Advanced Finance Modigliani Miller + Debt and Taxes

Advanced Finance 2007-2008 Modigliani Miller + Debt and Taxes
Corporate Financial Policy 2. Debt and taxes Advanced Finance Modigliani Miller + 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 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 MM + Debt and taxes

MM 58: Proof by arbitrage Consider two firms (U and L) with identical operating cash flows X VU = EU VL = EL + DL Current cost Future payoff Buy α% shares of U αEU = αVU αX ______________________________ Buy α% bonds of L αDL αrDL Buy α% shares of L αEL α(X – rDL) Total αDL + αEL = αVL αX As the future payoffs are identical, the initial cost should be the same. Otherwise, there would exist an arbitrage opportunity In 1958, when MM published their paper, the Capital Asset Pricing Model did not exist. Modigliani and Miller were among the first authors to base their result on the absence of arbitrage opportunities in competitive markets. When asked to explain the theorem of American TV viewers, Miller presented the proposition as follow “Think of the firm as a gigantic pizza, divided into quarter. If now you cut each quarter in half into eights, the M and M proposition says that you will have more pieces but not more pizza” Or, as Yogi Berra, the famous basket ball player, would put it: “You better cut the pizza in four pieces because I’m not hungry enough to eat six” References: Miller, M., The history of finance, Journal of Portfolio Management, Summer 1999 Advanced Finance MM + Debt and taxes

MM 58: Proof using CAPM 1-period company C = future cash flow, a random variable Unlevered company: Levered (assume riskless debt): So: E + D = VU The CAPM can be used to prove MM Proposition I. Remember, however, that the proposition does not require the CAPM. Reference: Rubinstein, M., A Mean-Variance Synthesis of Corporate Financial Policy =VU Advanced Finance MM + Debt and taxes

MM 58: Proof using state prices
Corporate Financial Policy 2. Debt and taxes MM 58: Proof using state prices 1-period company, risky debt: Vu>F but Vd<F If Vd < F, the company goes bankrupt Current value Up Down Cash flows VUnlevered Vu Vd Equity E Vu – F Debt D F Example. Consider an unlevered company with a market value equal to 100. Suppose that the length of one period is 1 year. The continuously compounded risk-free interest rate is 5%. The volatility of the unlevered company is 69.31%. During the period, the value of the company will either double (u = 2) or be divided by 2 (d = 0.5). Based on these parameters, the state prices are vu = and vd = 0.602 The company decides to borrow and to use the proceed to buy back some of its shares. It issues a one-year zero-coupon with a face value F = 60. In the up state: Vu = 200 The company repays its debt The market value of the equity is equal to 200 – 60 = 140 The market value of the debt is equal to 60 If the down state: Vd = 50 The company is unable to repay its debt: it goes bankrupt Stockholders lose everything. The market value of equity is 0 Bondholder take over the company. The market value of the debt is 50 Using the state prices, we can calculate the initial value of the equity and of the debt: E = × 140 = 48.94 D = × × 50 = 51.06 Notice that the value of the risky debt is lower than the value of the riskless debt (60 × e-5% = 57.07) More on this later in the course. Advanced Finance MM + Debt and taxes

Weighted average cost of capital
Corporate Financial Policy 2. Debt and taxes Weighted average cost of capital V (=VU ) = E + D Value of equity rEquity Value of all-equity firm rAsset rDebt Value of debt We now want the understand the implication of MM Proposition I on the weighted average cost of capital of a company. Consider the balance sheet (using market values) of a company. It can be viewed either from the asset side or from the liability side. When viewed from the liability side, the weighted average cost of capital is the expected return on a portfolio of both equity and debt. Consider someone owning a portfolio of all firm’s securities (debt and equity) with XEquity = E/V and XDebt = D/V Expected return on portfolio = rEquity * XEquity + rDebt * XDebt This is equal to the WACC (see definition): rPortoflio = WACC But she/he would, in fact, own a fraction of the company. The expected return would be equal to the expected return of the unlevered (all equity) firm rPortoflio = rAsset The weighted average cost of capital is thus equal to the cost of capital of an all equity firm WACC = rAsset WACC Advanced Finance MM + Debt and taxes

MM II Required return to equityholders: Expected return on equity is an increasing function of leverage. Beta Equity vs Beta Asset: Weighted Average Cost of Capital: This is another presentation of the equality: WACC = rAsset This presentation shows that the cost of equity increases with leverage. If a company replace equity with debt, two things happens: The company saves money because the cost of debt is lower than the cost of equity On the other hand, the remaining equity becomes more costly. The reason why the cost of equity increases with leverage is because the risk is higher. Remember that the beta of a portfolio is equal to the weighted average of the betas of the individual securities in the portfolio. In the MM 58 framework, the two effects offset each other. Advanced Finance MM + Debt and taxes

Advanced Finance MM + Debt and taxes

Summary: the Beta-CAPM diagram
Corporate Financial Policy 2. Debt and taxes Summary: the Beta-CAPM diagram   Beta L βEquity U βAsset r rEquity rAsset rDebt=rf D/E The IS-LM diagram used by economist is the source of inspiration for this figure. For many years, I have tried to create a figure which would look as impressive as the IS-LM diagram. Here is the result. The figure in the first quadrant shows the relationship between the debt-equity ratio and the beta equity. The figure is based on the assumption that the debt is riskless. In that case, the relationship is linear. The security market line in illustrated in the second quadrant.  The relationship between the debt-equity ratio and the cost of equity, the cost of debt and the WACC is in the third quadrant  This is simply a -45% line. This diagram can be used to show that investors can choose the level of leverage that they wish by rebalancing their portfolios. If the company has no debt (point U), an investor can create leverage by borrowing at the risk-free interest to reach L, the risk and expected returns of a levered company. If, on the hand, the company is levered (point L), an investor can allocate his money between the stock of the levered company and the risk free asset to undo the leverage and reach point U.   rEquity rDebt D/E WACC Advanced Finance MM + 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 MM + 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 MM + 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 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 MM + 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 MM + Debt and taxes

Advanced Finance MM + 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 MM + 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 MM + 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 MM + 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 MM + 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 MM + 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 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 MM + 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 MM + 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 MM + 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 MM + Debt and taxes

Advanced Finance Modigliani Miller + Debt and Taxes

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