【正文】 d ?sustainable growth rate? Corporate Finance Pitfalls ? The dgrowth model makes a number of assumptions: ? constant growth rate ? constant dividend yield ? The validity of the model depends on the validity of these assumptions Corporate Finance Cost of Debt ? The rate of return that debtholders demand to hold the debt ? Remember: it is the expected return and not the promised one ? For highrated bonds, promised is probably a good proxy Corporate Finance Discount Rate for Debt ? In practice: ? Rate on new or recent borrowings ? Yield on parable 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 II] Corporate Finance Discount Rate for Debt ? Same logic can be used to calculate expected returns ? Assuming EAD = 1: rD = (1 – PD) x i + PD x LGD ? . interest (i) is 14%, PD is 4%, recovery rate is 60%. Then, cost of debt is: rD = x 14% + x 40% = % Corporate Finance Discount rate for debt ? Alternative ways: ? CAPM: ? if there is little debt, assume bD =0 ? if debt is risky, use proxies based on empirical research: Type Beta 15 years .08 610 years .13 Government Bonds Type Beta Aaa .20 Aa .20 A .21 Baa .23 Lower Grade .31 Corporate Bonds Corporate Finance Example ? Company XYZ wants to issue a 30year bond, coupon 5% ? No bonds outstanding, credit risk similar to General Tool Company ? The latter issued last year a 31year bond, coupon %, selling today at 97% ? 3month Tbills pay 5% a year ? Which discount rate should be used? Corporate Finance Example ? 1. Direct parison: %)(0)1(1060...)1(60160970302????????????y i e l dI R RI R RI R RI R RCorporate Finance Example ? 2. CAPM: ?A? bond: ? Beta of an Abond is ? Using CAPM, and a market premium of 6%: ? E(rD) = % + .21 x 6% = % Capital budgeting Corporate Finance Capital 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 estimate Corporate Finance A fresh look at NPV NPV = PV – investment ? PV = value of a tracking portfolio that replicates the project?s payoffs ? NPV 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?? Corporate Finance Riskfree project: NPV Month 0 6 12 Project 200 100 120 TBill 97 100 TBond 90 100 Replicating portfolio (NPV) T Bill 1 T Bond Payoff rep. portf. 100 120 Corporate Finance Riskfree project: NPV (cont) ? The NPV is thus the difference, the arbitrage opportunity [ = 90 x + 97] Costs Repl. Port. 205 Project 200 Project39。 CAPM ? This is the socalled Hamada model, used to calculate cost of equity for different capital structures ? In practice, used to “unlever” and “relever” betas ???????? ???LCUEL EDT )1(1bbCorporate Finance Reference ? MM in 559564 ? MM amp。M II, rLE = r + (r – rD) (1Tc)D/EL Hence, it must be true that: r + (r – rD) (1Tc)D/EL = r f + biE[Rm – rf] where r = r f + bUE[Rm – rf ] Corporate Finance MM amp。 industries ? Taxes (. nondebt tax shields), asset structure (through costs of financial distress and availability of collateral), risk (uncertainty of cash flows) are significant ? Some evidence in favour of the pecking order theory Corporate Finance MM amp。 ? There are no transaction costs, ? No arbitrage opportunities exist, ? Then the total market value of the firm (the sum of the values all sources of capital) is independent of how the firm is financed Corporate Finance Proof ? Suppose firms U and L are identical, except for their capital structures ? U (unlevered) is 100% equity financed, and is worth 800 ? L (levered) is (partially) financed with debt. It has a zero coupon bond with a face value of 600 ? Consider two time periods only: t = 0 (now) and t = 1 ? CF at t = 1 is random: x ? {0, 600, 1000, 2020}, all equally likely Corporate Finance Proof ? For the levered firm, payoffs to equity and debt are: xD = xD = 600 xD = 600 xD = 600 xD = 0 xD = xE = 0 xE = 1400 xE = 400 xE = 0 Corporate Finance Proof ? Claim: VU = VL , ? where VL = VEL + VDL ? Suppose not. Then: ? Strategy A: Buy 50% of firm U ? Strategy B: buy 50% of the debt of L and 50% of its equity Corporate Finance Proof ? The two strategies provide exactly the same payoffs