PRC Appraiser cheat sheet

Value types: market value (公允价值/市场价值) assumes a willing buyer and willing seller, neither under compulsion, both reasonably informed; investment value reflects a specific owner's expectations; liquidation value assumes forced sale and is normally the lowest of the three.

The three approaches: cost approach (成本法) = replacement cost minus depreciation; income approach (收益法) = present value of expected future benefits; market approach (市场法) = pricing by reference to comparable transactions with adjustments.

Cost approach formula: 评估值 = 重置成本 − 实体性贬值 − 功能性贬值 − 经济性贬值. Depreciation here means all three forms of value loss, not accounting depreciation.

Replacement cost (重置成本) is the cost to build or acquire an equivalent new asset with current technology; reproduction cost (复原成本) rebuilds the identical asset. Use replacement cost when technology has advanced.

Obsolescence split: 实体性贬值 from wear, tear and age; 功能性贬值 from new technology or excess operating cost; 经济性贬值 from external factors (policy, market, supply) outside the asset.

Income approach core: V = Σ CFt/(1+r)^t + terminal value/(1+r)^n. Growth handled either by explicit forecast plus terminal value or by the Gordon form V = CF1/(r − g), valid only when r > g and growth is sustainable.

Discount rate = risk-free rate + risk premium(s); it must match the cash-flow definition (nominal rate with nominal cash flows, pre-tax rate with pre-tax flows, equity rate with equity flows).

Market approach: select at least three comparables, then adjust for time, location, condition, transaction terms and scale. Adjustment factors multiply the comparable price: 评估值 = 参照物价格 × 交易情况 × 交易时间 × 区域 × 个别因素.

Valuation premise (评估假设): going concern (持续经营), liquidation (清算), or 公开市场; the premise must be stated and must be consistent with the chosen approach and value type.

Machinery cost approach: 评估值 = 重置成本 × 综合成新率. 综合成新率 = 年限成新率 × 40% + 观察法成新率 × 60% is a common weighting; 年限成新率 = 尚可使用年限 ÷ (已使用年限 + 尚可使用年限).

For imported equipment, replacement cost = FOB price × exchange rate + overseas freight and insurance + import duty + consumption tax + VAT (non-deductible portion) + bank fees + domestic freight and installation + capital cost during construction.

Real property cost approach: 房地产价值 = 土地取得成本 + 开发成本 + 管理费用 + 投资利息 + 销售税费 + 开发利润 − 建筑物折旧. Land value is often derived separately by 基准地价系数修正法 or 市场法.

Real property income approach: V = a/(r − g) for a constant-growth perpetuity, or V = a/r × [1 − 1/(1+r)^n] for a finite level annuity. Net operating income = effective gross income − operating expenses (exclude depreciation, income tax and loan principal/interest).

Capitalization rate build-up: r = 无风险报酬率 + 风险调整值, or r = 安全利率 + 风险补偿. Land and building may be capitalized separately: V = L × rL/(r) ... use the weighted rate when land and building have different risks.

Market approach for real property: 比准价格 = 可比实例价格 × 交易情况修正 × 交易日期修正 × 区域因素修正 × 个别因素修正; the final value is a weighted or simple average of at least three comparables.

Highest and best use (最高最佳利用) requires legal permissibility, physical feasibility, financial feasibility and maximum productivity; it governs the choice of development assumptions.

Building depreciation in the cost approach: 年限法 (straight-line over economic life), 观察法 (component scoring), and 成新率折余法; land is not depreciated, so separate the land value before applying building depreciation.

Leasehold and encumbrance adjustments: an existing lease below market rent lowers value; the loss equals the present value of the rent differential over the remaining lease term, added back after the lease expires.

Intangible asset income approach: V = Σ (incremental cash flow attributable to the asset) / (1+r)^t. The 分成率 (royalty/relief-from-royalty) method uses V = Σ (revenue × 分成率 × (1 − tax rate)) / (1+r)^t.

Relief-from-royalty rate selection considers industry benchmark royalty rates, the asset's contribution to profit, and the license terms; the rate applies to the revenue base the asset actually drives.

Cost approach for intangibles: replacement cost of recreating the asset, often adjusted by a functional/technological obsolescence factor; weak where the asset's value lies in future earnings.

Enterprise value: EV = equity value + interest-bearing debt − cash, or equivalently the present value of FCFF discounted at WACC. Equity value = EV − net debt.

FCFF = EBIT × (1 − t) + depreciation and amortization − capital expenditure − increase in net working capital. FCFE = net income + D&A − capex − ΔNWC + net borrowing.

WACC = E/(D+E) × Re + D/(D+E) × Rd × (1 − t). Re by CAPM: Re = Rf + β × (Rm − Rf). Use target or market-value weights, not book weights.

Terminal value: Gordon growth TV = FCFF(n+1)/(WACC − g), or exit multiple TV = EBITDA(n) × multiple. g must not exceed long-run nominal GDP growth in a stable-currency economy.

Minority interest and control premium: a controlling stake commands a control premium; a minority stake may take a discount for lack of control (DLOC) and lack of marketability (DLOM). Apply DLOM after DLOC, multiplicatively.

Other assets: 长期股权投资 valued by cost, market or income approach depending on control level; 商誉 only recognized in a business combination and tested for impairment, never amortized under IFRS-style rules; 递延所得税 from temporary differences.

Time value: FV = PV(1+r)^n; PV = FV/(1+r)^n; annuity PV = A × [1 − (1+r)^−n]/r; perpetuity PV = A/r. Effective annual rate = (1 + r/m)^m − 1.

Capital budgeting: NPV = Σ CFt/(1+r)^t − initial outlay; accept if NPV > 0. IRR is the rate making NPV = 0. Profitability index = PV of inflows / initial outlay. NPV and IRR agree unless cash-flow signs change more than once.

Leverage: DOL = contribution margin / EBIT; DFL = EBIT / (EBIT − interest); DTL = DOL × DFL. Break-even quantity = fixed costs / (price − variable cost per unit).

Working capital: current ratio = current assets / current liabilities; quick ratio excludes inventory. Cash conversion cycle = inventory days + receivable days − payable days.

DuPont: ROE = net profit margin × total asset turnover × equity multiplier. A rising ROE from leverage alone signals higher financial risk, not better operations.

Cost of capital: after-tax cost of debt = Rd(1 − t); cost of equity by CAPM or by the dividend growth model Re = D1/P0 + g. Marginal WACC is used for new projects, not historical average cost.

Contract law basics: an offer plus acceptance forms a contract; 要约 vs 要约邀请 (invitation to treat); a contract is void (无效) for illegality or lack of capacity, voidable (可撤销) for fraud, duress or material misunderstanding.

Company law: shareholders' liability is limited to subscribed capital; a shareholder who abuses the independent legal personality to evade debts may be held jointly liable (揭开公司面纱). Capital contributions must not be withdrawn.

Tax and securities rules: VAT is a turnover tax with input credit; enterprise income tax is 25% standard; goodwill impairment is not tax-deductible until realized. Insider information and false statements trigger administrative and criminal liability.

Accounting equation: Assets = Liabilities + Owners' equity. Double entry keeps it balanced; every transaction affects at least two accounts.

Accrual basis: revenue recognized when earned, expenses when incurred, regardless of cash timing. Cash basis is used for cash-flow statements only.

Measurement attributes: historical cost, replacement cost, net realizable value, present value, fair value. Fair value is an exit price in an orderly transaction between market participants at the measurement date.

Depreciation methods: straight-line = (cost − residual)/useful life; double-declining = 2/life × carrying amount; units-of-production = (cost − residual) × units used / total units.

Inventory: lower of cost and net realizable value. Cost includes purchase price, duties, freight and attributable conversion costs; NRV = estimated selling price − completion and selling costs.

Revenue recognition (five steps): identify the contract; identify performance obligations; determine transaction price; allocate the price to obligations; recognize revenue when each obligation is satisfied.

Impairment: carrying amount compared with recoverable amount (higher of fair value less costs of disposal and value in use); the write-down goes to profit or loss and is not reversed for goodwill.

Financial statements link: net income flows to retained earnings; ending retained earnings = opening + net income − dividends. Cash-flow statement reconciles operating, investing and financing activities.

Value types: market value assumes willing, informed parties without compulsion; investment value reflects a specific owner's expectations; liquidation value assumes forced sale and is normally the lowest.

Three approaches: cost approach = replacement cost minus depreciation; income approach = present value of expected benefits; market approach = comparable transactions with adjustments.

Cost approach: 评估值 = 重置成本 − 实体性贬值 − 功能性贬值 − 经济性贬值. Depreciation means all three forms of economic value loss, not accounting depreciation.

Replacement cost rebuilds an equivalent new asset with current technology; reproduction cost rebuilds the identical asset. Use replacement cost when technology has advanced.

Obsolescence: physical from wear and age; functional from new technology or excess operating cost; economic from external factors such as policy, market or supply changes.

Income approach: V = Σ CFt/(1+r)^t + terminal/(1+r)^n, or Gordon form V = CF1/(r − g), valid only when r > g and growth is sustainable.

Discount rate = risk-free rate + risk premiums; it must match the cash-flow definition (nominal with nominal, pre-tax with pre-tax, equity rate with equity flows).

Market approach: use at least three comparables and adjust for time, location, condition, transaction terms and scale; 评估值 = 参照物价格 × 交易情况 × 交易时间 × 区域 × 个别因素.

Valuation premise (评估假设): going concern, liquidation or open market; it must be stated and consistent with the chosen approach and value type.

Machinery: 评估值 = 重置成本 × 综合成新率. 年限成新率 = 尚可使用年限 ÷ (已使用年限 + 尚可使用年限). Composite rates often weight age-based and observation-based scores.

Imported equipment replacement cost = FOB × exchange rate + overseas freight and insurance + customs duty + consumption tax + non-deductible VAT + bank charges + domestic freight and installation + capital cost during construction.

Real property cost approach: value = land acquisition cost + development cost + management fee + investment interest + sales taxes + developer profit − building depreciation. Land is not depreciated.

Real property income approach: V = a/(r − g) for a growth perpetuity; V = a/r × [1 − (1+r)^−n] for a finite level annuity. NOI excludes depreciation, income tax and loan principal/interest.

Capitalization rate build-up: r = 无风险报酬率 + 风险调整值, or safe rate plus risk compensation; use a weighted rate when land and building carry different risks.

Market approach: 比准价格 = 可比实例价格 × 交易情况 × 交易日期 × 区域因素 × 个别因素修正; final value is a weighted or simple average of at least three comparables.

Highest and best use (最高最佳利用) requires legal permissibility, physical feasibility, financial feasibility and maximum productivity; it governs development assumptions.

Building depreciation by 年限法 (straight line over economic life), 观察法 (component scoring) or 成新率折余法; separate land value before applying building depreciation.

Below-market leases reduce value by the present value of the rent differential over the remaining lease term; add back the market-rent value after the lease expires.

Intangible income approach: V = Σ incremental cash flow attributable to the asset / (1+r)^t. Relief-from-royalty: V = Σ revenue × 分成率 × (1 − tax rate) / (1+r)^t.

Royalty rate selection considers industry benchmark rates, the asset's contribution to profit and license terms; apply the rate to the revenue base the asset actually drives.

Cost approach for intangibles: replacement cost of recreating the asset with an obsolescence adjustment; weak where value lies in future earnings rather than cost.

Enterprise value: EV = equity value + interest-bearing debt − cash, equal to the present value of FCFF discounted at WACC. Equity value = EV − net debt.

FCFF = EBIT × (1 − t) + D&A − capex − ΔNWC. FCFE = net income + D&A − capex − ΔNWC + net borrowing.

WACC = E/(D+E) × Re + D/(D+E) × Rd × (1 − t); Re = Rf + β(Rm − Rf). Use target or market-value weights, not book weights.

Terminal value: Gordon TV = FCFF(n+1)/(WACC − g), or exit multiple TV = EBITDA(n) × multiple. g should not exceed long-run nominal GDP growth in a stable-currency economy.

Control and marketability: a controlling stake commands a control premium; a minority stake may take a lack-of-control discount (DLOC) and lack-of-marketability discount (DLOM), applied multiplicatively.

Other assets: long-term equity investments by cost, market or income approach depending on control; goodwill only from a business combination and tested for impairment, not amortized; deferred tax from temporary differences.

Time value: FV = PV(1+r)^n; PV = FV/(1+r)^n; annuity PV = A × [1 − (1+r)^−n]/r; perpetuity PV = A/r. Effective annual rate = (1 + r/m)^m − 1.

Capital budgeting: NPV = Σ CFt/(1+r)^t − outlay, accept if positive. IRR sets NPV to zero. Profitability index = PV inflows / outlay. NPV and IRR agree unless cash-flow signs change more than once.

Leverage: DOL = contribution margin / EBIT; DFL = EBIT/(EBIT − interest); DTL = DOL × DFL. Break-even quantity = fixed costs / (price − variable cost per unit).

Working capital: current ratio = current assets / current liabilities; quick ratio excludes inventory; cash conversion cycle = inventory days + receivable days − payable days.

DuPont: ROE = net profit margin × total asset turnover × equity multiplier. Rising ROE from leverage alone signals higher financial risk, not better operations.

Cost of capital: after-tax cost of debt = Rd(1 − t); cost of equity by CAPM or Re = D1/P0 + g. Use marginal WACC for new projects, not historical average cost.

Contract law: offer plus acceptance forms a contract; 要约 vs 要约邀请 (invitation to treat); a contract is void for illegality or incapacity and voidable for fraud, duress or material misunderstanding.

Company law: shareholders' liability is limited to subscribed capital; abuse of independent legal personality to evade debts can trigger joint liability (揭开公司面纱); capital contributions must not be withdrawn.

Tax and securities: VAT is a turnover tax with input credit; standard enterprise income tax rate is 25%; goodwill impairment is not tax-deductible until realized; insider trading and false statements carry administrative and criminal liability.

Accounting equation: Assets = Liabilities + Owners' equity. Double entry keeps it balanced; every transaction affects at least two accounts.

Accrual basis: revenue recognized when earned, expenses when incurred, regardless of cash timing; the cash-flow statement alone uses cash timing.

Measurement attributes: historical cost, replacement cost, net realizable value, present value and fair value. Fair value is an exit price in an orderly transaction between market participants at the measurement date.

Depreciation: straight-line = (cost − residual)/useful life; double-declining = 2/life × carrying amount; units-of-production = (cost − residual) × units used / total units.

Inventory: lower of cost and net realizable value. Cost includes purchase price, duties, freight and attributable conversion costs; NRV = estimated selling price − completion and selling costs.

Revenue recognition (five steps): identify the contract; identify performance obligations; determine transaction price; allocate the price; recognize revenue when each obligation is satisfied.

Impairment: compare carrying amount with recoverable amount (higher of fair value less costs of disposal and value in use); the write-down goes to profit or loss and is not reversed for goodwill.

Financial statement links: net income flows to retained earnings; ending retained earnings = opening + net income − dividends; the cash-flow statement reconciles operating, investing and financing activities.

Value types: market value assumes willing, informed parties without compulsion; investment value reflects a specific owner's expectations; liquidation value assumes forced sale and is normally the lowest.

Three approaches: cost approach = replacement cost minus depreciation; income approach = present value of expected benefits; market approach = comparable transactions with adjustments.

Cost approach: 评估值 = 重置成本 − 实体性贬值 − 功能性贬值 − 经济性贬值. Depreciation means all three forms of economic value loss, not accounting depreciation.

Replacement cost rebuilds an equivalent new asset with current technology; reproduction cost rebuilds the identical asset. Use replacement cost when technology has advanced.

Obsolescence: physical from wear and age; functional from new technology or excess operating cost; economic from external factors such as policy, market or supply changes.

Income approach: V = Σ CFt/(1+r)^t + terminal/(1+r)^n, or Gordon form V = CF1/(r − g), valid only when r > g and growth is sustainable.

Discount rate = risk-free rate + risk premiums; it must match the cash-flow definition (nominal with nominal, pre-tax with pre-tax, equity rate with equity flows).

Market approach: use at least three comparables and adjust for time, location, condition, transaction terms and scale; 评估值 = 参照物价格 × 交易情况 × 交易时间 × 区域 × 个别因素.

Valuation premise (评估假设): going concern, liquidation or open market; it must be stated and consistent with the chosen approach and value type.

Machinery: 评估值 = 重置成本 × 综合成新率. 年限成新率 = 尚可使用年限 ÷ (已使用年限 + 尚可使用年限). Composite rates often weight age-based and observation-based scores.

Imported equipment replacement cost = FOB × exchange rate + overseas freight and insurance + customs duty + consumption tax + non-deductible VAT + bank charges + domestic freight and installation + capital cost during construction.

Real property cost approach: value = land acquisition cost + development cost + management fee + investment interest + sales taxes + developer profit − building depreciation. Land is not depreciated.

Real property income approach: V = a/(r − g) for a growth perpetuity; V = a/r × [1 − (1+r)^−n] for a finite level annuity. NOI excludes depreciation, income tax and loan principal/interest.

Capitalization rate build-up: r = 无风险报酬率 + 风险调整值, or safe rate plus risk compensation; use a weighted rate when land and building carry different risks.

Market approach: 比准价格 = 可比实例价格 × 交易情况 × 交易日期 × 区域因素 × 个别因素修正; final value is a weighted or simple average of at least three comparables.

Highest and best use (最高最佳利用) requires legal permissibility, physical feasibility, financial feasibility and maximum productivity; it governs development assumptions.

Building depreciation by 年限法 (straight line over economic life), 观察法 (component scoring) or 成新率折余法; separate land value before applying building depreciation.

Below-market leases reduce value by the present value of the rent differential over the remaining lease term; add back the market-rent value after the lease expires.

Intangible income approach: V = Σ incremental cash flow attributable to the asset / (1+r)^t. Relief-from-royalty: V = Σ revenue × 分成率 × (1 − tax rate) / (1+r)^t.

Royalty rate selection considers industry benchmark rates, the asset's contribution to profit and license terms; apply the rate to the revenue base the asset actually drives.

Cost approach for intangibles: replacement cost of recreating the asset with an obsolescence adjustment; weak where value lies in future earnings rather than cost.

Enterprise value: EV = equity value + interest-bearing debt − cash, equal to the present value of FCFF discounted at WACC. Equity value = EV − net debt.

FCFF = EBIT × (1 − t) + D&A − capex − ΔNWC. FCFE = net income + D&A − capex − ΔNWC + net borrowing.

WACC = E/(D+E) × Re + D/(D+E) × Rd × (1 − t); Re = Rf + β(Rm − Rf). Use target or market-value weights, not book weights.

Terminal value: Gordon TV = FCFF(n+1)/(WACC − g), or exit multiple TV = EBITDA(n) × multiple. g should not exceed long-run nominal GDP growth in a stable-currency economy.

Control and marketability: a controlling stake commands a control premium; a minority stake may take a lack-of-control discount (DLOC) and lack-of-marketability discount (DLOM), applied multiplicatively.

Other assets: long-term equity investments by cost, market or income approach depending on control; goodwill only from a business combination and tested for impairment, not amortized; deferred tax from temporary differences.

Time value: FV = PV(1+r)^n; PV = FV/(1+r)^n; annuity PV = A × [1 − (1+r)^−n]/r; perpetuity PV = A/r. Effective annual rate = (1 + r/m)^m − 1.

Capital budgeting: NPV = Σ CFt/(1+r)^t − outlay, accept if positive. IRR sets NPV to zero. Profitability index = PV inflows / outlay. NPV and IRR agree unless cash-flow signs change more than once.

Leverage: DOL = contribution margin / EBIT; DFL = EBIT/(EBIT − interest); DTL = DOL × DFL. Break-even quantity = fixed costs / (price − variable cost per unit).

Working capital: current ratio = current assets / current liabilities; quick ratio excludes inventory; cash conversion cycle = inventory days + receivable days − payable days.

DuPont: ROE = net profit margin × total asset turnover × equity multiplier. Rising ROE from leverage alone signals higher financial risk, not better operations.

Cost of capital: after-tax cost of debt = Rd(1 − t); cost of equity by CAPM or Re = D1/P0 + g. Use marginal WACC for new projects, not historical average cost.

Contract law: offer plus acceptance forms a contract; 要约 vs 要约邀请 (invitation to treat); a contract is void for illegality or incapacity and voidable for fraud, duress or material misunderstanding.

Company law: shareholders' liability is limited to subscribed capital; abuse of independent legal personality to evade debts can trigger joint liability (揭开公司面纱); capital contributions must not be withdrawn.

Tax and securities: VAT is a turnover tax with input credit; standard enterprise income tax rate is 25%; goodwill impairment is not tax-deductible until realized; insider trading and false statements carry administrative and criminal liability.

Accounting equation: Assets = Liabilities + Owners' equity. Double entry keeps it balanced; every transaction affects at least two accounts.

Accrual basis: revenue recognized when earned, expenses when incurred, regardless of cash timing; the cash-flow statement alone uses cash timing.

Measurement attributes: historical cost, replacement cost, net realizable value, present value and fair value. Fair value is an exit price in an orderly transaction between market participants at the measurement date.

Depreciation: straight-line = (cost − residual)/useful life; double-declining = 2/life × carrying amount; units-of-production = (cost − residual) × units used / total units.

Inventory: lower of cost and net realizable value. Cost includes purchase price, duties, freight and attributable conversion costs; NRV = estimated selling price − completion and selling costs.

Revenue recognition (five steps): identify the contract; identify performance obligations; determine transaction price; allocate the price; recognize revenue when each obligation is satisfied.

Impairment: compare carrying amount with recoverable amount (higher of fair value less costs of disposal and value in use); the write-down goes to profit or loss and is not reversed for goodwill.

Financial statement links: net income flows to retained earnings; ending retained earnings = opening + net income − dividends; the cash-flow statement reconciles operating, investing and financing activities.

Value types: market value assumes willing, informed parties without compulsion; investment value reflects a specific owner's expectations; liquidation value assumes forced sale and is normally the lowest.

Three approaches: cost approach = replacement cost minus depreciation; income approach = present value of expected benefits; market approach = comparable transactions with adjustments.

Cost approach: 评估值 = 重置成本 − 实体性贬值 − 功能性贬值 − 经济性贬值. Depreciation means all three forms of economic value loss, not accounting depreciation.

Replacement cost rebuilds an equivalent new asset with current technology; reproduction cost rebuilds the identical asset. Use replacement cost when technology has advanced.

Obsolescence: physical from wear and age; functional from new technology or excess operating cost; economic from external factors such as policy, market or supply changes.

Income approach: V = Σ CFt/(1+r)^t + terminal/(1+r)^n, or Gordon form V = CF1/(r − g), valid only when r > g and growth is sustainable.

Discount rate = risk-free rate + risk premiums; it must match the cash-flow definition (nominal with nominal, pre-tax with pre-tax, equity rate with equity flows).

Market approach: use at least three comparables and adjust for time, location, condition, transaction terms and scale; 评估值 = 参照物价格 × 交易情况 × 交易时间 × 区域 × 个别因素.

Valuation premise (评估假设): going concern, liquidation or open market; it must be stated and consistent with the chosen approach and value type.

Machinery: 评估值 = 重置成本 × 综合成新率. 年限成新率 = 尚可使用年限 ÷ (已使用年限 + 尚可使用年限). Composite rates often weight age-based and observation-based scores.

Imported equipment replacement cost = FOB × exchange rate + overseas freight and insurance + customs duty + consumption tax + non-deductible VAT + bank charges + domestic freight and installation + capital cost during construction.

Real property cost approach: value = land acquisition cost + development cost + management fee + investment interest + sales taxes + developer profit − building depreciation. Land is not depreciated.

Real property income approach: V = a/(r − g) for a growth perpetuity; V = a/r × [1 − (1+r)^−n] for a finite level annuity. NOI excludes depreciation, income tax and loan principal/interest.

Capitalization rate build-up: r = 无风险报酬率 + 风险调整值, or safe rate plus risk compensation; use a weighted rate when land and building carry different risks.

Market approach: 比准价格 = 可比实例价格 × 交易情况 × 交易日期 × 区域因素 × 个别因素修正; final value is a weighted or simple average of at least three comparables.

Highest and best use (最高最佳利用) requires legal permissibility, physical feasibility, financial feasibility and maximum productivity; it governs development assumptions.

Building depreciation by 年限法 (straight line over economic life), 观察法 (component scoring) or 成新率折余法; separate land value before applying building depreciation.

Below-market leases reduce value by the present value of the rent differential over the remaining lease term; add back the market-rent value after the lease expires.

Intangible income approach: V = Σ incremental cash flow attributable to the asset / (1+r)^t. Relief-from-royalty: V = Σ revenue × 分成率 × (1 − tax rate) / (1+r)^t.

Royalty rate selection considers industry benchmark rates, the asset's contribution to profit and license terms; apply the rate to the revenue base the asset actually drives.

Cost approach for intangibles: replacement cost of recreating the asset with an obsolescence adjustment; weak where value lies in future earnings rather than cost.

Enterprise value: EV = equity value + interest-bearing debt − cash, equal to the present value of FCFF discounted at WACC. Equity value = EV − net debt.

FCFF = EBIT × (1 − t) + D&A − capex − ΔNWC. FCFE = net income + D&A − capex − ΔNWC + net borrowing.

WACC = E/(D+E) × Re + D/(D+E) × Rd × (1 − t); Re = Rf + β(Rm − Rf). Use target or market-value weights, not book weights.

Terminal value: Gordon TV = FCFF(n+1)/(WACC − g), or exit multiple TV = EBITDA(n) × multiple. g should not exceed long-run nominal GDP growth in a stable-currency economy.

Control and marketability: a controlling stake commands a control premium; a minority stake may take a lack-of-control discount (DLOC) and lack-of-marketability discount (DLOM), applied multiplicatively.

Other assets: long-term equity investments by cost, market or income approach depending on control; goodwill only from a business combination and tested for impairment, not amortized; deferred tax from temporary differences.

Time value: FV = PV(1+r)^n; PV = FV/(1+r)^n; annuity PV = A × [1 − (1+r)^−n]/r; perpetuity PV = A/r. Effective annual rate = (1 + r/m)^m − 1.

Capital budgeting: NPV = Σ CFt/(1+r)^t − outlay, accept if positive. IRR sets NPV to zero. Profitability index = PV inflows / outlay. NPV and IRR agree unless cash-flow signs change more than once.

Leverage: DOL = contribution margin / EBIT; DFL = EBIT/(EBIT − interest); DTL = DOL × DFL. Break-even quantity = fixed costs / (price − variable cost per unit).

Working capital: current ratio = current assets / current liabilities; quick ratio excludes inventory; cash conversion cycle = inventory days + receivable days − payable days.

DuPont: ROE = net profit margin × total asset turnover × equity multiplier. Rising ROE from leverage alone signals higher financial risk, not better operations.

Cost of capital: after-tax cost of debt = Rd(1 − t); cost of equity by CAPM or Re = D1/P0 + g. Use marginal WACC for new projects, not historical average cost.

Contract law: offer plus acceptance forms a contract; 要约 vs 要约邀请 (invitation to treat); a contract is void for illegality or incapacity and voidable for fraud, duress or material misunderstanding.

Company law: shareholders' liability is limited to subscribed capital; abuse of independent legal personality to evade debts can trigger joint liability (揭开公司面纱); capital contributions must not be withdrawn.

Tax and securities: VAT is a turnover tax with input credit; standard enterprise income tax rate is 25%; goodwill impairment is not tax-deductible until realized; insider trading and false statements carry administrative and criminal liability.

Accounting equation: Assets = Liabilities + Owners' equity. Double entry keeps it balanced; every transaction affects at least two accounts.

Accrual basis: revenue recognized when earned, expenses when incurred, regardless of cash timing; the cash-flow statement alone uses cash timing.

Measurement attributes: historical cost, replacement cost, net realizable value, present value and fair value. Fair value is an exit price in an orderly transaction between market participants at the measurement date.

Depreciation: straight-line = (cost − residual)/useful life; double-declining = 2/life × carrying amount; units-of-production = (cost − residual) × units used / total units.

Inventory: lower of cost and net realizable value. Cost includes purchase price, duties, freight and attributable conversion costs; NRV = estimated selling price − completion and selling costs.

Revenue recognition (five steps): identify the contract; identify performance obligations; determine transaction price; allocate the price; recognize revenue when each obligation is satisfied.

Impairment: compare carrying amount with recoverable amount (higher of fair value less costs of disposal and value in use); the write-down goes to profit or loss and is not reversed for goodwill.

Financial statement links: net income flows to retained earnings; ending retained earnings = opening + net income − dividends; the cash-flow statement reconciles operating, investing and financing activities.

Value types: market value assumes willing, informed parties without compulsion; investment value reflects a specific owner's expectations; liquidation value assumes forced sale and is normally the lowest.

Three approaches: cost approach = replacement cost minus depreciation; income approach = present value of expected benefits; market approach = comparable transactions with adjustments.

Cost approach: 评估值 = 重置成本 − 实体性贬值 − 功能性贬值 − 经济性贬值. Depreciation means all three forms of economic value loss, not accounting depreciation.

Replacement cost rebuilds an equivalent new asset with current technology; reproduction cost rebuilds the identical asset. Use replacement cost when technology has advanced.

Obsolescence: physical from wear and age; functional from new technology or excess operating cost; economic from external factors such as policy, market or supply changes.

Income approach: V = Σ CFt/(1+r)^t + terminal/(1+r)^n, or Gordon form V = CF1/(r − g), valid only when r > g and growth is sustainable.

Discount rate = risk-free rate + risk premiums; it must match the cash-flow definition (nominal with nominal, pre-tax with pre-tax, equity rate with equity flows).

Market approach: use at least three comparables and adjust for time, location, condition, transaction terms and scale; 评估值 = 参照物价格 × 交易情况 × 交易时间 × 区域 × 个别因素.

Valuation premise (评估假设): going concern, liquidation or open market; it must be stated and consistent with the chosen approach and value type.

Machinery: 评估值 = 重置成本 × 综合成新率. 年限成新率 = 尚可使用年限 ÷ (已使用年限 + 尚可使用年限). Composite rates often weight age-based and observation-based scores.

Imported equipment replacement cost = FOB × exchange rate + overseas freight and insurance + customs duty + consumption tax + non-deductible VAT + bank charges + domestic freight and installation + capital cost during construction.

Real property cost approach: value = land acquisition cost + development cost + management fee + investment interest + sales taxes + developer profit − building depreciation. Land is not depreciated.

Real property income approach: V = a/(r − g) for a growth perpetuity; V = a/r × [1 − (1+r)^−n] for a finite level annuity. NOI excludes depreciation, income tax and loan principal/interest.

Capitalization rate build-up: r = 无风险报酬率 + 风险调整值, or safe rate plus risk compensation; use a weighted rate when land and building carry different risks.

Market approach: 比准价格 = 可比实例价格 × 交易情况 × 交易日期 × 区域因素 × 个别因素修正; final value is a weighted or simple average of at least three comparables.

Highest and best use (最高最佳利用) requires legal permissibility, physical feasibility, financial feasibility and maximum productivity; it governs development assumptions.

Building depreciation by 年限法 (straight line over economic life), 观察法 (component scoring) or 成新率折余法; separate land value before applying building depreciation.

Below-market leases reduce value by the present value of the rent differential over the remaining lease term; add back the market-rent value after the lease expires.

Intangible income approach: V = Σ incremental cash flow attributable to the asset / (1+r)^t. Relief-from-royalty: V = Σ revenue × 分成率 × (1 − tax rate) / (1+r)^t.

Royalty rate selection considers industry benchmark rates, the asset's contribution to profit and license terms; apply the rate to the revenue base the asset actually drives.

Cost approach for intangibles: replacement cost of recreating the asset with an obsolescence adjustment; weak where value lies in future earnings rather than cost.

Enterprise value: EV = equity value + interest-bearing debt − cash, equal to the present value of FCFF discounted at WACC. Equity value = EV − net debt.

FCFF = EBIT × (1 − t) + D&A − capex − ΔNWC. FCFE = net income + D&A − capex − ΔNWC + net borrowing.

WACC = E/(D+E) × Re + D/(D+E) × Rd × (1 − t); Re = Rf + β(Rm − Rf). Use target or market-value weights, not book weights.

Terminal value: Gordon TV = FCFF(n+1)/(WACC − g), or exit multiple TV = EBITDA(n) × multiple. g should not exceed long-run nominal GDP growth in a stable-currency economy.

Control and marketability: a controlling stake commands a control premium; a minority stake may take a lack-of-control discount (DLOC) and lack-of-marketability discount (DLOM), applied multiplicatively.

Other assets: long-term equity investments by cost, market or income approach depending on control; goodwill only from a business combination and tested for impairment, not amortized; deferred tax from temporary differences.

Time value: FV = PV(1+r)^n; PV = FV/(1+r)^n; annuity PV = A × [1 − (1+r)^−n]/r; perpetuity PV = A/r. Effective annual rate = (1 + r/m)^m − 1.

Capital budgeting: NPV = Σ CFt/(1+r)^t − outlay, accept if positive. IRR sets NPV to zero. Profitability index = PV inflows / outlay. NPV and IRR agree unless cash-flow signs change more than once.

Leverage: DOL = contribution margin / EBIT; DFL = EBIT/(EBIT − interest); DTL = DOL × DFL. Break-even quantity = fixed costs / (price − variable cost per unit).

Working capital: current ratio = current assets / current liabilities; quick ratio excludes inventory; cash conversion cycle = inventory days + receivable days − payable days.

DuPont: ROE = net profit margin × total asset turnover × equity multiplier. Rising ROE from leverage alone signals higher financial risk, not better operations.

Cost of capital: after-tax cost of debt = Rd(1 − t); cost of equity by CAPM or Re = D1/P0 + g. Use marginal WACC for new projects, not historical average cost.

Contract law: offer plus acceptance forms a contract; 要约 vs 要约邀请 (invitation to treat); a contract is void for illegality or incapacity and voidable for fraud, duress or material misunderstanding.

Company law: shareholders' liability is limited to subscribed capital; abuse of independent legal personality to evade debts can trigger joint liability (揭开公司面纱); capital contributions must not be withdrawn.

Tax and securities: VAT is a turnover tax with input credit; standard enterprise income tax rate is 25%; goodwill impairment is not tax-deductible until realized; insider trading and false statements carry administrative and criminal liability.

Accounting equation: Assets = Liabilities + Owners' equity. Double entry keeps it balanced; every transaction affects at least two accounts.

Accrual basis: revenue recognized when earned, expenses when incurred, regardless of cash timing; the cash-flow statement alone uses cash timing.

Measurement attributes: historical cost, replacement cost, net realizable value, present value and fair value. Fair value is an exit price in an orderly transaction between market participants at the measurement date.

Depreciation: straight-line = (cost − residual)/useful life; double-declining = 2/life × carrying amount; units-of-production = (cost − residual) × units used / total units.

Inventory: lower of cost and net realizable value. Cost includes purchase price, duties, freight and attributable conversion costs; NRV = estimated selling price − completion and selling costs.

Revenue recognition (five steps): identify the contract; identify performance obligations; determine transaction price; allocate the price; recognize revenue when each obligation is satisfied.

Impairment: compare carrying amount with recoverable amount (higher of fair value less costs of disposal and value in use); the write-down goes to profit or loss and is not reversed for goodwill.

Financial statement links: net income flows to retained earnings; ending retained earnings = opening + net income − dividends; the cash-flow statement reconciles operating, investing and financing activities.

Value types: market value assumes willing, informed parties without compulsion; investment value reflects a specific owner's expectations; liquidation value assumes forced sale and is normally the lowest.

Three approaches: cost approach = replacement cost minus depreciation; income approach = present value of expected benefits; market approach = comparable transactions with adjustments.

Cost approach: 评估值 = 重置成本 − 实体性贬值 − 功能性贬值 − 经济性贬值. Depreciation means all three forms of economic value loss, not accounting depreciation.

Replacement cost rebuilds an equivalent new asset with current technology; reproduction cost rebuilds the identical asset. Use replacement cost when technology has advanced.

Obsolescence: physical from wear and age; functional from new technology or excess operating cost; economic from external factors such as policy, market or supply changes.

Income approach: V = Σ CFt/(1+r)^t + terminal/(1+r)^n, or Gordon form V = CF1/(r − g), valid only when r > g and growth is sustainable.

Discount rate = risk-free rate + risk premiums; it must match the cash-flow definition (nominal with nominal, pre-tax with pre-tax, equity rate with equity flows).

Market approach: use at least three comparables and adjust for time, location, condition, transaction terms and scale; 评估值 = 参照物价格 × 交易情况 × 交易时间 × 区域 × 个别因素.

Valuation premise (评估假设): going concern, liquidation or open market; it must be stated and consistent with the chosen approach and value type.

Machinery: 评估值 = 重置成本 × 综合成新率. 年限成新率 = 尚可使用年限 ÷ (已使用年限 + 尚可使用年限). Composite rates often weight age-based and observation-based scores.

Imported equipment replacement cost = FOB × exchange rate + overseas freight and insurance + customs duty + consumption tax + non-deductible VAT + bank charges + domestic freight and installation + capital cost during construction.

Real property cost approach: value = land acquisition cost + development cost + management fee + investment interest + sales taxes + developer profit − building depreciation. Land is not depreciated.

Real property income approach: V = a/(r − g) for a growth perpetuity; V = a/r × [1 − (1+r)^−n] for a finite level annuity. NOI excludes depreciation, income tax and loan principal/interest.

Capitalization rate build-up: r = 无风险报酬率 + 风险调整值, or safe rate plus risk compensation; use a weighted rate when land and building carry different risks.

Market approach: 比准价格 = 可比实例价格 × 交易情况 × 交易日期 × 区域因素 × 个别因素修正; final value is a weighted or simple average of at least three comparables.

Highest and best use (最高最佳利用) requires legal permissibility, physical feasibility, financial feasibility and maximum productivity; it governs development assumptions.

Building depreciation by 年限法 (straight line over economic life), 观察法 (component scoring) or 成新率折余法; separate land value before applying building depreciation.

Below-market leases reduce value by the present value of the rent differential over the remaining lease term; add back the market-rent value after the lease expires.

Intangible income approach: V = Σ incremental cash flow attributable to the asset / (1+r)^t. Relief-from-royalty: V = Σ revenue × 分成率 × (1 − tax rate) / (1+r)^t.

Royalty rate selection considers industry benchmark rates, the asset's contribution to profit and license terms; apply the rate to the revenue base the asset actually drives.

Cost approach for intangibles: replacement cost of recreating the asset with an obsolescence adjustment; weak where value lies in future earnings rather than cost.

Enterprise value: EV = equity value + interest-bearing debt − cash, equal to the present value of FCFF discounted at WACC. Equity value = EV − net debt.

FCFF = EBIT × (1 − t) + D&A − capex − ΔNWC. FCFE = net income + D&A − capex − ΔNWC + net borrowing.

WACC = E/(D+E) × Re + D/(D+E) × Rd × (1 − t); Re = Rf + β(Rm − Rf). Use target or market-value weights, not book weights.

Terminal value: Gordon TV = FCFF(n+1)/(WACC − g), or exit multiple TV = EBITDA(n) × multiple. g should not exceed long-run nominal GDP growth in a stable-currency economy.

Control and marketability: a controlling stake commands a control premium; a minority stake may take a lack-of-control discount (DLOC) and lack-of-marketability discount (DLOM), applied multiplicatively.

Other assets: long-term equity investments by cost, market or income approach depending on control; goodwill only from a business combination and tested for impairment, not amortized; deferred tax from temporary differences.

Time value: FV = PV(1+r)^n; PV = FV/(1+r)^n; annuity PV = A × [1 − (1+r)^−n]/r; perpetuity PV = A/r. Effective annual rate = (1 + r/m)^m − 1.

Capital budgeting: NPV = Σ CFt/(1+r)^t − outlay, accept if positive. IRR sets NPV to zero. Profitability index = PV inflows / outlay. NPV and IRR agree unless cash-flow signs change more than once.

Leverage: DOL = contribution margin / EBIT; DFL = EBIT/(EBIT − interest); DTL = DOL × DFL. Break-even quantity = fixed costs / (price − variable cost per unit).

Working capital: current ratio = current assets / current liabilities; quick ratio excludes inventory; cash conversion cycle = inventory days + receivable days − payable days.

DuPont: ROE = net profit margin × total asset turnover × equity multiplier. Rising ROE from leverage alone signals higher financial risk, not better operations.

Cost of capital: after-tax cost of debt = Rd(1 − t); cost of equity by CAPM or Re = D1/P0 + g. Use marginal WACC for new projects, not historical average cost.

Contract law: offer plus acceptance forms a contract; 要约 vs 要约邀请 (invitation to treat); a contract is void for illegality or incapacity and voidable for fraud, duress or material misunderstanding.

Company law: shareholders' liability is limited to subscribed capital; abuse of independent legal personality to evade debts can trigger joint liability (揭开公司面纱); capital contributions must not be withdrawn.

Tax and securities: VAT is a turnover tax with input credit; standard enterprise income tax rate is 25%; goodwill impairment is not tax-deductible until realized; insider trading and false statements carry administrative and criminal liability.

Accounting equation: Assets = Liabilities + Owners' equity. Double entry keeps it balanced; every transaction affects at least two accounts.

Accrual basis: revenue recognized when earned, expenses when incurred, regardless of cash timing; the cash-flow statement alone uses cash timing.

Measurement attributes: historical cost, replacement cost, net realizable value, present value and fair value. Fair value is an exit price in an orderly transaction between market participants at the measurement date.

Depreciation: straight-line = (cost − residual)/useful life; double-declining = 2/life × carrying amount; units-of-production = (cost − residual) × units used / total units.

Inventory: lower of cost and net realizable value. Cost includes purchase price, duties, freight and attributable conversion costs; NRV = estimated selling price − completion and selling costs.

Revenue recognition (five steps): identify the contract; identify performance obligations; determine transaction price; allocate the price; recognize revenue when each obligation is satisfied.

Impairment: compare carrying amount with recoverable amount (higher of fair value less costs of disposal and value in use); the write-down goes to profit or loss and is not reversed for goodwill.

Financial statement links: net income flows to retained earnings; ending retained earnings = opening + net income − dividends; the cash-flow statement reconciles operating, investing and financing activities.