What is Corporate Finance, the Cost of Capital, and the Debt Tax Shield?
Mathematical Foundation
Laws & Principles
- The Debt Tax Shield: Interest paid on debt is tax-deductible. At a 21% corporate tax rate, a $1M interest payment costs only $790K after tax — the government absorbs $210K. This makes debt systematically cheaper than equity post-tax. The Modigliani-Miller theorem (1963) showed firm value increases with leverage BECAUSE of this tax shield — up to the point where financial distress costs outweigh the benefit.
- Optimal Capital Structure: Pure equity companies leave the debt tax shield on the table. Pure debt companies face bankruptcy risk and agency costs. The optimal structure balances tax benefits of debt against distress probability. Investment-grade companies typically carry D/(D+E) of 20–40%. Utilities run 60–70% leverage because stable regulated cash flows support it.
- WACC as the NPV Hurdle Rate: In capital budgeting, a project with IRR > WACC creates value (positive NPV). IRR < WACC destroys value. NPV = Σ[CFt / (1+WACC)^t] − Investment. Many companies add a 2–5% hurdle premium above WACC to account for estimation error and execution risk.
- CAPM for Cost of Equity: Ke = Rf + β × ERP. Risk-free rate = 10-year Treasury yield. ERP historically 5.0–5.5%. Beta measures market sensitivity: β > 1.0 = more volatile than market (higher Ke required). β < 1.0 = defensive (lower Ke). The beta difference between software (β ≈ 1.4) and utilities (β ≈ 0.4) produces dramatically different WACC outputs even with identical capital structures.
Step-by-Step Example Walkthrough
" Company: $5M market cap (Ke = 8.5%), $2M in bonds (Kd = 5.0%), 21% corporate tax rate. Evaluate a $500K project with projected 9% IRR. "
- Total value: V = $5M + $2M = $7M.
- Weights: Wₑ = 5/7 = 71.43%, Wd = 2/7 = 28.57%.
- After-tax cost of debt: 5.0% × (1 − 0.21) = 3.95%.
- WACC = (71.43% × 8.5%) + (28.57% × 3.95%) = 6.071% + 1.129% = 7.20%.
- Annual debt tax shield = $2M × 5% × 21% = $21,000/year.
- Project: IRR = 9.0% > WACC = 7.20%. Spread = +1.8%. → ACCEPT.