1. 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

2. 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 WACC

3. 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 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 WACC

4. 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 WACC

5. 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 WACC

6. 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 WACC

7. 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 WACC

8. 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 WACC

9. 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 WACC

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

11. 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 WACC

12. 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 WACC

13. 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 WACC

14. 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 WACC

15. 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 WACC

16. 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 WACC

17. 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, , January 1995)
Executive Master of Finance WACC

18. 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 WACC