Advanced Finance 2005-2006 Debt and Taxes Corporate Financial Policy 2. Debt and taxes Advanced Finance 2005-2006 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.

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 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. Advanced Finance 2006 02 Debt and taxes

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 2006 02 Debt and taxes

Corporate Financial Policy 2. Debt and taxes Example U L Balance Sheet Total Assets 1,000 1,000 Book Equity 1,000 500 Debt (8%) 0 500 Income Statement EBIT 200 200 Interest 0 40 Taxable Income 200 160 Taxes (40%) 80 64 Net Income 120 96 Dividend 120 96 Total 120 136 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 = 1,200 + 320 = 1,520 (4) Market value of equity: D = 40/.05 = 800 EL = VL - D = 1,520 - 800 = 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 2006 02 Debt and taxes

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 2006 02 Debt and taxes

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 0.47 + 5% x 0.60 x 0.53 = 7.89% Advanced Finance 2006 02 Debt and taxes

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 2006 02 Debt and taxes

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 2006 02 Debt and taxes

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 2006 02 Debt and taxes

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 2006 02 Debt and taxes

Corporate Financial Policy 2. Debt and taxes MM formula: example Data Investment 100 Pre-tax CF 22.50 rA 9% rD 5% TC 40% Base case NPV: -100 + 22.5(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%(1-0.40 × 0.50) = 7.2% NPV = -100 + 22.5(1-0.40)/.072 = 87.50 Same as APV introduced previously? To see this, first calculate D. As: V =VU + TC D =150 + 0.40 D and: D = 0.50 V V = 150 + 0.40 ×0.50× V → V = 187.5 → D = 93.50 → APV = NPV0 + TC D = 50 + 0.40 × 93.50 = 87.50 Advanced Finance 2006 02 Debt and taxes

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 0.50 + 5% x (1– 0.40) x 0.50 = 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 2006 02 Debt and taxes

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 2006 02 Debt and taxes

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 2006 02 Debt and taxes

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 = 1,440 + 44 = 1,484 4. Value of debt 4. Value of equity E = 1,484 - 555 = 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 2006 02 Debt and taxes

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 819-843 Graham, J., How big are the tax benefits of debt? Journal of Finance, 55, 5 (October 2000) pp. 1901-1941 Kemsley, D. and D. Nissim, Valuation of the Debt Tax Shield, Journal of Finance, 57, 5 (October 2002) pp. 2045--2073 Advanced Finance 2006 02 Debt and taxes

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 1 1 - 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 2006 02 Debt and taxes

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 2006 02 Debt and taxes

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 2006 02 Debt and taxes

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 2006 02 Debt and taxes