Corporate Financial Policy 2004-2005 WACC Professor André Farber Solvay Business School Université Libre de Bruxelles In a previous lecture, we have analyzed the impact of taxes on the value of a company in a simplified setting: constant level of debt, perpetuities. We obtained the following results: 1.The value of a levered company is equal to the value of the unlevered company plus the value of the tax shield equal to market value of debt multiplied by the corporate tax rate V = VU + TCD 2. The cost of equity and the beta of equity are increasing functions of the debt-to-equiy ratio: rE = rA + (rA – rD)(1 – TC)(D/E) βE = β A + (β A – βD)(1 – TC)(D/E) 3.Two formulas can be used to calculate the WACC a. the textbook formula WACC = rE (1 – L) + rD(1 – TC) L b. a formula derived from the value of the tax shield WACC = rA(1 – TC L) with L = D/V The objective of this lecture is to generalize these results.

How to value a levered company? Corporate Financial Policy 3. WACC How to value a levered company? Value of levered company: V = VU + VTS = E + D 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: We first show that it is always possible to express the value of a levered company as the present value of the unlevered free cash flow discounted with the WACC. This is not however very useful because the WACC might vary over time as D/V and rE vary. Practioners use a constant WACC. The problem is to understand under what condition this practice is correct. Solve: Cofipo 2005 03 WACC

Corporate Financial Policy 3. WACC Comments In general, the WACC changes over time. But to be useful, we should have a constant WACC to use as the discount rate. This can be obtained by restricting the financing policy. 2 possible financing rules: Rule 1: Debt fixed 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) Two possible financing rules under which the WACC is constant have been identified in the litterature. Rule 1. Debt fixed + constant perpetual free cash flow. This is the situation analyzed by Modigliani and Miller. In this approach, D is a constant (and thus VTS = TCD). VU is also a constant because of the assumption of a constant perpetuity Rule 2. Debt rebalanced The level of debt is adjusted to keep the ratio D/V constant. This financing rule was introduced by Miles and Ezzel in 1980. It can be used to value any set of future cash flow. Cofipo 2005 03 WACC

Corporate Financial Policy 3. WACC A general framework V = VU + VTS = E + D Value of equity rA rE Value of all-equity firm rD Value of debt rTS Value of tax shield I propose here a general framework to understand the relationship between the value of the tax shield, the cost of equity and the weighted average cost of capital. Suppose that you have a model that gives the value of the tax shield. Let rTS be the discount rate used to calculate this value. As the balance sheet balances, the expected return on the liability side is equal to the expected return on the asset side: This equality leads to formulas for the expected return on equity rE (and the beta of equity) and the weighted average cost of capital WACC Cofipo 2005 03 WACC

Cost of equity calculation Corporate Financial Policy 3. WACC Cost of equity calculation If rTS = rD (MM) and VTS = TCD We derive here the expression for the expected return on equity. The MM formula turns out to be one particular case of this general formula. Similar formulas for beta equity (replace r by β) Cofipo 2005 03 WACC

Corporate Financial Policy 3. WACC If rTS = rD and VTS = TC D (MM) We now derive a general formula for the WACC. We show that the MM formula is a special case of the general formula. Cofipo 2005 03 WACC

Rule 1: Debt fixed (Modigliani Miller) Corporate Financial Policy 3. WACC Rule 1: Debt fixed (Modigliani Miller) Assumption: constant perpetuities FCFt = EBIT(1-TC) = rA VU D constant. Define: L = D/V In the fixed debt financing rule analyzed by MM: D is a constant →VTS = TCD is also a constant VU is a constant since EBIT is a constant perpetuity →V is a constant Cofipo 2005 03 WACC

Rule 2a: Debt rebalanced (Miles Ezzel) Corporate Financial Policy 3. WACC Rule 2a: Debt rebalanced (Miles Ezzel) Assumption: any cash flows Debt rebalanced Dt/Vt = L ( a constant) We now turn to rule 2. The level of debt is rebalanced to keep the ratio D/V constant. Consider a finite set of future cash flows FCF1,…,FCFT The value at time T-1 is: VT-1 = FCFT/(1+rA) + rDTCLVT-1/(1+rD) = VU,T-1+αVT-1 with α = rDTCL/(1+rD) Therefore: VT-1 = VU,T-1/(1 – α) = FCFT /[(1- α)(1+rA)] and VT-1 = VU,T-1 + VTST-1 = VU,T-1 + [α/(1 – α)]VU,T-1 This means that VT-1 is proportional to VU,T-1 and hence has the same risk. At time T-2: VT-2 = FCFT-1/(1+rA) + α VT-2 + VT-1/(1+rA) The subtle point (and the key insight of Miles and Ezzel) is to have proven that the discount rate to use for VT-1 is rA. Some tedious algebra leads to: VT-2 = FCFT-1 /[(1- α)(1+rA)] + FCFT /[(1- α)(1+rA)]² This expression shows that the weighted average cost of capital is: WACC = [(1- α)(1+rA)] = rA – rDTCL(1+rA)/(1+rD) and VT-2 = VU,T-2 + VTST-2 = VU,T-2 + [α/(1 – α)]VU,T-1 + VTST-1/ [(1 – α)(1+rA)] This last expression leads to the value of the tax shield. VTSt = [α/(1 – α)]VU,t +VTSt+1/[(1 – α)(1+rA)] Not a straightfoward expression, I agree. Cofipo 2005 03 WACC

Corporate Financial Policy 3. WACC Miles-Ezzel: example Base case NPV = -300 + 340.14 = +40.14 Data Investment 300 Pre-tax CF Year 1 50 Year 2 100 Year 3 150 Year 4 100 Year 5 50 rA 10% rD 5% TC 40% L 25% Using Miles-Ezzel formula WACC = 10% - 0.25 x 0.40 x 5% x 1.10/1.05 = 9.48% APV = -300 + 344.55 = 44.85 Initial debt: D0 = 0.25 V0 = (0.25)(344.55)=86.21 Debt rebalanced each year: Year Vt Dt 0 344.55 86.21 1 327.52 81.88 2 258.56 64.64 3 133.06 33.27 4 45.67 11.42 Using MM formula: WACC = 10%(1-0.40 x 0.25) = 9% APV = -300 + 349.21 = 49.21 Debt: D = 0.25 V = (0.25)(349.21) = 87.30 No rebalancing Cofipo 2005 03 WACC

Corporate Financial Policy 3. WACC Miles-Ezzel: example Table 1 Table 2 Here you have the details of the example. All calculations are performed starting from the final year and moving back in time. Table 1 shows the two possible decompositions of the value of the company: V = VU + VTS V = E + D where Vt = (FCFt+1+Vt+1)/(1+WACC) VU,t = (FCFt+1+Vt+1)/(1+rA) Table 2 verifies the relationship: It is based on the following equations: Divt = FCFt + TCrDDt-1 – rDDt-1 + (Dt – Dt-1) Intt = rDDt-1 rTS,t = (TC rDDt + VTSt+1 – VTSt)/VTSt rE,t = (Divt+1 + Et+1 – Et)/Et Note that both VTS/V and rTS vary of time. At time T-1 (year 4 in our example), the tax shield is riskless. As time to the final year increases, the risk of the tax shield increases. Cofipo 2005 03 WACC

Rule 2b: Debt rebalanced (Harris & Pringle) Corporate Financial Policy 3. WACC Rule 2b: Debt rebalanced (Harris & Pringle) Any free cash flows – debt rebalanced continously Dt = L Vt The risk of the tax shield is equal to the risk of the unlevered firm rTS = rA Rule 2b is a variant of the Miles-Ezzel method proposed by Harris and Pringle in 1985. As in the Miles-Ezzel setting, the level debt is rebalanced to keep the ratio Dt/Vt constant. However, this is done continuously. The only difference with the Miles-Ezzel analysis is that the tax shield of the following year is discounted with rA (the tax shield is the same risk as the cash flow of the unlevered firm). The rest of the development is identical to Miles-Ezzel. Consider again a finite set of future cash flows FCF1,…,FCFT The value at time T-1 is: VT-1 = FCFT/(1+rA) + rDTCLVT-1/(1+rA) = VU,T-1+αVT-1 with α = rDTCL/(1+rA) (instead of α = rDTCL/(1+rD) in Miles-Ezzel) This leads to: VT-2 = FCFT-1 /[(1- α)(1+rA)] + FCFT /[(1- α)(1+rA)]² The weighted average cost of capital is: WACC = [(1- α)(1+rA)] = rA – rDTCL and the value of the tax shield is VTSt = VU,t + [α/(1 – α)]VU,t + VTSt+1/ [(1 – α)(1+rA)] Cofipo 2005 03 WACC

Harris-Pringle: example Corporate Financial Policy 3. WACC Harris-Pringle: example Here we illustrate the Harris-Pringle method with the data used in the Miles-Ezzel example. The only noteworthy difference is that rTS is now a constant equal to rA Cofipo 2005 03 WACC

Corporate Financial Policy 3. WACC Summary of Formulas Modigliani Miller Miles Ezzel Harris-Pringle Operating CF Perpetuity Finite or Perpetual Finite of Perpetual Debt level Certain Uncertain First tax shield WACC L = D/V rE(E/V) + rD(1-TC)(D/V) rA (1 – TC L) rA – rD TC L Cost of equity rA+(rA –rD)(1-TC)(D/E) rA+(rA –rD) (D/E) Beta equity βA+(βA – βD) (1-TC) (D/E) βA +( βA – βD) (D/E) Source: Taggart – Consistent Valuation and Cost of Capital Expressions With Corporate and Personal Taxes Financial Management Autumn 1991 Cofipo 2005 03 WACC

Constant perpetual growth Corporate Financial Policy 3. WACC Constant perpetual growth Which formula to use if unlevered free cash flows growth at a constant rate? In a provocative paper, Fernandez (2004) challenges the solutions currently proposed in the leading corporate finance textbooks. Fernandez claims that the value of tax shields is not the present value of tax shields. He argues that the correct value of tax shields is equal to the difference between the present value of taxes paid by the unlevered company and the present value of taxes paid by the levered company. These present values should be calculated using different discount rates. The example shows that substantial valuation differences appear depending on the method. A lively debate is currently taking place to clarify the issue. Cofipo 2005 03 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) Cofipo 2005 03 WACC

Capital Cash Flow Valuation Assumptions: CAPM holds PV(Tax Shield) as risky as operating assets Capital cash flow =FCF unlevered +Tax shield Cofipo 2005 03 WACC

Capital Cash Flow Valuation: Example Cofipo 2005 03 WACC