Cost of Capital and Investment decisionsWACCWACC Under the assumptions of MM, If the company undertakes a new investment project with same risk as the rest of the company, the change in value is:3WACC The new investment is financed with debt or equity or both The change in value can also be seen from the liability side:4WACC If DBo = 0, and using the fact that DI = DSn +DBn The project adds value for the shareholders if5WACC Using (*) in (*): If we assume that there is a target capital structure and therefore that DB/DI = D/(D+E), the termis the WACC6Derivation:7WACC lessons Notice that the standard WACC is a by product of MM, and therefore is relies on the same assumptions Notice also there is something intrinsically contradictory in the way it is often applied:You start assuming a constant debt level Then you assume a target debt ratio When the debt ratio is assumed constant, the WACC formula ought to be different8Miles-Ezzel WACC: dynamic debt If we assume the debt ratio is constant, the WACC formula is And the formula for relevering betas is9Cost of equity: CAPM The discount rate for risky investments (expected return) covers:The time value of money A risk premiumE(ri) = rf +bi(E(rm) - rf)This is the most used method to calculate costs of equityAlternative: APT (see book for details if interested)10Alternative: Dividend Growth Model Gordons growth model: Thus: 11Applying it: Need dividend yield and growth rate:use analysts forecasts use the plowback ratio formula: g = b x ROE, where b is the retention ratio Note: this g is the so-called sustainable growth rate 12Pitfalls The d-growth model makes a number of assumptions:constant growth rate constant dividend yield The validity of the model depends on the validity of these assumptions13Cost of Debt The rate of return that debt-holders demand to hold the debt Remember: it is the expected return and not the promised one For high-rated bonds, promised is probably a good proxy14Discount Rate for Debt In practice:Rate on new or recent borrowings Yield on comparable bonds Both are measures of promised yield Expected return depends on:Probability of default Exposure at default Loss given default Expected loss on a loan is:PD x EAD x LGD These are the terms used by Basel II15Discount Rate for Debt Same logic can be used to calculate expected returns Assuming EAD = 1:rD = (1 PD) x i + PD x LGDE.g. interest (i) is 14%, PD is 4%, recovery rate is 60%. Then, cost of debt is:rD = 0.96 x 14% + 0.04 x 40% = 11.84% 16Discount rate for debt Alternative ways: CAPM: if there is little debt, assume D =0 if debt is risky, use proxies based on empirical research:TypeBeta 1-5 years.08 6-10 years.13Government Bonds TypeBeta Aaa.20 Aa .20 A.21 Baa.23 Lower Grade.31Corporate Bonds17ExampleCompany XYZ wants to issue a 30-year bond, coupon 5% No bonds outstanding, credit risk similar to General Tool Company The latter issued last year a 31-year bond, coupon 6.0%, selling today at 97% 3-month T-bills pay 5% a year Which discount rate should be used?18Example 1. Direct comparison:19Example 2. CAPM: A bond: Beta of an A-bond is 0.21 Using CAPM, and a market premium of 6%: E(rD) = 5.0% + .21 x 6% = 6.26%20Capital budgetingCapital Budgeting The CB problem amounts to deciding which projects a firm should undertake NPV is the most sound rule for CB A project should be undertaken if NPV 0 To implement NPV one needs:cash flow estimates cost of capital estimate22A fresh look at NPVNPV = PV investmentPV = value of a tracking portfolio that replicates the projects payoffsNPV 0 same payoffs can be obtained in a cheaper way in the (financial) markets Thus positive NPV projects are “arbitrage opportunities”Q: Why do they not disappear immediately?23Risk-free project: NPVMonth0612Project-200100120T-Bill-97100 T-Bond-90100Replicating portfolio (NPV)T Bill1 T Bond1.2Payoff rep. portf.10012024Risk-free project: NPV (cont) The NPV is thus the difference, the arbitrage opportunity = 90 x 1.2 + 97CostsRepl. Port.-205Project-200Projects NPV525Risk-free project: DCF 3.09% (11.11%) is the yield on the 6-month (12- month) T Bill:= 120 / 1.1111= 100 / 1.0309DCFDiscount rates3.09%11.11%PV cash flows-20097108NPV526Risky Projects The underlying principles are the same Replicating portfolio Discount rates (now risk-adjusted)27CAPM Rewriting the CAPM formula we get:E(ri) = rf +bi(E(rm) - rf) = rf (1 bi) + bi E(rm) ie the expected return on the project equals the expected return on a portfolio consisting of:A fraction of the investment in the market portfolio 1 in the risk-free asset which is the tracking portfolio for the investment.28Discount Rate for a Project In theory, a projects discount rate:reflects the expected return investors require to hold financial assets (those in the replicating portfolio) whose cash flows are thus in the same risk class as the