Textbook Chapter Cross-Reference

This index maps every function in the library to its corresponding chapter in the Startup Valuation textbook.

Chapter 2: Mathematical Foundations

Probability Theory

Function	Module	Description
expected_value_discrete	probability	E[X] = Σ xᵢ × P(X=xᵢ)
expected_value_continuous	probability	E[X] = ∫ x × f(x) dx
joint_probability	probability	P(total) = Π Pᵢ
probability_weighted_value	probability	E[V] = Σ pᵢ × Vᵢ
portfolio_expected_return	probability	E[R] = Σ pᵢ × Rᵢ
poisson_probability	probability	P(X=k) = e⁻λ·λᵏ/k!

Time Value of Money

Function	Module	Description
present_value	tv	PV = C/(1+r)ᵗ
net_present_value	tv	NPV = Σ Cₜ/(1+r)ᵗ
annuity_present_value	tv	PV = C×[(1-(1+r)⁻ⁿ)/r]

Risk-Adjusted Discount Rates

Function	Module	Description
capm	capm	E(Rᵢ) = Rf + βᵢ(E(Rm) - Rf)
portfolio_beta	capm	βp = Σ wᵢβᵢ
startup_adjusted_capm	capm	CAPM + size + startup premiums
portfolio_variance	capm	Var(Rp) = ΣΣ wᵢwⱼCov(Rᵢ,Rⱼ)

Chapter 3: Core Valuation Models

Function	Module	Description
scorecard_valuation	core	V = V_avg × Σ(wᵢ × sᵢ)
berkus_valuation	core	V = Σ vᵢ (max $500K per factor)
risk_factor_summation	core	V = V_base + Σ(rᵢ × $250K)
vc_method_post_money	core	Post = Terminal/ROI
vc_method_pre_money	core	Pre = Post - Investment
terminal_value_multiple	core	TV = Revenue × Multiple

Chapter 4: Advanced Techniques

Function	Module	Description
black_scholes	advanced	C = N(d₁)S - N(d₂)Ke⁻ʳᵀ
binomial_tree	advanced	u, d, p factors + tree valuation
binomial_valuation	advanced	High-resolution binomial (steps=50)
monte_carlo_valuation	advanced	Simulation with distributions
scenario_analysis	advanced	E[V] = Σ pᵢ × Vᵢ
ltv_cac_valuation	advanced	(LTV/CAC) × Market Size × 0.1

Chapter 5: Market Comparables

Function	Module	Description
pe_ratio	comparables	P/E = Market Cap / Net Income
ps_ratio	comparables	P/S = Market Cap / Revenue
ev_ebitda	comparables	EV/EBITDA
ev_revenue	comparables	EV/Revenue
regression_adjusted_multiple	comparables	Multiple = β₀ + β₁g + β₂M + ...
target_valuation_multiple	comparables	Valuation = Multiple × Metric

Chapter 11: Industry-Specific Frameworks

SaaS

Function	Module	Description
arr	saas	Annual Recurring Revenue
mrr	saas	Monthly Recurring Revenue
cac	saas	Customer Acquisition Cost
ltv_saas	saas	LTV = (ARPU × GM) / Churn
net_revenue_retention	saas	NRR = Revenue_end / Revenue_start
cac_payback_period	saas	CAC / (MRR × GM)
magic_number	saas	Net New ARR / S&M Expense
rule_of_40	saas	Growth + Profit ≥ 40%
saas_revenue_multiple_valuation	saas	ARR × Multiple

Biotech

Function	Module	Description
rnPV	biotech	Risk-adjusted NPV
decision_tree_ev	biotech	EV = Π pᵢ × Terminal Value
peak_sales	biotech	Population × Penetration × Price
pipeline_valuation	biotech	Σ(Peak × Multiple × P_success)/(1+r)ⁿ
overall_success_probability	biotech	P_total = Π P_stage

Fintech

Function	Module	Description
payment_revenue	fintech	Volume × Take Rate
max_loan_portfolio	fintech	Equity / Capital Ratio
network_effects_value	fintech	Value ∝ Users^α
lending_fintech_valuation	fintech	Loan Book × ROE × P/E
payment_processor_valuation	fintech	DCF of payment revenue
neobank_valuation	fintech	Customers × LTV × P/E

Marketplace

Function	Module	Description
gmv	marketplace	Gross Merchandise Value
take_rate	marketplace	Revenue / GMV
liquidity	marketplace	Successful / Total Attempts
gmv_multiple_valuation	marketplace	GMV × Multiple
network_value	marketplace	k × Users^α
buyer_retention	marketplace	Repeat Buyers / Period 1 Buyers
network_density	marketplace	Actual / Potential Connections

Hardware

Function	Module	Description
trl_adjusted_valuation	hardware	Market × Share × Margin × Multiple × (1-TRL)
gross_margin_hardware	hardware	(ASP - COGS) / ASP
break_even_volume	hardware	Fixed Costs / (ASP - Variable Cost)
probability_weighted_dcf	hardware	E[V] = Σ pᵢ × Vᵢ

Chapter 12: International Valuation

Function	Module	Description
purchasing_power_parity	international	Eₜ = E₀ × (1+π_f)/(1+π_d)
interest_rate_parity	international	F = S × (1+r_f)/(1+r_d)
currency_adjusted_dcf	international	PV = Σ[CFₜ^local/Eₜ]/(1+r_USD)^t
country_risk_premium	international	Sovereign Spread
country_risk_premium_damodaran	international	Default Spread × (σ_equity/σ_bond)
adjusted_capm_international	international	r = Rf + β×MRP + CRP
after_tax_cash_flow	international	Pre-Tax × (1-T_local) × (1-T_withhold)
sum_of_parts_valuation	international	Σ V_market × P(success)

Chapter 13: Stakeholder Perspectives

Function	Module	Description
single_round_dilution	stakeholders	Ownership × (1 - Investment/Post)
multi_round_dilution	stakeholders	Π(1 - Investmentᵢ/Postᵢ)
acquisition_value	stakeholders	Standalone + Synergies - Integration
opm_common_stock	stakeholders	Black-Scholes for common stock
pwerm	stakeholders	Σ pᵢ × CommonValueᵢ
common_stock_discount	stakeholders	(Preferred - Common) / Preferred
liquidation_value	stakeholders	Σ(Asset × Recovery Rate)
venture_debt_dilution	stakeholders	Warrant Coverage × Loan / Post
risk_adjusted_synergy	stakeholders	PV of risk-adjusted synergies
intrinsic_option_value	stakeholders	max(FMV - Strike, 0) × Shares
probability_weighted_employee_value	stakeholders	E[V] across exit scenarios
vesting_adjusted_value	stakeholders	Vested + Σ(unvested × vest × retention)
cash_equity_breakeven	stakeholders	Salary tradeoff analysis
max_asset_based_loan	stakeholders	Collateral-based loan calculation

Chapter 14: Emerging Topics

Function	Module	Description
safe_conversion_discount	emerging	Series A × (1 - Discount)
safe_conversion_cap	emerging	SAFE conversion with valuation cap
safe_expected_value	emerging	Expected value across cap/discount
equation_of_exchange	emerging	MV = PQ → Token Value
nvt_ratio	emerging	Market Cap / Daily Volume
protocol_value	emerging	TVL × Multiple
esg_adjusted_discount_rate	emerging	r = base + risk - opportunity
esg_premium_valuation	emerging	Base × (1 + ESG × premium)
esg_discount_valuation	emerging	Base × (1 - risk × discount)
metcalfes_law	emerging	V = k × n²
modified_metcalfes	emerging	V = k × n^α
network_density_valuation	emerging	Users × Connections × Value
remote_cost_savings_npv	emerging	Savings / r (perpetuity)
data_moat_value	emerging	DCF of data advantage
remote_first_premium	emerging	Base × (1 + savings + talent + productivity)