Modigliani-Miller Theorem with Corporate Taxes

Overview

• Previous discussion: MM theorem without taxes and bankruptcy costs.
• Current focus: MM theorem with corporate taxes.

Impact of Corporate Taxes on Capital Structure

• Interest on Debt: Tax deductible in the U.S.
  • Adds debt -> reduces taxes -> increases cash flow.

Example

• Unlevered Firm (U):

  • Earnings Before Interest and Taxes (EBIT): $1,000
  • Taxable Income: $1,000
  • Taxes (30%): $300
  • Net Income: $700

• Levered Firm (L):

  • EBIT: $1,000
  • Interest: $80
  • Taxable Income: $920
  • Taxes (30%): $276
  • Net Income: $644

Cash Flow from Assets

• Unlevered Firm: EBIT - Taxes = $700
• Levered Firm: EBIT - Taxes = $724
• Interest Tax Shield: Adds $24 to cash flow.

Valuation Impact

• Interest Tax Shield:

  • Assumes perpetual debt maintaining: $1,000 debt.
  • Tax Shield Value: $24 annually or $300 present value.

• Graphical Representation:

  • Unlevered firm value remains constant.
  • Levered firm value = Unlevered firm value + Tax Shield.
  • More debt -> increases firm value (with tax-deductible interest).

Proposition Two: Weighted Average Cost of Capital (WACC)

• Unleveraged Return: Upward sloping with increased debt due to higher risk.
• Effect of Tax Deductibility:
  • WACC decreases with more debt.
  • Approaches the rate on debt with 100% debt.

Conclusion

• Optimal capital structure with corporate taxes and no bankruptcy costs is to use 100% debt.
• Next topic: Case three with bankruptcy costs.