Formulas Midterm 1. Cost of Capital 1.1 Basic Formula cov( ri , rM ) Equity 2 M The Equity-Beta is the covariance of the stock-return with the market-return 1.2 Betas Non Investment Grade (< BBB) The Equity-Beta can be analyzed as follows: Equity E0 D0 (1 T ) Asset D0 (1 T ) Debt E0 E0 The Equity-Beta is a function of the risk of a firm’s assets (operating risk) and the amount of financial leverage. Asset D0 (1 T ) E0 Debt Equity E0 D0 (1 T ) E0 D0 (1 T ) An Asset-Beta (= unlevered Beta) reflects a firm’s operating risks without the effects of leverage. The Debt-Beta is the covariance of a firm’s debt with the market. A relevered Beta is the Equity-Beta of a firm with a new capital structure, underlying the old Asset-Beta. 1.3 Betas Investment Grade (>= BBB) E D0 (1 T ) Asset Equity 0 E0 Asset E0 Equity E0 D0 (1 T ) Debt-Beta for Investment Grade firms is statistically not relevant and can be dropped. 1.4 Financial/Operating/Market Risk D (1 T ) Equity Asset 0 ( Asset Debt ) E0 asset = operating risk Formulas for CorpFin Midterm page 2/5 Rest of term = financial risk (drops out when debt = 0) debt = 0 if debt carries no market risk 1.5 Cost of Debt rD = rf + Credit Spread 1.6 Cost of Equity CAPM: rE = rf + E(rm-rf) 1.7 Cost of Capital (WACC) D E rW ACC rD (1 T ) rE DE DE Capital structure components should be measured on a market value basis, not a book value or historic basis Use a target capital structure rather than the current or historic capital structure T always means the incremental tax-rate Debt includes long-term debt, financing leases, short-term debt, operating leases used as permanent financing, off-balance financing transactions If cash flows are real, first compute nominal WACC, then subtract inflation to get the real WACC (or better use transformation formula) Use firm or divisional capital structure not project 1.8 Divisional WACC 1. Determine capital structure of division 2. Find comparable firm (pure play) equity of comparable 3. equity of comparable: remove effects of capital structure asset of comparable 4. Assume asset of comparable = best estimate of asset of division 5. asset of division: apply divisional capital structure equity of division 6. Determine Cost of Equity and Debt of division 7. Calculate WACC Formulas for CorpFin Midterm page 3/5 2. Terminal Values 2.1 Perpetuity CF VT rW ACC 2.2 Growing Perpetuity VT CF rW ACC g 2.3 Declining Perpetuity VT CF rW ACC ( g ) 2.4 Earnings Multiple VT = Net Income * P/E P/E 1 rW ACC In simply looking at the P/E multiple, we don’t know what part of the multiple comes from the discount rate and what part comes from the growth rate. 2.5 Multiple of Sales or Book Value marketvalue VT * sales sales VT marketvalue * bookvalue bookvalue 2.6 Book Value in Liquidation Liquidation value 2.7 Time Horizon CF0 CF1 TV0 TV5 (1 rW ACC ) 5 CF2 CF3 CF4 CF5 TV5 CF6 CF6 rW ACC Formulas for CorpFin Midterm page 4/5 3. Investment Calculation 3.1 NPV “normal” NPV, incremental NPV 3.2 Payback Formula Time it takes to pay back initial investment (using undiscounted cash flows) Problems Cash Flows can be high in total but low at the beginning No consideration of time value Arbitrary choice of cut-off date 3.3 Discounted Payback Formula Same procedure but discounted cash flows Problems Same problems 3.4 Average Accounting Return Formula ARR = Average Net Income / Average Investment Problems No accounting for time values Arbitrary choice of cut-off date 3.5 IRR Formula Find discount rate where NPV is 0 (“normal” IRR and incremental IRR) Problems No consideration of scale Cannot be calculated when signs switch several time Formulas for CorpFin Midterm page 5/5 Remedy Incremental IRR (calculate IRR or NPV of incremental cash flows of two projects to compare) 3.6 Profitability Index Formula PV of cash flows after initial investment divided by initial investment 3.7 Decision rule Choose the project with the highest NPV If the incremental IRR is greater than the discount rate, choose the bigger project If the incremental NPV is positive, choose the bigger project 4. Varia 4.1 Inflation (1 + % Nominal) = (1 + % Real) + (1 + % Inflation) 4.2 Cash Flow according to Aggarwal Free Cash Flow to the firm = Net Income + Interest * (1 - Tax rate) Depreciation/Amortization - CapEx Noncash working capital Free Cash Flow to equity = see separate sheet