Section A: Finance Theory II - WACC and APV 1

What Next? • We need to incorporate the effects of financial policy into our valuation models. Ÿ Question: How do we incorporate debt tax shields (if any) into our valuation? Two Approaches: • Weighted Average Cost of Capital (WACC): → Discount the FCF using the weighted average of after-tax debt costs and equity costs WACC = k D (1 − t ) D E + kE D+E D+E • Adjusted Present Value (APV): → Value the project as if it were all-equity financed → Add the PV of the tax shield of debt and other side effects Recall: Free Cash Flows are cash flows available to be paid to all capital suppliers ignoring interest rate tax shields (i.e., as if the project were 100% equity financed). WACC Weighted Average Cost of Capital (WACC) • Step 1: Generate the Free Cash Flows (FCFs) • Step 2: Discount the FCFs using the WACC WACC = k D (1− t ) D E + kE D+E D+E WARNING!!! • The common intuition for using WACC is: → “To be valuable, a project should return more than what it costs us to raise the necessary financing, i.e., our WACC” → This intuition is wrong. • Using WACC this way is OK sometimes... but “by accident”. • Most of the time, it is plain wrong: → conceptually, i.e., the logic is flawed → practically, i.e. gives you a result far off the mark Discount rates and hence the WACC are project specific! Weighted Average Cost of Capital (WACC) • Discount rates are project-specific ==> Imagine the project is a stand alone, financed as a separate firm. ==> The WACC inputs should be project-specific as well: WACC = k D (1 − t ) D E + kE D+E D+E • Let’s look at each WACC input in turn: Leverage Ratio D/(D+E) • D/(D+E) should be the target capital structure (in market values) for the particular project under consideration. • Common mistake 1: → Using a priori D/(D+E) of the firm undertaking the project. • Common mistake 2: → Use D/(D+E) of the project’s financing → Example: Using 100% if project is all debt financed. Caveat: We will assume that the target for A+B is the result of combining target for A and target for B. It’s OK most of the time. Leverage Ratio (cont.) • So how do we get that “target leverage ratio”? • Use comparables to the project: → “Pure plays” in the same business as the project → Trade-off: Number vs. “quality” of comps • Use the firm undertaking the project if the project is very much like the rest of the firm (i.e. if the firm is a comp for the project). • Introspection, improved by checklist,... Important Remark: • If the project maintains a relatively stable D/V over time, then WACC is also stable over time. • If not, then WACC should vary over time as well and we should compute a different WACC for each year. • In practice, firms tend to use a constant WACC. • So, in practice, the WACC method does not work well when the capital structure is expected to vary substantially over time. Cost of Debt Capital: kD (cont.) • Can often look it up: Should be close to the interest rate that lenders would charge to finance the project with the chosen capital structure. • Caveat: Cannot use the interest rate as an estimate of kD when: → Debt is very risky. We would need default probabilities to estimate expected cash flows. → If there are different layers of debt. We would need to calculate the average interest rate. Marginal Tax Rate: t • It’s the marginal tax rate of the firm undertaking the project (or to be more precise, of the firm including the project). • Note that this is the rate that is going to determine the tax savings associated with debt. • We need to use the marginal as opposed to average tax rate t. → In practice, the marginal rate is often not easily observable. Cost of Equity Capital: kE • Cannot look it up directly. • Need to estimate kE from comparables to the project: → “Pure Plays”, i.e. firms operating only in the project’s industry. → If the firm undertaking the project is itself a pure play in the project’s industry, can simply use the kE of the firm. • Problem: → A firm’s capital structure has an impact on kE → Unless we have comparables with same capital structure, we need to work on their kE before using it. Using CAPM to Estimate kE 1) Finds comps for the project under consideration. 2) Unlever each comp’s βE (using the comp’s D/(D+E)) to estimate its βA. When its debt is not too risky (and its D/V is stable), we can use: ȕA = ȕE E E +D 3) Use the comps’ βA to estimate the project’s βA (e.g. take the average). 4) Relever the project’s estimated βA (using the project’s D/(D+E) to estimate its βE under the assumed capital structure. When the project’s debt is not too risky (and provided its D/V is stable), we can use: ȕE = E+D ª Dº ȕ A = «1 + » ȕ A E ¬ E¼ 5) Use the estimated βE to calculate the project’s cost of equity kE: kE = rf + βE * Market Risk Premium Remarks on Unlevering and Relevering: • Formulas: → Relevering formulas are reversed unlevering formulas. • Procedure: → Unlever each comp, i.e., one unlevering per comp. → Estimate one βA by taking the average over all comps’ βA possibly putting more weight on those we like best. → This is our estimate of the project’s βA. → Relever that βA. • In the course, we use mostly the formula for a constant D/(D+E). More on Business Risk and Financial Risk βA = βE E E +D ⇔ § D· βE = ¨1+ ¸ × βA © E¹ ⇔ βE − βA = D ×β E A • Comparable firms have similar Business Risk ==> Similar asset beta βA and, consequently, similar unlevered cost of capital kA • Comparable firms can have different Financial Risk (different βE- βA) if they have different capital structures ==> Different equity beta βE and thus different required return on equity kE • In general, equity beta βE increases with D/E → Consequently the cost of equity kE increases with leverage. Business Risk and Financial Risk: Intuition • Consider a project with βA>0 • Its cash flows can be decomposed into: → Safe cash-flows → Risky cash-flows that are positively correlated with the market. • As the level of debt increases (but remains relatively safe): → A larger part of the safe cash-flows goes to debtholders; → The residual left to equityholders is increasingly correlated with the market. Note: If cash-flows were negatively correlated with the market (βA<0), increasing debt would make equity more negatively correlated with the market and would reduce the required return on equity. WACC – A simple example: You are evaluating a new project. The project requires an initial outlay of $100 million and you forecast before-tax profits of $25 million in perpetuity. The marginal tax rate is 40%, the project has a target debt-to-value ratio of 25%, the interest rate on the project’s debt is 7%, and the cost of equity is 12%. After-tax CFs = $25 × 0.60 = $15 million After-tax WACC = D/V * (1–t) * rd + E/V * re = 0.25 × 0.60 × 0.07 + 0.75 × 0.12 = 10.05% NPV = -100 + 15 / 0.1005 = $49.25 million How Firms Tend to Use WACC: They calculate their WACC using: • Their current cost of debt kD • Their own current capital structure D/(D+E) • Their own current cost of equity capital kE • The marginal tax rate they are facing They discount all future FCF with: • this (single) discount rate • maybe adjusted for other things (e.g., project’s “strategic value”) Ÿ This practical approach can be very misleading, especially if the new project is very different from the firm undertaking it. Selected Industry Capital Structures, Betas, and WACCs Industry Electric and Gas Food production Paper and plastic Equipment Retailers Chemicals Computer software Average of all industries Debt ratio (%) 43.2 22.90 30.40 19.10 21.70 17.30 3.50 Equity beta 0.58 0.85 1.03 1.02 1.19 1.34 1.33 Asset beta 0.33 0.66 0.72 0.83 0.93 1.11 1.28 WACC (%) 8.1% 11.0% 11.4% 12.4% 13.2% 14.7% 16.2% 21.50 1.04 0.82 12.3% Assumptions: Risk-free rate 6%; market risk premium 8%; cost of debt 7.5%; tax rate 35% APV Adjusted Present Value • Separates the effects of financial structure on value from the estimation of asset values. • Step 1: Value the project or firm as if it were 100% equity financed. • Step 2: Add the value of the tax shield of debt. Note: • This is simply applying MM-Theorem with taxes • APV = Valuation by Components = ANPV Step 1: Value as if 100% Equity Financed • Cash-flows: Free Cash Flows are exactly what you need. • You need the rate that would be appropriate to discount the firm’s cash flows if the firm were 100% equity financed. • This rate is the expected return on equity if the firm were 100% equity financed. • To get it, you need to: → Find comps, i.e., publicly traded firms in same business. → Estimate their expected return on equity if they were 100% equity financed. Step1: Value if 100% Equity Financed (cont.) • Unlever each comp’s βE to estimate its asset beta (or all equity or unlevered beta) βA using the appropriate unlevering formula ȕA = ȕE E E +D or ȕA = ȕE E E + (1 − t)D • Use the comps’ βA to estimate the project’s βA (e.g. average). • Use the estimated βA to calculate the all-equity cost of capital kA kA = rf + βA * Market Risk Premium • Use kA to discount the project’s FCF Step 2: Add PV(Tax Shield of Debt) • Cash-flow: The expected tax saving is tkDD where kD is the cost of debt capital (discussed earlier). • If D is expected to remain stable, then discount tkDD using kD PVTS = tkDD/ kD= tD • If D/V is expected to remain stable, then discount tkDD using kA PVTS = tkDD/ kA • Intuition: → If D/V is constant, D (tkDD) and thus moves up/down with V → The risk of tkDD is similar to that of the firm’s assets: use kA Step 2: Add PVTS (cont.) • For many projects, neither D nor D/V is expected to be stable. • For instance, LBO debt levels are expected to decline. • In general you can estimate debt levels using: → repayment schedule if one is available, → financial forecasting and discount by a rate between kD and kA. Extending the APV Method • One good feature of the APV method is that it is easy to extend to take other effects of financing into account. • For instance, one can value an interest rate subsidy separately as the PV of interest savings. APV= NPV(all-equity) + PV(Tax Shield) + PV(other stuff) WACC vs. APV Pros of WACC: Most widely used • Less computations needed (important before computers). • More literal, easier to understand and explain (?) Cons of WACC: • Mixes up effects of assets and liabilities. Errors/approximations in effect of liabilities contaminate the whole valuation. • Not very flexible: What if debt is risky? Cost of hybrid securities (e.g., convertibles)? Other effects of financing (e.g., costs of distress)? Non-constant debt ratios? Personal taxes? Note: For non-constant debt ratios, could use different WACC for each year (see appendix) but this is heavy and defeats the purpose. WACC vs. APV (cont.) Advantages of APV: • No contamination. • Clearer: Easier to track down where value comes from. • More flexible: Just add other effects as separate terms. Cons of APV: • Almost nobody uses it. Overall: • For complex, changing or highly leveraged capital structure (e.g., LBO), APV is much better. • Otherwise, it doesn’t matter much which method you use. Appendix I - Relation to MM Theorem Relation to MM Theorem • Without taxes, WACC is independent of leverage. • Indeed, for simplicity, think in terms of CAPM (although the result does not rely on CAPM being true). D E WACC = kD + kE D+E D+E D E = [r f + ȕD ⋅ Mkt Prem.] + [r f + ȕE ⋅ Mkt Prem.] D+E D+E E º D ª ⋅ Mkt Prem. = r f + «ȕD + ȕE D + E »¼ ¬ D+E = r f + ȕA ⋅ Mkt Prem. • The last expressions does not contain leverage – WACC does not depend on it. The WACC Fallacy (Revisited) • The cost of debt is lower than the cost of equity (true). • Does this mean that projects should be financed with debt? WACC = k D D E + kE D +E D +E • No: WACC is independent • As you are tapping into cheap debt, you are increasing the cost of equity (its financial risk increases). Without taxes, WACC is independent of leverage: 20% rE 18% 16% 14% rA = WACC 12% 10% rD 8% 6% 0 0.2 0.4 0.6 Debt-to-equity 0.8 1 1.2