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Executive Master in Finance Capital Structure – Wrap up

Executive Master in Finance Capital Structure – Wrap up. Professor André Farber Solvay Business School Université Libre de Bruxelles. Notations (based on RWJ 7th ed.). V market value of levered firm S market value of equity B market value of debt r 0 cost of capital of unlevered firm

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Executive Master in Finance Capital Structure – Wrap up

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  1. Executive Master in FinanceCapital Structure – Wrap up Professor André Farber Solvay Business School Université Libre de Bruxelles

  2. Notations (based on RWJ 7th ed.) V market value of levered firm S market value of equity B market value of debt r0cost of capital of unlevered firm β0 systematic risk (beta) of unlevered firm rScost of equity of levered firm βS systematic risk (beta) of equity rBcost of debt βBsystematic risk (beta) of debt L leverage ratio L = B/V TCcorporate tax rate Executive Master of Finance 2006 03 WACC

  3. MM 58 Debt policy doesn’t matter in perfect capital market • MM I: market value of company independent of capital structure V = S + B=VU • MM II: WACC independent of capital structure • Underlying assumptions: • No taxes! • Symetric information Executive Master of Finance 2006 03 WACC

  4. Weighted average cost of capital V (=VU ) = S + B Value of equity rS Value of all-equity firm r0 rB Value of debt WACC Executive Master of Finance 2006 03 WACC

  5. Summary: the Beta-CAPM diagram   Beta L βS U β0 r0 r rB=rF rS 0 B/S   rS B/S rB WACC=r0 Executive Master of Finance 2006 03 WACC

  6. Corporate Tax Shield • Interest payments are tax deductible => tax shield • Tax shield = Interest payment × Corporate Tax Rate = (rB× B) × TC • rB: cost of new debt • B : market value of debt • Value of levered firm = Value if all-equity-financed + PV(Tax Shield) • PV(Tax Shield) - Assume permanent borrowing V=VU + TCB Executive Master of Finance 2006 03 WACC

  7. MM 63 V = VU + VTS = S + B Value of equity rS r0 Value of all-equity firm rB Value of debt Value of tax shield rB Executive Master of Finance 2006 03 WACC

  8. Weighted average cost of capital Cost of equity Beta of equity Weighted average cost of capital Executive Master of Finance 2006 03 WACC

  9. The Beta-CAPM diagram revised   Beta βS β0 r r0 rB=rF rS 0 B/S   rS rB B/S Executive Master of Finance 2006 03 WACC

  10. Valuing the levered company. 2 approaches: APV approach: WACC approach: Executive Master of Finance 2006 03 WACC

  11. Beyond MM 63 • Value of levered company: V = VU + VTS = S + B • In general, WACC changes over time Expected payoff =Free cash flow unlevered+ Interest Tax Shield+ Expected value Expected return for debt and equity investors Rearrange: Solve: Executive Master of Finance 2006 03 WACC

  12. When can the WACC be used? • 2 possible financing rules: • Rule 1: Debt fixed (MM 61 see before) • Borrow a fraction of initial project value • Interest tax shields are constant. They are discounted at the cost of debt. • Rule 2: Debt rebalanced • Adjust the debt in each future period to keep it at a constant fraction of future project value. • Interest tax shields vary. They are discounted at the opportunity cost of capital (except, possibly, for next tax shield –cf Miles and Ezzel) Executive Master of Finance 2006 03 WACC

  13. Debt rebalanced (Harris & Pringle) Any free cash flows – debt rebalanced continously Bt = L Vt The risk of the tax shield is equal to the risk of the unlevered firm rTS = r0 Executive Master of Finance 2006 03 WACC

  14. Debt rebalanced – Harris Pringle V = VU + VTS = S + B Value of equity=(1-L)V rS r0 Value of all-equity firm rB Value of debt=LV Value of tax shield r0 Executive Master of Finance 2006 03 WACC

  15. Debt rebalanced (Miles Ezzel) Similar to Harris Pringle but next tax shield discount at rB Assumption: any cash flows Debt rebalanced Dt/Vt = L ( a constant) Executive Master of Finance 2006 03 WACC

  16. Summary of Formulas Adadpted from: Taggart – Consistent Valuation and Cost of Capital Expressions With Corporate and Personal Taxes Financial Management Autumn 1991 Executive Master of Finance 2006 03 WACC

  17. Varying debt levels • How to proceed if none of the financing rules applies? • Two important instances: • (i) debt policy defined as an amount of borrowing instead of as a target percentage of value • (ii) the amount of debt changes over time • Use the Capital Cash Flow method suggested by Ruback • (Ruback, Richard A Note on Capital Cash Flow Valuation, Harvard Business School, 9-295-069, January 1995) Executive Master of Finance 2006 03 WACC

  18. Capital Cash Flow Valuation • Assumptions: • CAPM holds • PV(Tax Shield) as risky as operating assets Capital cash flow =FCF unlevered+Tax shield Executive Master of Finance 2006 03 WACC

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