1. Advanced Finance 2005-2006 Debt and Taxes
Corporate Financial Policy 2. Debt and taxes
Advanced Finance Debt and Taxes
Professor André Farber
Solvay Business School
Université Libre de Bruxelles
This lecture has a first look at the impact of taxes on the value of a levered company.
Our most important results is that leverage increases the value of a company and decreases it weighted average cost of capital.

2. Corporate Financial Policy 2. Debt and taxes
Review: MM 58
Debt policy doesn’t matter in perfect capital market
MM I: market value of company independent of capital structure
V = E + D=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.
Advanced Finance Debt and taxes

3. Corporate Financial Policy 2. Debt and taxes
Corporate Tax Shield
Interest payments are tax deductible => tax shield
Tax shield = Interest payment × Corporate Tax Rate
= (rD × D) × TC
rD : cost of new debt
D : market value of debt
Value of levered firm
= Value if all-equity-financed + PV(Tax Shield)
PV(Tax Shield) - Assume permanent borrowing
V=VU + TCD
Interest payments are tax deductible. As a consequence, the taxes paid by a levered company are lower than if it were unlevered. The tax shield is the tax saving due to leverage. To see this, consider two companies with identical EBITs: company U has no debt whereas company L is levered. The corporate taxes paid by these two companies are:
TaxesU = EBIT × TC
TaxesL = (EBIT – Interest) × TC = EBIT× TC – Interest × TC
= TaxesU – Tax shield
As a consequence, the total cash flow payable to both stockholders (dividend) and debtholders (interest) is higher with leverage:
For U: DivU = EBIT(1-TC)
For L: DivL + Interest = (EBIT – Interest) ×(1-TC) + Interest = EBIT(1-TC) + Interest × TC
This is the reason why the value of the levered firm should be higher than the value of the unlevered.
The additional value due to leverage is the present value of the tax shield. Its calculation is tricky as: 1) the level of debt can change over time 2) an assumption is required on the risk of the tax shield to determine the discount factor to use.
In this lecture, we look at the simplest case analyzed by Modigliani and Miller in 1963: 1) Expected EBIT is a constant perpetuity 2) The level of debt is constant 3) The tax shield has the same risk as the debt.
Advanced Finance Debt and taxes

4. Corporate Financial Policy 2. Debt and taxes
Example
U L
Balance Sheet
Total Assets 1,000 1,000
Book Equity 1,
Debt (8%)
Income Statement
EBIT
Interest
Taxable Income
Taxes (40%)
Net Income
Dividend
Total
Adjusted Present Value approach (APV)
Assume rA= 10%, rD = 5%
(1) Value of all-equity-firm:
VU = 120 / 0.10 = 1,200
(2) PV(Tax Shield):
Tax Shield = 40 x 0.40 = 16
PV(TaxShield) = 16/0.05 = 320
(3) Value of levered company:
VL = 1, = 1,520
(4) Market value of equity:
D = 40/.05 = 800
EL = VL - D = 1, = 720
Here is an example.
Notice that the taxes paid by L are lower than those paid by U. The difference (16) is the annual tax shield.
The total cash flow paid out by is higher for L (136) than for U (120). The difference is equal to the tax shield.
3 steps are required to calculate the value of the levered firm: 1) compute the value of the unlevered firm 2) calculate the present value of the tax shield 3) add the two previous results
The market value of equity is obtained by subtracting the value of the debt from the value of equity. Note that in this example, the market value of the debt is different from the book value.
Why not calculate E and D to get V=E+D
Because the discount rate to use to calculate E is not known at this stage.
Advanced Finance Debt and taxes

5. What about cost of equity?
Corporate Financial Policy 2. Debt and taxes
What about cost of equity?
Proof:
But VU = EBIT(1-TC)/rA
and E = VU + TCD – D
Replace and solve
1) Cost of equity increases with leverage:
2) Beta of equity increases
In example:
rE = 10% +(10%-5%)(1-0.4)(800/720)
= 13.33% or
rE = DIV/E = 96/720 = 13.33%
These formulas generalize the formulas that we found previously in the absence of taxes.
As before, the cost of equity and the beta of equity (assuming that the debt is riskless) are linear function of the debt-equity ratio. However, the slope is lower (the ratio D/E is multiplied by 1-TC)
Can these formulas be used to get a direct calculation of the market value of equity? Unfortunately, not directly.
To see this, notice that the cost of equity is a function of D/E. So, you need to know E, the market value of equity, to calculate rE.. But you need rE to calculate E. So, you are in trouble.
There is however one way around the problem.
From the cost of equity formula, we get:
rEE = rAE +(rA – rD)(1 – TC)D
But, using the formula for E, we also have:
rEE = (EBIT – rDD)(1 – TC)
This leads to:
rAE +(rA – rD)(1 – TC)D = (EBIT – rDD)(1 – TC)
rAE +rA (1 – TC)D = EBIT (1 – TC)
and
E = [EBIT (1 – TC) -rA (1 – TC)D] / rA
Advanced Finance Debt and taxes

6. What about the weighted average cost of capital?
Corporate Financial Policy 2. Debt and taxes
What about the weighted average cost of capital?
Weighted average cost of capital: discount rate used to calculate the market value of a firm by discounting net operating profit less adjusted taxes NOPLAT = EBIT(1-TC)
V = EBIT(1-TC) / WACC
As: V>VU WACC < rA
The definition of the weighted average cost of capital is very general. The WACC is the discount rate such that the value of the levered firm is equal to discounted free cash flows of the unlevered company.
In this lecture, we are analyzing a simplified situation: expected EBIT is constant and replacement investment equal to depreciation. In this setting:
FCF = EBIT(1 – TC) + Depreciation – Depreciation = EBIT(1 – TC)
If there are tax benefits of debt, the value of the levered firm is greater the value of the unlevered firm. As the consequence, the weighted average cost of capital is lower.
We then derive the formula for the WACC. It differs from the formula derived in the absence of tax benefits: the cost of debt (rD) is multiplied by (1 – TC) to take into account the tax saving.
In example: NOPLAT = 120
V = 1,520
WACC = 13.33% x % x 0.60 x 0.53 = 7.89%
Advanced Finance Debt and taxes

7. The Beta-CAPM diagram revised
Corporate Financial Policy 2. Debt and taxes
The Beta-CAPM diagram revised  
Beta
βEquity
βAsset r
rEquity
rAsset
rDebt=rf
D/E
Back to the Beta-CAPM diagram.  
rEquity
rDebt
D/E
WACC
Advanced Finance Debt and taxes

8. Cost of equity calculation
Corporate Financial Policy 2. Debt and taxes
Cost of equity calculation
V = VU + TCD = E + D
Value of equity rA rE
Value of all-equity firm rD
Value of debt rD
Value of tax shield = TCD
Up to now, we have fixed the level of debt. We then calculated:
The value of the levered firm
The value of equity
The cost of equity
The WACC
We now want to start from the WACC to calculate the value of the levered firm.
Advanced Finance Debt and taxes

9. WACC – Modigliani Miller formula
Corporate Financial Policy 2. Debt and taxes
WACC – Modigliani Miller formula
We first show two different formulas for the WACC:
The standard formula
An alternative formula
Advanced Finance Debt and taxes

10. WACC – using Modigliani-Miller formula
Corporate Financial Policy 2. Debt and taxes
WACC – using Modigliani-Miller formula
Assumptions:
1. Perpetuity
2. Debt constant
3. D/V = L
Proof:
Market value of unlevered firm:
VU = EBIT (1-TC)/rAsset
Market value of levered firm:
V = VU + TC D
Define: L≡D/V
Solve for V:
Here we show that the value of the levered firm is indeed equal to the free cash flow of the unlevered firm discounted at the WACC.
In order to use the WACC to value the company (or the project), we have to introduce a financing rule. Instead of fixing the level of debt, we fix debt ratio (L), the fraction of debt in the total value of the company.
Advanced Finance Debt and taxes

11. Corporate Financial Policy 2. Debt and taxes
MM formula: example
Data
Investment 100
Pre-tax CF
rA 9%
rD 5%
TC 40%
Base case NPV: (1-0.40)/.09 = 50
Financing:
Borrow 50% of PV of future cash flows after taxes
D = 0.50 V
Using MM formula: WACC = 9%( × 0.50) = 7.2%
NPV = (1-0.40)/.072 = 87.50
Same as APV introduced previously? To see this, first calculate D.
As: V =VU + TC D = D
and: D = 0.50 V
V = ×0.50× V → V = → D = 93.50
→ APV = NPV0 + TC D = × = 87.50
Advanced Finance Debt and taxes

12. Using the standard WACC formula
Corporate Financial Policy 2. Debt and taxes
Using the standard WACC formula
Step 1: calculate rE using
As D/V = 0.50, D/E = 1
rE = 9% + (9% - 5%)(1-0.40)(0.50/(1-0.50)) = 11.4%
Step 2: use standard WACC formula
WACC = 11.4% x % x (1– 0.40) x = 7.2%
If you want to calculate the WACC using the standard formula, you first have to calculate the cost of equity rE and then apply the standard formula. The result is of course the same as with the MM formula.
Same value as with MM formula
Advanced Finance Debt and taxes

13. Adjusting WACC for debt ratio or business risk
Corporate Financial Policy 2. Debt and taxes
Adjusting WACC for debt ratio or business risk
Step 1: unlever the WACC
Step 2: Estimate cost of debt at new debt ratio and calculate cost of equity
Step 3: Recalculate WACC at new financing weights
Or (assuming debt is riskless)
Step 1: Unlever beta of equity
Step 2: Relever beta of equity and calculate cost of equity
Step 3: Recalculate WACC at new financing weights
Advanced Finance Debt and taxes

14. Corporate Financial Policy 2. Debt and taxes
Debt not permanent 1 2 3 4 5 6
EBITDA
340
Dep
100
EBIT
240
Interest 40 32 24 16 8
Taxes 80 83 86 90 93 96
Earnings
120
125
130
134
139
144
CFop
220
225
230
234
239
277
CFinv
-100
DIV
-20
-25
-30
-34
-39
-144
∆Debt
Book eq.
500
600
700
800
900
1,000
Debt
400
300
200
We consider here a company that plans to reduce its level of debt to zero over the next five years. The repayment schedule is fixed (ΔD = -100 from year 1 to year 5)
The financial plan is based on the following assumptions:
EBITDA is expected to remain constant
The coupon rate on the debt is 8%
Interestt = 8% Dt-1
The corporate tax rate is 40%
Cash flow from operations = Earnings + Depreciation (ΔWCR = 0)
Investment is equal to depreciation
Dividend = FCF - ΔD
Advanced Finance Debt and taxes

15. Valuation of the company
Corporate Financial Policy 2. Debt and taxes
Valuation of the company
Assumptions: rA = 10%, rD = 4%
1. Value of unlevered company
As Unlevered Free Cash Flow = 144, VU = FCFU / rA = 1,440
2. Value of tax shield (discounted with rD )
3. Value of levered company
V = 1, = 1,484
4. Value of debt
4. Value of equity
E = 1, = 980
Notice that the coupon rate on the debt is higher than the current cost of debt. Both the value of tax shields and the value of debt are calculated using rD.
Note also that the expected return on equity decrease progressively. It is calculated as follow:
rE,t = (Divt+1 + Et+1 – Et)/Et
As for the WACC it increases at the value of the tax shield decreases.
Advanced Finance Debt and taxes

16. Corporate Financial Policy 2. Debt and taxes
The leverage puzzle
If V>VU, companies should borrow as much as possible to reduce their taxes.
But observed leverage ratios are fairly low
For the US, median D/V ≈ 23%
Assume TC = 40%
Value of tax shield = TCD
Median VTS ≈ 9%
Why don’t companies borrow more?
The value of the tax shield reminds me of Nessie, the Monster of Loch Ness: everyone talks and writes about but it is very difficult to spot.
Remember that V is straightforward to observe but not VU. Recent researches have attempted to measure the value of the tax shield of US firms. Their results are still inconclusive.
For instance, Fama and French (1998) – one of the most famous team of academics - fail to find any increase in firm value associated with debt tax savings. They write: “The full regressions produce no evidence that debt has net tax benefits that enhance firm value”
On the other hand, Graham (2000) estimates the mean corporate tax benefit of debt equals approximately 10 percent of total firm value. Kemsley and Nissim (2002) find that the net tax advantage to debt is similar to the corporate tax rate.
References Fama, E. and K. French, Taxes, Financing Decisions, and Firm Value, Journal of Finance, 53, 3 (June 1998) pp Graham, J., How big are the tax benefits of debt? Journal of Finance, 55, 5 (October 2000) pp Kemsley, D. and D. Nissim, Valuation of the Debt Tax Shield, Journal of Finance, 57, 5 (October 2002) pp
Advanced Finance Debt and taxes

17. Corporate and Personal Taxes
Corporate Financial Policy 2. Debt and taxes
Corporate and Personal Taxes
Suppose operating income = 1
If paid out ast Interest Equity income
Corporate tax 0 TC
Income after corporate tax TC
Personal tax TP TPE(1-TC)
Income after all taxes 1- TP (1-TPE)(1-TC)
Several reasons have been explored to understand why companies do not borrow more. We first look at the impact of personal taxes.
A numerical example will help to understand the point.
Suppose that the corporate tax rate TC = 40%
Imagine that the company does not pay any dividend. Returns on equity are realized as capital gains. If capital gains are not taxed (as it is the case in Belgium, for instance), the personal tax rate on equity income is TPE = 0.
Suppose that, on the other hand, interest are taxed at the personal marginal tax.
Consider first an investor in very high tax bracket: TP = 60%
This investor would prefer equity to debt as the income after taxes is higher:
Income after tax = Operating income – Corporate tax – Personal tax
Interest : 1 – 0 – 0.60 = 0.40
Equity: 1 – 0.40 – 0 = 0.60
An investor in a low tax bracket (say TP = 20%) would reach the opposite conclusion:
Interest: 1 – 0 – 0.20 = 0.80
Equity: 1 – 0.40 – 0 = 0.60
She would prefer debt to equity.
Advanced Finance Debt and taxes

18. VTS with corporate and personal taxes
Corporate Financial Policy 2. Debt and taxes
VTS with corporate and personal taxes
Tax advantage of debt is positive if:
1-TP >(1-TC)(1-TPE)
Note: if TP = TPE, then VTS = TCD
Proof of VTS formula:
After taxes income for
Stockholders: (EBIT – rDD)(1 – TC)(1 – TPE)
Debtholders: rDD(1-TP)
Total: (EBIT – rDD)(1 – TC)(1 – TPE) + rDD(1-TP)
This can be written as:
Market values VU D
Advanced Finance Debt and taxes

19. Corporate Financial Policy 2. Debt and taxes
Still a puzzle….
If VTS >0, why not 100% debt?
Two counterbalancing forces:
cost of financial distress
As debt increases, probability of financial problem increases
The extreme case is bankruptcy.
Financial distress might be costly
agency costs
Conflicts of interest between shareholders and debtholders (more on this later in the Merton model)
The trade-off theory suggests that these forces leads to a debt ratio that maximizes firm value (more on this in the Leland model)
Advanced Finance Debt and taxes

20. Corporate Financial Policy 2. Debt and taxes
Trade-off theory
Market value
PV(Costs of financial distress)
PV(Tax Shield)
Value of all-equity firm
Debt ratio
Advanced Finance Debt and taxes