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Building the after-tax WACC

A firm's cost of capital is the market-value-weighted blend of what debt and equity holders require: WACC = w_d·k_d·(1 − T) + w_e·k_e. Equity is priced by the CAPM, k_e = r_f + β·ERP, while debt is taken after the interest tax shield, k_d·(1 − T). Only debt earns the shield, so it usually sits below equity in the blend.

Weighted average cost of capital7.50%
0%2%4%6%8%10%12%1.80%5.70%WACC 7.50%Debt w_d·k_d·(1 − T)Equity w_e·k_e
Cost of equity k_e 9.50%After-tax k_d 4.50%WACC 7.50%
Weight of debt w_d40%
Equity weight w_e = 60%
Pre-tax cost of debt k_d6.0%
Tax rate T25%
Cost of equity (CAPM)
Risk-free rate r_f4.0%
Equity beta β1.10x
Equity risk premium ERP5.0%
Equity costs 9.50% (=4.0% + 1.10x × 5.0%), debt costs 4.50% after the 25% shield. Blended at 40/60 they give a WACC of 7.50%.
Try this

Shift weight toward debt and WACC usually falls, because shielded debt is cheaper than equity. Raising the tax rate deepens the shield and lowers the after-tax cost of debt.

Note: only debt carries the (1 − T) tax shield, since interest is tax-deductible and dividends are not. The weights w_d and w_e should be market values of debt and equity, not book values, because WACC is the return the market requires today.

Reflect: if cheap shielded debt always lowers WACC, why not finance the firm almost entirely with debt? What does this model leave out about how k_d and k_e respond as leverage climbs?

Weighted Average Cost of Capital (WACC)Open in Dr Phil's Quant Lab ↗