Executive Master in Finance Capital Structure – Wrap up Executive Master in Finance 3. WACC Executive Master in Finance Capital Structure – Wrap up Professor André Farber Solvay Business School Université Libre de Bruxelles

Notations (based on RWJ 7th ed.) Executive Master in Finance 3. WACC Notations (based on RWJ 7th ed.) V market value of levered firm S market value of equity B market value of debt r0 cost of capital of unlevered firm β0 systematic risk (beta) of unlevered firm rS cost of equity of levered firm βS systematic risk (beta) of equity rB cost of debt βB systematic risk (beta) of debt L leverage ratio L = B/V TC corporate tax rate Executive Master of Finance 2006 03 WACC

Executive Master in Finance 3. WACC 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 We do not live in the world imagined by Modigliani and Miller in 1958. Their propositions were based on the following assumptions: Capital market are frictionless. There are no corporate or personal income taxes. Securities can be purchased or sold costlessly. There are no bankruptcy costs Both individuals and corporations can borrow or lend at the same interest rate. Investors have homogeneous expectations about the future cash flows. These assumptions tell us why capital structure might matter. In the following lectures, we will explore the consequences of dropping some of the assumptions. We will first consider the role of taxes. In most countries, interest payments are tax deductible. It is therefore in the interest of a firm to increase its debt in order to minimize tax payments. As a consequence, the market value of a levered firm should be higher than the market value of an unlevered firm with the same future free cash flows. We will show how to calculate the additional value due to leverage (the value of the tax shield). We will also analyze the relationship between the value of the tax shield and the weighted average cost of capital. But this will lead us to a new puzzle: why are companies so conservative in their use of debt? Why do some companies, such as Microsoft, have no debt? The trade-off theory suggests that this might be due to the costs of financial distress (bankrupcy is one extreme example). The optimal level of debt is reached when the present value of tax saving due to additional borrowing is just offset by increases in the present value of costs of distress. A good understanding of the theory will require models to analyze risky debt. The Merton model (based on the Black Scholes formula) is the classic in this area. We will also introduce a new approach recently proposed by Leland in 1994. Executive Master of Finance 2006 03 WACC

Weighted average cost of capital Executive Master in Finance 3. WACC 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

Summary: the Beta-CAPM diagram Executive Master in Finance 3. WACC Summary: the Beta-CAPM diagram   Beta L βS U β0 r rS r0 rB=rF B/S   rS rB B/S WACC=r0 Executive Master of Finance 2006 03 WACC

Executive Master in Finance 3. WACC 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

Executive Master in Finance 3. WACC MM 63 V = VU + VTS = S + B Value of equity r0 rS Value of all-equity firm rB Value of debt rB Value of tax shield Executive Master of Finance 2006 03 WACC

Weighted average cost of capital Executive Master in Finance 3. WACC Weighted average cost of capital Cost of equity Beta of equity Weighted average cost of capital Executive Master of Finance 2006 03 WACC

The Beta-CAPM diagram revised Executive Master in Finance 3. WACC The Beta-CAPM diagram revised   Beta βS β0 r rS r0 rB=rF B/S   rS rB B/S Executive Master of Finance 2006 03 WACC

Valuing the levered company. Executive Master in Finance 3. WACC Valuing the levered company. 2 approaches: APV approach: WACC approach: Executive Master of Finance 2006 03 WACC

Executive Master in Finance 3. WACC 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

When can the WACC be used? Executive Master in Finance 3. WACC 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

Debt rebalanced (Harris & Pringle) Executive Master in Finance 3. WACC 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

Debt rebalanced – Harris Pringle Executive Master in Finance 3. WACC Debt rebalanced – Harris Pringle V = VU + VTS = S + B Value of equity =(1-L)V r0 rS Value of all-equity firm rB Value of debt =LV r0 Value of tax shield Executive Master of Finance 2006 03 WACC

Debt rebalanced (Miles Ezzel) Executive Master in Finance 3. WACC 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

Executive Master in Finance 3. WACC Summary of Formulas Modigliani Miller Harris-Pringle Miles Ezzel Operating CF Perpetuity Finite or Perpetual Finite of Perpetual Debt level Certain Uncertain First tax shield WACC L = B/V rS(1-L) + rB(1-TC)(L) r0 (1 – TC L) r0 – rD TC L Cost of equity r0+(r0 –rB)(1-TC)(B/S) r0+(r0 –rB) (B/S) Beta equity β0+(β0 – βB) (1-TC) (B/S) β0 +( β0 – βB) (B/S) 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

Executive Master in Finance 3. WACC 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

Capital Cash Flow Valuation Executive Master in Finance 3. WACC 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