--- name: cost-of-capital-wacc description: Calculate weighted average cost of capital (WACC), cost of equity (CAPM, build-up), cost of debt, and marginal cost of capital for capital budgeting, valuation, and performance measurement. Use when determining hurdle rates, evaluating projects, pricing capital allocations, or computing economic profit metrics. Triggers on phrases like "WACC", "cost of capital", "weighted average cost of capital", "cost of equity", "CAPM", "capital asset pricing model", "beta", "cost of debt", "hurdle rate", "marginal cost of capital", "economic value added", "EVA", "residual income", "required rate of return", "discount rate", "risk-free rate", "equity risk premium", "country risk premium", "size premium". --- # Cost of Capital & WACC Calculate weighted average cost of capital (WACC), cost of equity, cost of debt, and marginal cost of capital for investment decisions, valuation, and performance measurement. ## Workflow ### 1. WACC Framework ``` WACC CALCULATION FRAMEWORK ═══════════════════════════════════════ WACC = (E/V × Re) + (D/V × Rd × (1 - T)) Where: E = Market value of equity D = Market value of debt V = E + D (total market value of capital) Re = Cost of equity Rd = Cost of debt (pre-tax) T = Corporate tax rate ADDITIONAL COMPONENTS (if applicable): ═══════════════════════════════════════ WACC = (E/V × Re) + (D/V × Rd × (1 - T)) + (P/V × Rp × (1 - T)) P = Preferred stock Rp = Cost of preferred stock MULTIPLE BUSINESS UNITS / SBU APPROACH: ═══════════════════════════════════════ When divisions have different risk profiles: → Calculate divisional WACC using pure-play betas → Use build-up method for unique divisions → Apply build-up to cash flows (not to WACC components) ``` ### 2. Cost of Equity (CAPM) ``` COST OF EQUITY — CAPM METHOD ═══════════════════════════════════════ CAPM Formula: Re = Rf + β × ERP + Other Premiums Where: Rf = Risk-free rate β = Levered beta (company-specific) ERP = Equity risk premium Other Premiums = Size premium, country risk premium, specific risk premium INPUTS: ═══════════════════════════════════════ Risk-Free Rate: ═══════════════════════════════════════ → Use long-term government bond yield matching cash flow duration → US: 10-year Treasury yield → Current 10-yr Treasury: 4.25% → Alternative: 20-yr Treasury for long-duration assets: 4.50% → Recommended: 4.25% (10-yr Treasury) Beta: ═══════════════════════════════════════ Step 1: Collect comparable company betas Step 2: Unlever each beta Step 3: Average unlevered betas Step 4: Relever using target capital structure Comparable Company Betas: ═══════════════════════════════════════ Company Levered β D/E Ratio Tax Rate Unlevered β (from Bloomberg) ─────────────────────────────────────────────────────────────── Comp A 1.15 0.20 21% 0.99 Comp B 1.35 0.35 21% 1.07 Comp C 0.95 0.10 21% 0.88 Comp D 1.25 0.25 21% 1.03 Comp E 1.05 0.15 21% 0.93 ─────────────────────────────────────────────────────────────── Average Unlevered Beta: 1.00 Unlevering Formula: βu = βl / [1 + (1 - T) × (D/E)] Relevering Formula: βl = βu × [1 + (1 - T) × (D/E)] Target D/E: 0.25 (company target) Relevered Beta: 1.00 × [1 + (1 - 0.21) × 0.25] = 1.00 × 1.198 = 1.20 Equity Risk Premium: ═══════════════════════════════════════ → Historical ERP: 5.5% - 6.5% → Ibbotson/SBBI: 6.0% → Damodaran (updated): 5.8% → Aswath Damodaran (Jan 2024): 5.5% → Company policy: 6.0% Recommended: 6.0% (balanced approach) Size Premium: ═══════════════════════════════════════ Market Cap Category Size Premium ───────────────────────────────────── Mega cap (> $10B) 0.0% Large cap ($5-10B) 0.5% Mid cap ($1-5B) 1.5% Small cap ($250M-$1B) 2.5% Micro cap (<$250M) 3.5% Company market cap: $500M → Size Premium: 2.5% Country Risk Premium: ═══════════════════════════════════════ For US companies: 0% For emerging markets: S&P rating differential × spread → Example: Country rated BBB (vs AAA for US) → Sovereign spread: 1.50% → CRP: 1.50% × 0.7 (equity volatility adjustment) = 1.05% COST OF EQUITY CALCULATION: ═══════════════════════════════════════ Component Amount ───────────────────────────────────────────── Risk-free rate (Rf): 4.25% Beta (levered): 1.20 ERP: 6.00% Market risk premium (β × ERP): 7.20% Size premium: 2.50% ───────────────────────────────────────────── COST OF EQUITY (Re): 13.95% ALTERNATIVE: BUILD-UP METHOD (for private companies) ═══════════════════════════════════════ Component Amount ───────────────────────────────────────────── Risk-free rate: 4.25% Equity risk premium: 6.00% Size premium (small cap): 3.00% Company-specific risk: 2.00% Industry risk premium: 1.00% ───────────────────────────────────────────── COST OF EQUITY (Build-up): 16.25% NOTE: Build-up typically yields higher rates for private/small companies ``` ### 3. Cost of Debt ``` COST OF DEBT CALCULATION ═══════════════════════════════════════ Method 1: Yield to Maturity (YTM) on Existing Debt ═══════════════════════════════════════ Outstanding Debt Instruments: ═══════════════════════════════════════ Instrument Face Value Coupon YTM Maturity Book Value ──────────────────────────────────────────────────────────────────────────── Term Loan A $100,000K 5.50% 5.75% 2027 $98,000K Term Loan B $50,000K 4.75% 5.25% 2028 $49,500K Revolver (drawn) $25,000K SOFR+1.5% 5.85% 2026 $25,000K Bond (Senior) $75,000K 4.50% 5.00% 2030 $73,500K ──────────────────────────────────────────────────────────────────────────── Total: $250,000K $246,000K Weighted Average Pre-Tax Cost of Debt: ═══════════════════════════════════════ Instrument Market Value Weight YTM Weighted YTM ─────────────────────────────────────────────────────────────────────── Term Loan A $98,000K 40.0% 5.75% 2.30% Term Loan B $49,500K 20.3% 5.25% 1.07% Revolver $25,000K 10.3% 5.85% 0.60% Bond (Senior) $73,500K 30.1% 5.00% 1.51% ─────────────────────────────────────────────────────────────────────── TOTAL PRE-TAX COST OF DEBT: 5.48% AFTER-TAX COST OF DEBT: Rd × (1 - T) = 5.48% × (1 - 0.21) = 5.48% × 0.79 = 4.33% Method 2: Credit Spread Approach (if no traded debt) ═══════════════════════════════════════ → Company credit rating: BBB- → BBB- corporate bond spread (over Treasuries): 2.50% → Risk-free rate (10-yr): 4.25% → Pre-tax cost of debt: 4.25% + 2.50% = 6.75% → After-tax: 6.75% × 0.79 = 5.33% Method 3: Implied from Equity (HAM) ═══════════════════════════════════════ → Implied yield = (Cost of Equity - ERP) / (1 - T) → = (13.95% - 6.00%) / 0.79 = 10.06% → Less risk-free rate: 10.06% - 4.25% = 5.81% credit spread → This is HIGH → suggests either: · Beta is too high (overestimated risk) · ERP is too low · Actual credit risk is higher than reflected in ratings ``` ### 4. WACC Calculation ``` WACC CALCULATION ═══════════════════════════════════════ CAPITAL STRUCTURE (Market Values): ═══════════════════════════════════════ Component Market Value Weight ──────────────────────────────────────────── Equity: $500,000K 67.1% (50M shares × $10/share) Debt: $246,000K 32.9% (Sum of market values above) ──────────────────────────────────────────── Total (V): $746,000K 100.0% WACC CALCULATION: ═══════════════════════════════════════ Component Weight Cost After-Tax Cost Weighted ──────────────────────────────────────────────────────────────── Equity 67.1% 13.95% 13.95% 9.36% Debt 32.9% 5.48% 4.33% 1.42% ──────────────────────────────────────────────────────────────── WACC: 10.79% DIVISIONAL WACC (if multiple SBU): ═══════════════════════════════════════ Division Unlevered β Relevered β Cost of Equity Divisional WACC ──────────────────────────────────────────────────────────────────────────────── Core Software 0.90 1.08 12.75% 10.10% Hardware 1.30 1.55 15.05% 11.75% Services 0.75 0.90 11.65% 9.50% ──────────────────────────────────────────────────────────────────────────────── Company-weighted: 10.79% MARGINAL COST OF CAPITAL (MCC): ═══════════════════════════════════════ Breakpoint Analysis: ═══════════════════════════════════════ Current equity: $500M (internal) Internal equity capacity: $150M (before issuing new shares) After internal equity exhausted: → Flotation cost on new equity: 5% → Adjustment to Re: 13.95% + 0.50% = 14.45% → New WACC: (67.1% × 14.45%) + (32.9% × 4.33%) = 9.69% + 1.42% = 11.12% Breakpoint: $150M of additional investment Below $150M: WACC = 10.79% Above $150M: WACC = 11.12% ``` ### 5. Application to Capital Budgeting ``` WACC APPLICATION — PROJECT EVALUATION ═══════════════════════════════════════ Project: New Product Development Initial Investment: $50,000,000 Cash Flow Projections: ═══════════════════════════════════════ Year Cash Flow PV Factor (10.79%) PV ───────────────────────────────────────────────── 0 ($50,000K) 1.0000 ($50,000K) 1 $5,000K 0.9026 $4,513K 2 $8,000K 0.8147 $6,518K 3 $12,000K 0.7353 $8,824K 4 $15,000K 0.6635 $9,952K 5 $18,000K 0.5989 $10,780K 6 $20,000K 0.5406 $10,812K 7 $22,000K 0.4880 $10,736K 8 $24,000K 0.4405 $10,572K 9 $25,000K 0.3977 $9,943K 10 $28,000K 0.3589 $10,049K ───────────────────────────────────────────────── NPV: $36,699K PROJECT EVALUATION: ═══════════════════════════════════════ NPV at WACC (10.79%): $36,699K → ACCEPT ✓ IRR: 26.5% → > WACC ✓ Payback period: 4.2 years → < 5-year threshold ✓ Profitability index: $86,699K / $50,000K = 1.73 → > 1.0 ✓ ECONOMIC VALUE ADDED (EVA): ═══════════════════════════════════════ EVA = NOPAT - (Capital Employed × WACC) Year NOPAT Capital WACC Charge EVA ──────────────────────────────────────────────────── 1 $4,000K $50,000K $5,395K ($1,395K) 2 $6,400K $48,000K $5,179K $1,221K 3 $9,600K $45,000K $4,856K $4,744K 4 $12,000K $40,000K $4,316K $7,684K 5 $14,400K $35,000K $3,777K $10,623K Cumulative EVA (5-year): $32,877K (positive economic profit created) HURDLE RATE ADJUSTMENTS: ═══════════════════════════════════════ For higher-risk projects, add risk premium to WACC: Project Type WACC Risk Premium Hurdle Rate ────────────────────────────────────────────────────────────── Core product enhancement 10.79% 0.00% 10.79% New product (same market) 10.79% 2.00% 12.79% New market expansion 10.79% 3.50% 14.29% International expansion 10.79% 4.00% 14.79% M&A / strategic 10.79% 3.00% 13.79% R&D / R&D 10.79% 5.00% 15.79% ``` ## Edge Cases - **Negative interest rates**: Risk-free rate may be negative (Europe/Japan); adjust CAPM - **High debt companies**: WACC may be misleading; use APV (adjusted present value) - **Changing capital structure**: Use flow-to-equity (APV or FTE) instead of WACC - **Project-specific risk**: Don't use company WACC; use project-specific discount rate - **Real options**: WACC doesn't capture option value; use real options analysis for flexibility ## Integration Points - **Market data**: Bloomberg, FactSet, Capital IQ (beta, risk-free rates, spreads) - **Financial models**: Excel, Adaptive Insights, Anaplan (WACC calculations) - **ERP**: Oracle, SAP (capital structure data) - **Capital allocation systems**: Board portals, investment committees - **EVA platforms**: Stern Stewart, custom EVA dashboards - **Research**: Damodaran Online (ERP, country risk premiums) ## Output ### WACC Summary ``` COST OF CAPITAL SUMMARY — Q1 2024 ═══════════════════════════════════════ WACC: 10.79% → Cost of equity: 13.95% (CAPM) → Pre-tax cost of debt: 5.48% → After-tax cost of debt: 4.33% Capital structure: 67.1% equity / 32.9% debt Hurdle rates by project type: → Core projects: 10.79% → New products: 12.79% → M&A: 13.79% → R&D: 15.79% Sensitivity: ±100 bps change in WACC impacts NPV by ~$3.7M on $50M project ```