt is often −$500m or lower, so WACC is nearly identical to CoE.

In distress (bond YTM >15%, equity value collapsing), standard WACC is unreliable. Problems:

• The cost of debt is effectively a distressed equity return.
• The market value of equity trends toward zero — the weights become absurd.
• The tax shield doesn't apply fully when there is no taxable income. Solutions: (1) adjusted present value (APV): standalone valuation plus a separate tax-shield value, less distress costs. (2) Restructuring valuation: value under the new post-restructuring capital structure. (3) Liquidation floor: run-off or asset-sale value.

Firm value is independent of the capital structure. If you increase leverage, CoE rises by exactly enough to keep WACC constant. MM (with taxes): value rises with leverage because of the tax shield — until distress costs kick in. Consequence for IB practice: reducing WACC through more leverage is NOT a real value gain — you trade equity risk for a lower cost of capital. Real value comes only from the tax shield (and the discipline of debt service).

• Bank-centric financing: relationship-bank loans and private placements instead of public bonds, and limited access to high-yield markets.
• Conservative ownership: family owners often run lower leverage than sponsor-backed companies and many large listed peers, prioritising control and independence over tax-shield optimisation.
• Pension liabilities: in markets where unfunded, book-reserved pension plans are common (e.g. Germany), these are debt-like 'hidden debt' and must be included in net debt.
• Hybrids and shareholder funding: shareholder loans, mezzanine and local hybrid instruments (e.g. profit-participation rights or silent partnerships in Germany/Austria) are common.

a standard public-comps WACC can be too low for a family-owned middle-market business: size and illiquidity risk, key-person risk and a more complex financing mix mean the risk is priced higher.

The group WACC is the weighted average of the segment WACCs — but for an SOTP you need segment-specific WACCs.

• Find pure-play comps for each segment — the auto division via pure auto suppliers, the healthcare division via pharma comps.
• Unlever the segment-specific beta and relever it with the group capital structure (or with the segment-typical structure when segments are valued separately for spin-off scenarios).
• Derive the segment cost of debt from pure-play bonds.

A ±50bps change in WACC → a ±5–7% change in EV in a standard DCF. ±100bps → ±10–14%. Sensitivity increases with forecast length and growth rate. Standard sensitivity slide in an IB pitch: a two-variable table with WACC (columns: 8.0%, 8.5%, 9.0%, 9.5%, 10.0%) and g (rows: 1.5%, 2.0%, 2.5%) — showing the EV range. The Football Field reflects this: the DCF range comes mainly from the WACC bandwidth.

Whose WACC do you use — acquirer or target? Answer: the target WACC is the valuation benchmark because it reflects the risk of the cash flows (location, industry, business). Use the acquirer WACC only when synergy NPV is valued separately. Target-specific: USD cost of capital (US Treasury Rf, US ERP, US comps for beta). The valuation is then converted into the home currency at spot FX. Pitfall: if the acquirer values with its own lower WACC ('because we can finance more cheaply'), it pays full value plus a premium and gives its cost-of-capital advantage away to the seller.

Publicly listed companies with a similar business model, size, and risk profile — from their multiples (EV/EBITDA, EV/Sales, P/E) you derive a valuation range for the target.

The market prices comparable companies every day — those prices reflect consensus expectations on growth, margins, and risk.

market-based, easy to communicate
Disadvantages: no perfect comps, no M&A control premium priced in

One of the three core methods alongside DCF and precedents.

• + Market-based, easy to communicate, fewer assumptions, fast
• − No perfect comps, follows market trends (including hype), a static snapshot

• + Fundamental, independent of market sentiment
• − Many assumptions, sensitive to WACC + growth

Both in parallel — triangulation. Both have weaknesses; together they give a more robust range.

• Business model: same industry, products, customers
• Geography: match the target's region (e.g. European targets with European comps)
• Size: market cap 0.5x−2x of the target
• Margins: similar EBITDA margin
• Growth: comparable top-line growth
• Capital structure: similar D/E range

industry-code screen (GICS, NACE) − qualitative filtering − 6−12 final comps. In the pitch: Tier 1 (closest) + Tier 2 (more peripheral).

Senior MDs look closely at the universe logic — comp-set selection often gets 'gamed'.

• EV/EBITDA: universal, capital-structure neutral
• EV/EBIT: capital-intensive businesses (D&A differences matter)
• EV/Sales: pre-profitability (SaaS, biotech)
• P/E: banks, insurers, REITs
• EV/EBITDAR: lease-intensive (airlines, hotels)

• Banks: P/Book
• Utilities: EV/MWh
• Mining: EV/Reserves
• Telecom: EV/Pop

EV/EBITDA + P/E.

• LTM (last twelve months): trailing EBITDA from the most recently reported quarters. Robust, but backwards-looking.
• NTM (next twelve months): consensus forecast for the coming 12 months, drawn from equity research (Bloomberg, Refinitiv).
• FY+1, FY+2: consensus for the next and the following fiscal year.

NTM as the primary multiple, LTM as a sanity check. For growth companies add FY+2 — the forward multiple shows the valuation relative to future profitability.

Consistency between target EBITDA and comp EBITDA — if you strip restructuring at the target, you must do it at the comps too.

At comps with large pension obligations, pension service cost sits in EBITDA, but interest cost and plan-asset returns often sit in the financial result. Adjustment options:

• Take reported EBITDA (service cost stays in) — simple, but inconsistent across companies with funded vs. unfunded plans.
• Pension adjustment: use cash service cost instead of P&L service cost.
• Pure operating EBITDA: strip out all pension items, then treat the pension liability separately as 'debt-like'. IB standard: method (3), for clean comparability.

Consistency between target and comps. At US tech comps (Adobe, Salesforce historically 8−12% of revenue in SBC) this drives large multiple differences. Middle-market companies: typically no SBC programs — the adjustment is rarely relevant.

adjusting comps with different fiscal-year-ends onto a common calendar-year basis.

Inputs:

• Market cap (EqV): $1,200m
• Net debt: $200m
• NTM EBITDA: $150m

Calculation:
```
EV = EqV + Net Debt = $1,200 + $200 = $1,400m
EV/EBITDA = $1,400 / $150 = 9.33x
```

9.3x is plausible for a mid-cap tech company with moderate growth. If the sector median is 11x, the target trades at a discount — the pitch has to explain why (growth below sector, margin compression, a family-control discount).

current market cap / EV against LTM EBITDA — a trailing multiple. Forward multiple (NTM, FY+1, FY+2): market cap / EV against forecast EBITDA — a forward multiple. For growth companies, forward multiples are lower than trailing (because EBITDA grows). IB standard: the NTM multiple is the primary benchmark. Rationale: the market prices in future cash flows, so a forward multiple is 'apples-to-apples'. LTM only as a sanity check. Pitfall: the NTM multiple rests on consensus EPS forecasts — after recent earnings misses or guidance cuts, consensus can be stale.

The median is the IB standard. Rationale: robust against outliers (one extreme comp doesn't distort the result). The mean only makes sense when the comp set is very homogeneous with no outliers. In practice:

• Median as the primary.
• 25th and 75th percentile as a range indicator.
• Mean as a cross-check.
• Exclude min/max for a trimmed mean. Pitfall: with only 4−5 comps the median is not very robust — median and mean often sit close together.

a range approach. Methodology:

• Low multiple (25th percentile or median minus 0.5−1.0x) − target EBITDA = lower bound.
• High multiple (75th percentile or median plus 0.5−1.0x) − target EBITDA = upper bound.
• A midpoint or 'point of view' somewhere in between, based on target specifics (growth vs. comp median, margin position).

−0.5x to −1.5x EV/EBITDA for a 50% smaller market cap.

• If the target is larger: a slightly higher multiple. But: adjusting heavily is confirmation bias. The better method: choose the comp set so the target sits within 0.5x−2x of the size. If that's impossible (e.g. a unique middle-market size): mid-cap comps + small-cap comps in two tranches, then a middle path.

Net-debt definitions vary across Bloomberg, CapitalIQ, and Reuters:

• 'Strict net debt': total debt − cash.
• 'Adjusted net debt': adds lease liabilities (post-IFRS 16), pension liabilities, preferred equity, and NCI.
• 'CapIQ default': often includes more debt-like items than Bloomberg.

In acute market dislocations, spot multiples are not representative — sentiment dominates over fundamentals. Adjustments:

• Use pre-crisis multiples (e.g. a 6-month average before the dislocation).
• Wait for post-recovery multiples (3−6 months after stabilization).
• Combined approach: 'normalized multiple' = median(LTM, 1Y avg, 3Y avg). Example COVID April 2020: equities traded at multiples 30−50% below normal levels — if a PE sponsor wanted to buy at that time, a pre-crisis multiple would be more realistic than spot.

Broken comps are comps that no longer trade or show unrepresentative multiples. Four typical triggers:

• Buyout / takeover in the comp set — the stock no longer trades actively.
• Major restructuring underway — a spin-off assumption, no 'going concern'.
• Accounting scandal — a fraud blowup.
• Distress — a price collapse from a rating downgrade.

exclude broken comps from the universe and document them in the pitch footnote.

if 3 of 8 comps are 'broken', the remaining set is too small — then widen the universe to adjacent sectors or move the reference date back.

Closed M&A deals in the same industry/geography over the last 3–5 years — you derive a valuation range from the deal multiples.

What have buyers historically paid for comparable targets?

Reflects real transaction prices, including the control premium.

Data sources are incomplete; deals older than 12 months are often not representative because of market changes.

One of the three core methods alongside DCF and Trading Comps.

Precedents include a control premium: the markup for acquiring control (typically 20–35%). Trading Comps reflect minority investments without control.

Precedent multiples are typically 20–40% above Trading Comps.

• M&A valuation → Precedents (acquisition pricing)
• Equity valuation for public investors → Trading Comps

Mixing the two without context — a senior will immediately ask why precedents are 12x and trading is 9x.

• S&P Capital IQ: the most comprehensive coverage, deal terms + multiples
• Mergermarket: deal news with multiple information
• Refinitiv Eikon (formerly Thomson): historical depth
• Bloomberg M&A: combines with other Bloomberg data
• PitchBook: strong on PE deals
• DEF 14A / annual reports: deal details for public deals

many private transactions with no multiple disclosure → a data problem.

Always cite the source for each deal — senior MDs check this.

• Sector: the same industry as the target.
• Geography: preferably the domestic region/Europe, with US deals as a supplement subject to a caveat.
• Size: deal EV in a 0.3x–3x range of the target EV.
• Vintage: typically the last 3–5 years; older deals only as context.
• Deal type: strategic vs. financial — separate buckets, because the multiples differ.
• Exclude: distressed sales, government-mandated transactions, family-internal transfers.

8–15 deals.

In a middle-market context with thin deal flow, broaden the universe to European mid-cap industrials.

the multiple comes from offer price × shares + net debt = EV, divided by disclosed EBITDA. Very precise, because all the data is public. Private deals: the multiple is often only indirect — the buyer discloses the deal value, but the EBITDA basis and net-debt adjustments aren't clear.

EV / EBITDA for the last 12 months before the deal announcement. Robust, based on historical figures. NTM multiple (forward): EV / EBITDA for the next 12 months from the deal announcement, from consensus forecast or the management plan. IB standard: LTM is the primary multiple for precedents (unlike Trading Comps, where NTM dominates). Reason: LTM is the number the buyer historically used for its valuation — based on realized performance.

Forward figures can be set too inconsistently. Pitfall: if the target had an anomaly in the deal year (an acquisition, a large one-off order), LTM is distorted — some bankers use a 'mid-year' multiple or 'run-rate' EBITDA.

• Paid multiple — what the buyer actually paid.
• Implied multiple — what the buyer would have valued on a "standalone" basis, without synergies.

```
Paid Multiple = Deal Value / Target EBITDA at Closing
Implied Multiple = (Deal Value − Synergy Value) / Target EBITDA
```

Deal Value (equity purchase price) + Net Debt at Closing + Minority Interests at Closing − Cash Bridge Adjustments = Deal EV.

the target is a business unit/division sold out of a group. EBITDA often contains 'synergies' or 'standalone costs' that disappear after closing. Adjustment: calculate standalone EBITDA (with a cost-allocation model). Distressed sales: the seller was forced to liquidate (insolvency, forced sale). The multiple is often 30–50% below going-concern pricing. Adjustment: bucket distressed deals separately or exclude them entirely. Spin-offs / demergers: not pure M&A transactions, often misleading multiples.

For every precedent deal, understand the deal logic, or the multiple is misleading.

Implied EV/equity from a comp multiple:

Inputs:

• Target EBITDA: $80m
• Sector median multiple: 9.5x EV/EBITDA
• Net Debt: $100m

Calculation:
```
Implied EV = $80 × 9.5 = $760m
Implied EqV = EV − Net Debt = $760 − $100 = $660m
```

9.5x is the sector median — if Trading Comps come in at 8.0x, 9.5x implies a 19% control premium. Plausible for a strategic buyer.

typically ±0.5–1.0x around the median → 8.5–10.5x → EV $680–840m → EqV $580–740m. Show it in the Football Field as the precedent range.

Control premium = (Offer Price − Pre-Announcement Stock Price) / Pre-Announcement Stock Price. Standard data point: the share price 1 day or 30 days before the announcement date. A 30-day average reduces the noise from leak rumors.

Hot-market effects (e.g. 2021 post-COVID liquidity, 2007 pre-GFC):

• Multiples 30–50% above the long-run average.
• Strategic-premium inflation (FOMO).
• PE valuations shaped by a cheap-debt market.
• High auction intensity. Cold markets (2008–2009, the 2022–2023 tech reset): (1) multiples 30% below the long-run average. (2) little auction activity, buy-side dominance. (3) distressed deals dominate the universe. Consequence for precedent valuation: a vintage effect — if 60% of your universe comes from the hot 2021 market, the multiples are inflated. Adjustment: a 12-month rolling median instead of the universe mean; or a vintage weighting.

typically pay 1–2x EBITDA more than financial buyers, because they expect synergies. Example range: strategic 10–13x, financial 8–10x for the same sector. Financial buyers (PE sponsors): more disciplined, return-focused (a 20%+ target IRR demands multiple discipline). Consequence for valuation: if your buyer universe is mixed, bucket it separately — strategic multiples for a strategic-bid estimate, financial multiples for the PE floor. Pitfall: PE deals in hot markets can reach strategic multiples (a cheap-debt effect) — contextual caution. Example: large-cap PE sponsors typically pay 9–10x for an industrial mid-cap; strategic players (global industrial and consumer majors) 11–13x.

If the universe contains strategic deals, a synergy premium is priced into the multiple. Adjustment to recover "pure standalone pricing":

```
Synergy Value = Cost Synergies × 8x + Revenue Synergies × 6x
Seller Share = Synergy Value × 50% (typical allocation)
Standalone EV = Strategic Deal EV − Seller Share
Adj. Multiple = Standalone EV / Target EBITDA
```

Cross-border deals (e.g. a US buyer and a European target, or vice versa) bring FX and region-risk-premium complications. Adjustments:

• Currency conversion: convert the deal value into the target's currency at spot FX on the closing date. The multiple is FX-neutral, so there's no direct distortion.
• Region premium: foreign buyers often pay 5–10% more for domestic targets out of a desire for FX diversification. Bucket it in the comp set — 'domestic-domestic' and 'cross-border' separately.
• Regulatory adjustments: foreign-investment reviews (e.g. CFIUS in the US, and equivalent national screening regimes elsewhere) can affect bid floors. Cross-border deals are useful for a 'maximum-bid estimate' (a strategic foreign buyer with an FX advantage), not for 'floor pricing'.

In some sectors it is structurally uninformative.

• Banks: no EBITDA logic (net interest margin = 'revenue') → P/B, P/E
• Real estate: cap rate (NOI/value) instead of EBITDA
• Pre-profitability SaaS: EBITDA negative → EV/Revenue
• Capital-intensive mining: EV/Reserves
• Asset managers: P/AUM

A multiple needs an economically meaningful link to its driver.

Sector-specific multiples show sector understanding — senior MDs pay particular attention in industry pitches.

• EV/EBITDA: the primary multiple, mid-cap typically 7–10x
• EV/EBIT: for capital-intensive businesses (where D&A matters)
• P/E: a cross-check, typically 12–18x
• EV/Revenue: secondary, where margin dispersion is low

• Auto suppliers: 5–7x
• Specialty machinery: 8–12x
• Engineered components: 7–9x

For cyclical industrials (steel, commodity chemicals) use mid-cycle multiples, not spot. A senior MD will ask about the point in the cycle.

• EV/Revenue: the primary multiple for pre-profitability names, 5–15x depending on growth
• EV/ARR (annual recurring revenue): more precise, weighting recurring vs. services
• Rule of 40: growth % + EBITDA margin % ≥ 40 as a quality signal
• EV/EBITDA for profitable SaaS: 15–25x (higher than industrials because of growth)
• Net revenue retention (NRR): a quality driver, not a multiple

some markets show less EV/Revenue hype, with multiples typically 30–40% lower than US peers.

Always show the Rule of 40 as a cross-check — it prevents hype without profit underpinning.

P/B (price-to-book) or P/TBV (tangible book value).

• Logic: equity × ROE-to-CoE premium (rule of thumb).
• Range: 0.8–1.5x P/B; premium banks (UBS, JPMorgan) >1.5x.

• Life: embedded-value multiple.
• P&C: P/B.
• Large listed insurers: 1.2–1.5x.

• NAV discount/premium, P/AFFO, cap rate (NOI/property value).
• Large listed residential REITs: 0.7–1.1x NAV.

'For financials and real estate, EBITDA multiples are not informative — sector convention is P/B for banks, P/AFFO for REITs.'

EV/EBITDAR adjusts for operating leases:

```
EV/EBITDAR = Enterprise Value / (EBITDA + Rent Cost)
```

Pre-IFRS 16, this mattered for lease-intensive sectors where operating leases were shown as a P&L expense (rather than as a capital lease) — hotels, airlines, restaurant chains, retail.

Operating-lease cost behaves like quasi-debt; EBITDAR neutralizes the own-vs-lease choice.

Operating leases are capitalized, so EBITDA implicitly contains the lease adjustment — EBITDAR becomes less relevant. For US-GAAP comparisons against pre-IFRS-16 data, EBITDAR can still be useful.

P/B (price-to-book) = market cap / book value of equity, the standard multiple for banks.

A bank's value comes from equity × a multiple, where the multiple reflects the ROE-to-CoE relationship.

```
P/B = (ROE − g) / (CoE − g)
```

with g = sustainable growth.

P/TBV (price-to-tangible book): equity excluding goodwill and intangibles — more meaningful for banks with large acquisition goodwill.

Inputs:

• ROE: 12%
• CoE: 10%
• g (sustainable growth): 2%

Calculation:
```
P/B = (ROE − g) / (CoE − g)
= (12% − 2%) / (10% − 2%)
= 10% / 8%
= 1.25x
```

If the bank trades at 0.9x, the discount signals a lower ROE expectation or a higher CoE.

some large universal banks have historically traded below 0.5x P/B (low ROE), stressed names at 0.3–0.5x, while high-ROE private banks trade at 1.5–2.5x.

EV/Revenue for SaaS varies strongly with growth.

```
30%+ growth: 8–12x EV/Revenue
20–30% growth: 5–8x
10–20% growth: 3–5x
<10% growth: 2–3x
```

• Top-line growth: the primary driver.
• NRR (net revenue retention): above 120%, a premium multiple.
• Gross margin: above 75% is premium.
• Rule of 40: above 40, a premium.

listed software companies in some markets typically trade around 30% below their US peers because of market structure.

Rule of 40 = revenue growth rate (%) + EBITDA margin (%) ≥ 40%.

EV/Subscriber (pay-TV, mobile, streaming, pay-per-use software): enterprise value divided by the number of subscribers.

Value per customer, independent of the marketing-spend cycle.

EV/Subscriber × customer lifetime (years) × ARPU = the implied customer lifetime value. Application:

• Mobile: typically $300–600 per subscriber for large listed operators.
• Pay-TV: $600–1,200 per subscriber.
• Streaming (Netflix): higher multiples because of global scale. Pitfall: subscriber quality varies (postpaid vs. prepaid, premium vs. basic) → build a 'blended ARPU' into the multiple.

EV/Reserves measures the value per proven reserve unit (ton of coal, barrel of oil, cubic foot of gas).

Value comes from the asset base, not from the current production margin.

• Oil & gas: EV/2P reserves.
• Mining: EV/resource tons.
• Forestry: EV/hectare.

value per unit produced per year, useful for mature assets with no further reserve expansion. Oil & gas example: typically $30k–80k per barrel of production per day.

1P proven, 2P proven+probable, 3P plus possible. Lower categories mean a lower multiple.

EV/Bed measures value per bed of capacity, useful when the asset base is limited and profitability is driven by occupancy.

hospitals, care homes, hotels.

• Hospitals: $100–250k per bed.
• Care homes: $50–100k.
• Hotel beds: $100–500k (budget vs. luxury).

EV/Room (hotels), EV/Patient (outpatient clinics), EV/Resident (care homes).

Asset-quality differences are huge — location, renovation status, occupancy.

EV/Bed × annual revenue per bed gives the implied EV/Revenue multiple. In the wave of care-home consolidation (and the distress at some large listed operators), EV/Bed multiples were central and swung sharply over 2018–2024.

P/AUM = market cap / assets under management — the value per dollar of managed assets.

Asset managers generate fees as a % of AUM, so AUM is the primary value driver.

• Active managers: 1–3% of AUM (fee margins of 50–80bps).
• Passive (ETFs): 0.3–0.8% (lower fees, but scale advantages).

large listed active managers trade around 1.5–2% of AUM, while private banks that combine asset and wealth management run at 3–5%.

fee margins × profit conversion. Mix effect: a higher passive share pushes multiples down.

Historical EV/EBITDA ranges for industrials by sector:

• Specialty chemicals: 9–13x — higher than commodity chemicals because of margin resilience and patent protection.
• Commodity chemicals: 5–7x.
• Industrial engineered components: 7–10x.
• Mid-cap machinery: 8–11x.
• Auto suppliers: 5–7x — low because of cyclical exposure and EV-transition risk.
• Industrial electronics: 11–14x.
• Packaging: 7–9x.

margin stability, end-market diversification, pricing power, ESG profile.

The PEG ratio is the P/E ratio divided by the earnings growth rate (in %):

```
PEG = P/E / EPS growth (%)
```

PEG around 1.0 = fairly valued; <1.0 = cheap; >1.0 = expensive.

Mathematical bridges between multiples:

• EV/EBITDA → EV/EBIT: EV/EBIT = (EV/EBITDA) × (EBITDA / EBIT).
• EV/EBIT → P/E: more complex because of the tax shield and net debt. In practice, via a reverse calculation (EV → equity value → P/E).

what would it cost to rebuild the asset base today?

capital-intensive sectors (steel plants, chemical parks, semiconductor fabs), where a market price below replacement-cost value is the 'natural floor'. NAV (net asset value): the market value of all assets − liabilities.

holding structures, REITs, investment funds, BDCs. Multiple-based methods work poorly when:

• The earnings stream is highly volatile (cycle extremes).
• The business model is in transition.
• A liquidation scenario is more likely than a going concern.
• Asset value > earnings-power value.

Rule of 40 = 25% + 20% = 45 → passes with a premium.

SaaS at 25% growth: a multiple range of 6–10x EV/Revenue.

For premium quality (Rule of 40 at 45+, moderate customer concentration): 7.0x EV/ARR.

Inputs:

• ARR (annual recurring revenue): $100m
• EV/ARR multiple: 7.0x
• Net cash: $20m
• EBITDA margin: 20%

Calculation:
```
EV = $100 × 7.0 = $700m
EqV = EV − Net Debt = $700 − (−$20) = $720m
EBITDA = $100 × 20% = $20m
Implied EV/EBITDA = $700 / $20 = 35x
```

An EV/EBITDA of 35x is high and reflects the low current margin — EV/Revenue (or EV/ARR) is the more reliable method here; 35x EBITDA is defensible only as a cross-check and with a margin-expansion story.

In cyclical sectors (autos, steel, chemicals, construction) the spot multiple is misleading — peak EBITDA produces a low multiple ('looks cheap'), trough EBITDA a high one ('looks expensive').

• Mid-cycle EBITDA: a 7–10-year average. EV divided by mid-cycle EBITDA gives the through-the-cycle multiple.
• Cycle-adjusted multiple: spot multiple × (spot EBITDA / mid-cycle EBITDA).
• Peak/trough range: show the min/max multiple range across the cycle.

for steel producers, 2022 peak EBITDA was 4x higher than the 2020 trough.

NRR = (starting ARR + expansion − churn − contraction) / starting ARR. It measures how the customer base develops over a year without new logos. >100% = net expansion, <100% = net contraction. Premium SaaS: NRR of 120%+ (Snowflake historically 150%+). Average SaaS: 105–115%. As a multiple driver, NRR is a central quality indicator — at 130% NRR a company can grow with no new customer acquisition → a higher multiple.

NRR premium ≈ 0.3–0.5x EV/Revenue per 10% NRR difference vs. the sector median.

Bank multiples react strongly to the rate environment:

• Low rates (2014–2021): multiples depressed. NIM falls, CoE high. P/B for the sector 0.4–0.7x; the weakest names 0.2–0.4x.
• Rate turn (2022–2024): multiples rally. Net interest margin expands, ROE rises — P/B re-rates to 0.7–1.2x.
• High rates (steady state 4%+): P/B 0.9–1.3x. Solid ROEs (around 12%) justify a slight premium to book value.

In recessions, loan-loss provisioning rises, so ROE falls and the multiple falls with it.

The cap rate (capitalization rate) is the inverse of an EV/NOI multiple:

```
Cap Rate = NOI / Property Value
EV/NOI = 1 / Cap Rate
```

Distressed sectors (e.g. print media from 2015 on, coal/mining under ESG pressure) have structurally low multiples — but spot multiples are not the floor: further decline can compress them more. Methods:

• NAV-based instead of an EBITDA multiple: show liquidation value.
• Run-off DCF: explicit decline modeling instead of Gordon with a negative g.
• EV/Replacement cost: a floor for capital-intensive distressed sectors.
• Distressed comp universe: use only other distressed sectors as comps, not 'normal' industrials. Pitfall: 4x EV/EBITDA in a distressed sector looks 'cheap' but can be value-destroying under structural decline (FCF-negative).

For pre-revenue names (biotech, early SaaS, pre-launch hardware) classic multiples fail. Methods:

• Risk-adjusted DCF: cash-flow forecasts with probability weights (e.g. Phase-2 pharma: 30% probability of success through approval).
• Comparable pre-money valuations from VC funding rounds.
• Real options: for optionality (patent portfolios, drug pipelines), Black-Scholes-style option valuations.
• Replacement cost: the value to an acquirer who would build the asset / technology itself.
• EV/Customer for SaaS with an existing customer base but no significant revenue. For pre-revenue pharma, rNPV (risk-adjusted NPV) is the standard. Many biotech names were valued pre-revenue on exactly this rNPV logic before a product reached the market.

• Enterprise Value (EV): the total value of the operating business, belonging to all capital providers
• Equity Value: the value for equity holders, after deducting all debt-like items

```
EV = EqV + Net Debt + Minorities + Pension Underfunding − Associates − Excess Cash
```

• EV-based: EV/EBITDA
• Equity-based: P/E

it is capital-structure-neutral across companies financed differently.

```
EqV = EV
− Net Debt
− Minorities
− Pension Underfunding
− Lease Liabilities (post-IFRS 16)
− Other Debt-like Items
+ Associates (Equity Method)
+ Excess Cash
```

Some use total cash instead of excess cash. Others exclude operating cash.

Consistency between the comp set and the target − treat them all the same.

The bridge slide shows each component individually in $m − senior MDs check every line.

EV is capital-structure-neutral. Two identical businesses with different leverage have:

• the same EV
• a different Equity Value (more debt − less equity)

• EV/EBITDA stays comparable
• P/E varies with leverage (higher leverage − higher interest − lower net income − lower P/E at the same EV)

'EV-based multiples are the market standard for comps because they neutralize capital-structure differences.'

The standard net-debt definition:

```
Net Debt = Total Interest-Bearing Debt − Cash & Cash Equivalents
```

bank loans, bonds, privately-placed corporate loans, short-term credit lines.

trade receivables, tax liabilities.

• Reverse factoring (supplier programs) − debt-like?
• Customer deposits / advances − operating or financing?
• Drawn-down letters of credit.
• Frozen cash (guarantees, escrows).

privately-placed corporate loans are clearly debt, while profit-participation rights are often disputed.

Pension underfunding (DBO (Defined Benefit Obligation) − plan assets) is debt-like and is deducted from EV. Tax adjustment: gross underfunding × (1 − t), because a tax shield applies on unwind.

Since IFRS 16 (2019), operating leases sit on the balance sheet as lease liabilities. They are debt-like and are therefore deducted from EV.

Post-IFRS 16, EBITDA no longer contains any operating-lease expense (pre-IFRS 16 it did) − so the margin is arithmetically higher. This creates a structural break in the EV/EBITDA multiple across the 2018→2019 boundary.

For cross-time comps (pre vs. post-IFRS 16), either restate them all or flag it explicitly.

operating leases stay off-balance-sheet − check the notes for "hidden" lease debt.

Minority interests (NCI) are the NCI share of consolidated subsidiaries. Consolidated EBITDA includes 100% of the subsidiary, but the equity value belongs only to the majority. Solution: deduct NCI from EV.

• Market-value method: `NCI market value ≈ NCI EBITDA × sector multiple` (for listed stakes, use the share market value directly).
• Book-value method (default, when no data): deduct the NCI book value directly from EV.

Equity-method investments are stakes of 20–50% in a company that is not fully consolidated. EBITDA contains no share of them − so there is no "add" in EBITDA. But the value of the stake belongs to the equity value, which is why associates are added to EV (the opposite of NCI).

• Mark-to-market: for listed associates, the share value.
• Book value as a proxy for private stakes.
• Multiple-based: associate EBITDA × sector multiple.

Preferred equity is a hybrid − between debt and common equity. Treatment as debt-like: deduct from EV, because common-equity holders do not 'own' the preferred. Mark-to-market: for listed preferred, the market price × count. For private preferred: the liquidation preference (often book value + accrued dividends). Pitfall: convertible preferreds (mandatory or optional) − treasury-stock method or conversion adjustment depending on strike vs. stock price. Preferred equity is largely a US/UK phenomenon and rare in middle-market Europe. Where a listed company does have preference shares, take market value and disclose them separately.

Convertibles are debt with an equity conversion option. The treatment depends on whether the option is in-the-money (ITM) or out-of-the-money (OTM):

• ITM (share price > strike): as-if-converted method − treat as equity, increase the share count in the equity-value calculation, no debt deduction.
• OTM (share price < strike): treat as pure debt − deduct from EV, no dilution of the share count.

Black-Scholes valuation of the conversion option and hybrid treatment.

ITM as-if-converted, OTM as debt.

For in-the-money options, calculate the share dilution. Steps:

• ITM options: strike < current share price.
• Hypothetical exercise: number of options × strike = proceeds.
• Proceeds buyback: proceeds / current share price = shares repurchased.
• Net dilution: options − shares repurchased.

employee compensation in the form of promised shares (vesting over time). Unlike options, they have no strike − on vesting they convert 1:1 into shares. Treatment: the diluted share count already includes unvested RSUs (often in the 'diluted shares outstanding' reporting). For valuation: use diluted shares, not basic shares. Pitfall: RSUs vest over several years − in forecast modeling, add new RSU tranches each year. Relevant at US tech with 4–8% annual RSU dilution; rarely a program at middle-market companies.

Debt-like items become tax-deductible on unwind (pension payout, litigation settlement). The tax shield reduces the effective liability value. Method: gross liability × (1 − marginal tax rate).

cash needed for the operating business (working capital, supplier payments, payroll).

2–5% of revenue as operating. Excess cash: the balance beyond the operating-cash need − it can be paid out without disrupting the business (dividend, debt repayment). Bridge treatment:

• Strict method: operating cash stays in EV (part of the operating business), excess cash added separately to equity value.
• Standard IB method: subtract total cash from net debt ('Net Debt = Total Debt − Total Cash'). Method (2) is the standard, but for cash-rich targets (software, pharma) method (1) gives a cleaner valuation picture.

Equity value = EV − Net Debt − pension − NCI = 1,200 − 250 − 80 − 30 = $840m. Sanity check: bridge total $360m = 30% of EV − typical for a traditional industrial business with moderate leverage and large pension obligations. For a PE sponsor the bridge is often small (10–15%); for mature large-caps 25–40%. If further items are relevant (operating leases $40m, litigation reserve $15m after-tax): equity = 840 − 40 − 15 = $785m.

Hybrid instruments sit between debt and common equity — equity-like features (no voting rights, often a profit-dependent or deferrable coupon) but debt-like features (senior to common equity, fixed redemption or call, no real control). Examples across markets: preferred shares (US/UK), perpetual or subordinated hybrid bonds, profit-participation certificates (Germany/Austria, *Genussscheine*), silent participations (Germany/Austria).

like preferred equity → deduct from EV to get to common equity value. Value: for a listed hybrid, the market price; otherwise book value + accrued coupon (or redemption amount if higher and likely). Mezzanine and shareholder loans: usually treated as debt.

the IFRS classification (IAS 32 equity vs. liability) doesn't decide bridge treatment — the economics do.

Litigation reserves are handled differently depending on their accounting treatment:

• Reserved litigation (on the balance sheet): debt-like, deduct after-tax from EV.
• Unreserved but probable claims: IFRS reporters must recognize "probable" (>50%) claims and disclose only "possible" ones in the notes. In a valuation, "possible" risks belong as a sensitivity item − not in the base-case bridge.
• Large probable claims (historically, Bayer's glyphosate litigation, VW's diesel litigation, Wirecard investor claims): a concrete estimate with `probability factor × expected value × (1−t)` in the bridge.

Environmental reserves (site cleanup, decommissioning, asbestos) are debt-like and are deducted after-tax from EV. At industrials they are often significant − legacy contamination risks from historical sites (chemical sites, former gasworks, mining).

"Probable" reserves land on the balance sheet; "possible" risks appear only in the notes as contingent liabilities.

• Deduct reserved amounts × (1 − t) from EV.
• Disclosed-but-not-reserved risks as a sensitivity item.
• In capital-intensive sectors (mining, energy, old industrials), decommissioning reserves are often 5–15% of EV.

a plan with DBO (Defined Benefit Obligation) $300m, plan assets $200m, of which $50m in tax-privileged vehicles (CTA − Contractual Trust Arrangement). Net underfunding = DBO − total plan assets = 300 − 200 = $100m → after-tax at t = 30% → $70m. The CTA share: the $50m of CTA plan assets are assets dedicated to the plan and reduce the underfunding like any other plan assets; the CTA mainly changes the insolvency protection / tax privilege of the asset returns, not whether the assets cover the underfunding. Practical simplification: net underfunding (DBO − total plan assets) × (1 − t) as the standard assumption. In detailed DD: separate tax treatments for CTA vs. direct pension liability. Local specifics: unfunded direct pension promises (support funds, pension funds) − tax treatment varies.

a variable purchase-price component, dependent on post-closing performance (e.g. an EBITDA hurdle in Year 1–3). In a valuation from the buyer's perspective: treat the expected earn-out value like a debt-like item and deduct it from EV.

```
Earn-out bridge = maximum × hit probability × discount factor
```

the valuation date is fixed in the past (e.g. 31 Dec last year). The buyer takes on the EV from that date and benefits/suffers from the cash generation between the locked-box date and closing. Equity value = fixed at signing. The seller likes it (certainty). Closing accounts: working capital is measured at the closing date, and the buyer gets adjustments for deviations from 'normal NWC' (e.g. the average of the last 12 months). Equity value varies with the closing NWC. The buyer likes it (protection).

With a locked box, value 'as of the locked-box date'; with closing accounts, estimate the NWC adjustment in the bridge.

For cross-border targets (e.g. a European acquirer buying a US subsidiary), FX complications arise:

• Net debt in several currencies − convert all into the valuation currency at spot or forward rates.
• Pension liabilities often in local currency (e.g. a UK DBO (Defined Benefit Obligation) in GBP).
• The consolidated group has different currency exposures per division.
• Hedging programs: existing hedges are a 'hidden' asset/liability − mark them to market in the bridge. In practice: apply spot FX at the valuation date consistently. Forward FX for earn-outs in a foreign currency.

Visualizes valuation ranges from several methods (DCF, trading comps, precedents, LBO) as horizontal bars on an EV or equity-value axis.

No single method gives 'the' answer: triangulation shows a plausible range.

• Methods overlap → robust valuation
• Divergence → question the methods' assumptions critically

4–6 methods + a 52-week trading range for public targets.

Shows how EV or equity value responds to changes in assumptions.

WACC, terminal growth, exit multiple, margin assumptions.

Every valuation rests on uncertain assumptions — sensitivities quantify the risk.

An 'EV range of $1bn–$1.3bn' is more honest than a point estimate of $1.15bn.

Senior MDs look at the sensitivity slide first — 'what moves the value?' A structured answer signals maturity.

A range approach reflects real valuation uncertainty. A point estimate is pseudo-precision — it suggests more clarity than the methodology delivers. A range shows:

• Method differences (DCF intrinsic vs. comps market-based).
• Assumption sensitivities.
• Buyer-type differences (strategic premium vs. financial floor). Standard range: ±10–20% around the mid-point for a mature asset, ±25–40% for growth companies.

Ranges should be derived consistently within each method, not arbitrarily.

The overlap zone is the robust valuation range — the corridor where several methods land consistently. If DCF, comps, and precedents all overlap at $900–1,000m, that is a strong signal for roughly $950m as the mid-point.

Methodological differences must be explained:

• DCF higher than comps: the market is undervaluing the business (or the DCF is too optimistic).
• Precedents higher than comps: a control premium is normal.
• LBO below everything: a sponsor floor with return discipline.

WACC in columns (e.g. 8.0% / 8.5% / 9.0% / 9.5% / 10.0%), terminal growth in rows (1.5% / 2.0% / 2.5%). Each cell: EV at that combination of assumptions. The pivot value (center cell) = base case. Ranges: typically ±50bps and ±0.5% around the base.

The terminal-growth sensitivity shows the change in EV under different g assumptions. Typical range: 1.0% / 1.5% / 2.0% / 2.5% / 3.0%. The effect is non-linear — a higher g has a stronger effect, because g sits in the denominator of the Gordon growth formula.

the change in EV across the multiple range. Standard: 25th percentile / median / 75th percentile of the comp set, pivoting on the median multiple. 2D variant: add an EBITDA forecast range as a second axis to reflect forecast risk.

visualizes valuation sensitivity to several variables, ordered from high to low. Each variable appears as a horizontal bar — its length is proportional to the change in EV for a ±X% change in the variable.

• DCF: $900–1,100m (DCF with sensitivity range).
• Trading comps: $850–1,050m.
• Precedents: $950–1,250m.
• LBO floor: $750–900m.

Robust valuation range $900–1,050m (DCF, trading, and precedent overlap).

The LBO at about $800m provides downside protection.

The precedent upper end signals strategic-bid potential up to about $1,200m.

One variable in the column header (e.g. WACC: 8% / 8.5% / 9% / 9.5% / 10%), one in the row header (e.g. g: 1.5% / 2% / 2.5%). Each cell holds the calculated output variable — typically EV or equity value per share.

"Data Table" with a row input and a column input.

Heat-map coloring — lowest values red, highest green.

WACC × g (DCF), multiple × EBITDA (comps), entry multiple × exit multiple (LBO).

the Football Field skews toward higher values — multiple ranges at the upper end, precedent multiples favored, strategic-premium argumentation. Goal: justify the maximum bid. Buy-side (buyer's adviser): more conservative — median multiples, focused on trading comps, LBO floor prominent. Goal: defend a lower bid. Both sides show Football Fields, but with different range selections. IB reality: the methods are 'biased' depending on the mandate — good bankers account for this implicitly in the pitch, but also signal awareness of the opposing position.

Trading comps reflect no control premium (equity investments are minority stakes). Precedents include a control premium. The DCF value is 'standalone' — no control premium per se, but it can be extended via synergies. An LBO is acquisition pricing — control is implicit. Adjustment:

• Show trading comps + a control premium (typically 25–30%) to create comparability with precedents.
• Precedents are 'strategic bid' indicators — comparing them directly with trading comps shows the premium range.

If your DCF gives an EV of $1,000m and target EBITDA is $100m, then the DCF implies a 10x EV/EBITDA multiple. Compare with comps: if the sector median is 8x, the DCF is 'more aggressive' than the market — either your DCF has growth assumptions that are too high or the market is undervaluing the sector. Standard cross-checks:

• DCF implied EV/EBITDA vs. the trading multiple.
• DCF implied exit multiple vs. precedent multiples.
• DCF implied g vs. long-run GDP. A consistency slide in the pitch shows these bridges.

Values a diversified company segment by segment, then aggregates.

```
EV(group) = Σ EV(segments) − holding costs
```

• Conglomerates (Siemens, Henkel)
• Spinoff valuation
• Holding companies (EXOR, Berkshire)
• 'Conglomerate discount' cases

Different divisions have different risk and growth profiles — and therefore different WACCs and multiples.

SOTP often reveals 'hidden value' — activist investors use it to argue for spinoffs.

The market value of a diversified company is lower than the sum of its individual part valuations.

a 10–25% discount at conglomerates.

• Complexity → investors value it less clearly
• Capital-allocation inefficiency (divisions cross-subsidize each other)
• Management attention fragmented
• Investors want pure-play exposures

SOTP > trading valuation → activist investors push for spinoffs.

the Siemens-Healthineers spinoff, the Daimler-Truck spinoff.

Segment EBITDA must be clearly delineable — inter-segment eliminations, allocation assumptions for corporate overhead.

costs not allocated to segments (holding functions, corporate headquarters, treasury, corporate communications). Treatment:

• Pro-rata allocation: overhead × segment revenue / group revenue → reduces each segment's EBITDA.
• Separate deduction: overhead as a 'negative value' at the end of the SOTP — capitalized at a group-wide multiple (e.g. −$200m for $30m of overhead at a 6.7x multiple). IB standard: method (2), because overhead cannot be mapped one-to-one to segments.

when Segment 1 sells to Segment 2, the revenue is double-counted in the aggregate. IFRS 8 segment reporting shows sales with and without inter-segment. In an SOTP valuation: segment EBITDA margins should be based on 'external sales' — otherwise applying the segment multiples overstates the value.

non-operating value components not reflected in group EBITDA. Examples:

• Real estate portfolio (plant land carried below market value on the balance sheet).
• Tax loss carryforwards (NOLs).
• Unconsolidated holdings (e.g. JVs, equity method).
• Patents and trademark rights (often below book value).
• Future asset sales (restructuring options). Valuation: mark each component to market, add to the SOTP aggregate. In activist cases (Elliott at Bayer historically) hidden assets were the main point.

Industrial = 400 × 8 = 3,200m. Software = 80 × 15 = 1,200m. Real Estate = 600m (NAV). SOTP EV = 3,200 + 1,200 + 600 = 5,000m. Equity value = 5,000 − 700 (net debt) = 4,300m. Sanity check: total group EBITDA 480m + real estate rental income (say 50m) = 530m. Implied EV/EBITDA = 5,000 / 530 = 9.4x — a weighted blend of the segment multiples; read purely as a cross-check against a trading multiple of ~7.5x (not as a second discount figure). The conglomerate discount is defined cleanly as SOTP equity value vs. actual market cap (see pitch tip).

• Conglomerate discount >15% — material enough to act on.
• The segment is standalone-capable (its own customers, IT, management depth).
• Synergies with the group are minimal — no significant "lost economies".
• Activist pressure or investor expectations.

A spinoff creates costs that are absent in the integrated group:

• Its own corporate functions (CEO, CFO, treasury, legal, IR) — typically 0.3–0.8% of revenue.
• IT-systems duplication.
• Audit, compliance, regulatory.
• Real estate (its own HQ).