How does MM Proposition II relate cost of equity to leverage?

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AcadiFi · Accepted Answer

MM Proposition II states that the cost of equity rises linearly with the debt-to-equity ratio to exactly offset the cheaper cost of debt, keeping the weighted average cost of capital constant. Formally: r_E = r_U + (r_U - r_D) × (D/E), where r_U is the unlevered cost of capital (business risk only), r_D is cost of debt, and D/E is debt-equity ratio.

For Norriston Holdings: assume r_U = 9%, r_D = 5%, D/E = 0.8. Then r_E = 9% + (9% - 5%) × 0.8 = 9% + 3.2% = 12.2%. The equity holders demand 12.2% because the firm's operating cash flows are now levered; equity absorbs variability after debt service.

Key insight: the weighted average cost of capital remains r_U regardless of leverage in the no-tax MM world. WACC = (E/V) × r_E + (D/V) × r_D = (1/1.8)(12.2%) + (0.8/1.8)(5%) = 6.78% + 2.22% = 9% = r_U. The risk transfer from levered equity to the firm is exactly priced; no net gain from leverage.

With corporate taxes, Proposition II becomes: r_E = r_U + (r_U - r_D)(1-t)(D/E), and WACC falls with leverage because interest tax shields reduce the effective cost of debt. For Norriston with 25% tax: r_E = 9% + (9-5)(0.75)(0.8) = 11.4%, WACC decreases toward tax-shielded optimum.

Empirically, firms rarely sit at 100% debt because bankruptcy and agency costs re-introduce trade-offs beyond the pure tax benefit.

How does MM Proposition II relate cost of equity to leverage?

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