CFA Level II · CFA Level II Exam

Private Company Valuation: formula sheet

Full chapter guide

Key formulas

Fair market value: Hypothetical price between a willing buyer and a willing seller, both informed, neither under compulsion; Generic, not buyer-specific. Used often for tax and many transactions.
Investment value: Value to a specific buyer = standalone value + buyer-specific synergies (and own required return); Can be higher than fair market value. Depends on the buyer.
Fair value (financial reporting): Exit price in an orderly transaction between market participants at the measurement date; Reporting definition. Legal fair value can differ by jurisdiction.
Three purpose categories: Transactions | Compliance and reporting | Litigation; Match the situation in the vignette to one category first.
Level of value link: Purpose → standard of value → level of value and discounts; The standard chosen determines whether control or marketability adjustments apply.
Normalised earnings: Normalised earnings = Reported earnings ± adjustments for non-recurring items, owner compensation to market level, related-party items and policy differences; Adjust pre-tax, then reflect tax if the question asks for net income. Keep only recurring, business-related items.
Owner compensation adjustment: Adjustment = Owner pay actually charged − Market pay for the role; If owner is overpaid, add the excess back to earnings. If underpaid, deduct the shortfall.
Discount for lack of marketability (DLOM): Value (non-marketable) = Value (marketable) × (1 − DLOM); Applied to a marketable value of the stake. Apply it only when the base value is marketable. Do not apply it twice or to a value already reflecting illiquidity.
Discount for lack of control (DLOC): DLOC = 1 − [1 ÷ (1 + Control premium)]; Converts a control premium into the matching minority discount. Use only when moving between control and minority levels.
Control premium from a stake value: Value (controlling) = Value (minority) × (1 + Control premium); Applies when the starting value is a marketable minority value, such as from public comparables.
Combined adjustment: Value (non-marketable minority) = Marketable control value × (1 − DLOC) × (1 − DLOM); Use this form only when the base is a marketable control value being converted to a non-marketable minority value. Apply DLOC only if the base is a control value, and DLOM only if the base is marketable. If the base is already minority, apply DLOM alone. Multiply sequentially, never add the discounts.
FCFF (from net income): FCFF = NI + NCC + Int(1 − t) − FCInv − WCInv; NCC is non-cash charges. FCInv is fixed capital investment. WCInv is working capital investment.
FCFE from FCFF: FCFE = FCFF − Int(1 − t) + Net borrowing; Net borrowing = new debt issued − debt repaid.
Capitalized cash flow, firm: V(firm) = FCFF1 ÷ (WACC − g), where FCFF1 = FCFF0 × (1 + g); Valid only if WACC > g and growth is constant.
Capitalized cash flow, equity: V(equity) = FCFE1 ÷ (r − g), where FCFE1 = FCFE0 × (1 + g); r is the cost of equity. Capitalization rate = r − g.
Build-up method: r = Rf + ERP + Size premium + Company-specific premium; Implicitly assumes a beta of 1 for the market portion, since no beta term appears.
CAPM with adjustments: r = Rf + β × ERP + Size premium + Company-specific premium; Beta is usually estimated from guideline public companies and adjusted to the target's leverage.
WACC: WACC = E/(D+E) × r + D/(D+E) × Kd × (1 − t); Use target capital structure weights at market values.
Equity from firm value: Equity value = Firm value − Market value of debt; Used after discounting FCFF.
Value from a multiple (enterprise level): Enterprise value = Selected EV multiple × Subject company metric; Use EV/EBITDA, EV/EBIT or EV/Sales. Subtract net debt afterwards to get equity value.
Value from a multiple (equity level): Equity value = Selected P/E × Subject net income; Match the numerator and denominator: equity price with equity earnings.
Equity value from enterprise value: Equity value = Enterprise value − Debt + Cash (and other non-operating assets); Apply after using an EV multiple. Use the subject's own net debt.
Discount for lack of marketability applied to a value: Value after DLOM = Value × (1 − DLOM); Needed when GPCM gives a marketable value but the stake is not marketable.
Control premium and implied DLOC: Control value = Marketable minority value × (1 + Control premium); DLOC = 1 − 1 ÷ (1 + Control premium); Apply the control premium to the marketable minority equity value, not to enterprise value. Use these to move between minority and controlling values.
Level-of-value rule: GPCM: marketable minority; GTM: control; PTM: depends on the deal; State the level of value before adjusting.
Adjusted net asset value (equity value): Equity value = Fair value of assets − Fair value of liabilities; Every asset and liability is restated to fair value. Include items not on the balance sheet, such as unrecorded intangibles or contingent liabilities.
Adjustment to equity from one item: Change in equity = Fair value − Book value (for an asset); Change in equity = Book value − Fair value (for a liability); A higher asset fair value raises equity. A higher liability fair value lowers equity.
Adjusted equity from book equity: Adjusted equity = Book equity + Σ(asset fair value − book value) − Σ(liability fair value − book value); A shortcut when the vignette gives book equity and only some items change. Any item not mentioned keeps its book value.
Fit rule: Use when value comes mainly from identifiable assets, or when going-concern cash flows cannot be estimated; Typical cases: holding, real estate, natural resource, liquidating, early-stage and distressed firms.
DLOC from control premium: DLOC = 1 − [1 ÷ (1 + control premium)]; Use this to convert a control premium to the equivalent discount for lack of control.
Control premium from DLOC: Control premium = [1 ÷ (1 − DLOC)] − 1; Use this to convert a DLOC back to a premium. The premium is always larger than the DLOC.
Combined discount: Total discount = 1 − [(1 − DLOC) × (1 − DLOM)]; Discounts compound. Do not just add DLOC and DLOM. This applies when both are measured on the stated base in sequence.
Value after discounts: Value = Base value × (1 − DLOC) × (1 − DLOM); Apply each discount to the value left after the previous one.
Value with control premium: Controlling value = Minority value × (1 + control premium); The premium is applied to the marketable minority value.
Control premium from discount for lack of control: DLOC = 1 − [1 ÷ (1 + control premium)]; Use when the question gives a control premium and asks for the equivalent minority discount.
Control premium from DLOC: Control premium = [1 ÷ (1 − DLOC)] − 1; The inverse of the formula above. The premium is always larger than the discount in percentage terms.
Control to marketable minority: Marketable minority value = Control value × (1 − DLOC); Valid when DLOC is expressed as a percentage of control value.
Marketable minority to non-marketable minority: Non-marketable minority value = Marketable minority value × (1 − DLOM); DLOM is applied to the marketable minority value, not to the control value.
Chain of value: Control → (− DLOC) → Marketable minority → (− DLOM) → Non-marketable minority; Moving down the chain, apply discounts. Moving up, reverse them.
Combined discount: Total discount = 1 − [(1 − DLOC) × (1 − DLOM)]; Discounts are multiplied, not added.
Reconciled value: Final value = Σ (weight × approach value); Weights must sum to 100%, and all values must be at the same level of value first.

Quick revision

The purpose of the valuation sets the standard of value, the method and the adjustments.
Private firms need normalized earnings: remove unusual owner pay, perks and one-off items before valuing.
Income approach: use FCFF with WACC, or FCFE with cost of equity, and keep cash flow and rate consistent.
Capitalized cash flow applies a growing perpetuity: value = next-period cash flow ÷ (r − g), i.e. cash flow ÷ capitalization rate.
Market approach: guideline public company method uses multiples from similar traded firms, and the transaction method uses multiples from actual deals.
Multiples from public firms reflect a marketable, minority value, so check what the multiple implies.
The standard framework has four combinations of levels of value: controlling or non-controlling, each either marketable or non-marketable. The commonly used three-level chain, from highest to lowest, is controlling marketable > non-controlling marketable > non-controlling non-marketable.
Moving down between levels: from controlling marketable to non-controlling marketable, apply a discount for lack of control (DLOC). From non-controlling marketable to non-controlling non-marketable, apply a discount for lack of marketability (DLOM). Moving up reverses each step: remove the DLOM by dividing by (1 − DLOM), then apply a control premium by multiplying by (1 + control premium).
Asset-based approach suits asset-heavy or break-up cases, using fair values of assets less liabilities.
A discount for lack of marketability (DLOM) reduces value for poor liquidity.
A control premium raises value to reflect control, and a discount for lack of control (DLOC) reverses it.
The relation between DLOC and the control premium is DLOC = 1 − 1 ÷ (1 + control premium).
Apply adjustments in order: start from the level of value your base method produces, then move one level at a time toward the target level. Going down, apply DLOC first, then DLOM. Going up, remove DLOM first (divide by 1 − DLOM), then apply the control premium (multiply by 1 + control premium).
Combine discounts multiplicatively, not by adding: total discount = 1 − (1 − DLOC)(1 − DLOM). For example, a 20% DLOC and a 10% DLOM give 1 − 0.80 × 0.90 = 28%, not 30%.
Reconcile several value estimates by weighing them by reliability and data quality, not by a simple average.

Common mistakes

Treating fair market value and investment value as the same thing. Fix: Fair market value uses a hypothetical buyer and seller. Investment value uses one buyer's synergies and required return.
Saying a private company value is a quoted price that needs no estimate. Fix: Private firms have no observable price. The value is a model estimate that depends on the purpose.
Adding back owner pay in full instead of only the excess over market pay Fix: Add back only the amount above market pay for the role. A replacement manager would still be paid.
Removing recurring items because they look unusual Fix: Ask if it is likely to recur. Only non-recurring items are removed.
Dividing CF0 by (r − g) instead of CF1 Fix: Check the date label. Multiply by (1 + g) unless the cash flow is already next year's.
Discounting FCFF at the cost of equity or FCFE at WACC Fix: FCFF goes with WACC and gives firm value. FCFE goes with cost of equity and gives equity value.
Treating GPCM values as controlling values. Fix: Remember that trading prices reflect small, marketable minority stakes. Add a control premium if control is wanted.
Applying DLOM to a GTM value as if it were already non-marketable. Fix: Ask first what level of value the method gives. Only adjust for the difference between that level and the target level.
Using book values for some assets or liabilities that the vignette gives at fair value. Fix: Underline the fair value column before calculating. Use book value only for items with no fair value given.
Adding a liability's increase to equity instead of subtracting it. Fix: Remember liabilities reduce equity. A higher liability fair value lowers adjusted equity.

Exam tips

Start every item set by writing the purpose in the margin. Most answers depend on it.
Watch for a named buyer with synergies. That signals investment value, not fair market value.
Expect scope questions to be embedded in larger valuation vignettes, so link the standard to the later choice of discounts.
Do not guess a legal rule from reporting definitions. Choose the answer that says legal fair value depends on jurisdiction.
There is no penalty for wrong answers, so answer every question.
Read the vignette for the stake and purpose first. Most wrong answers come from using the wrong level of value.
For normalisation questions, mark each item as recurring or non-recurring and at-market or off-market before calculating.
Know the direction: overpaid owner increases adjusted earnings; underpaid owner reduces them.