Formulas for Corpfin Midterm Page 2/1

Formulas Midterm

1. Cost of Capital

1.1 Basic Formula

Equity cov(ri ,rM )   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: E  D (1 T) D (1 T )  Equity  0 0  Asset  0  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. D (1 T) E  Asset  0  Debt  0  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  D (1 T)  Equity  0 0  Asset E0 E  Asset  0  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 Formulas for CorpFin Midterm page 2/5

asset = operating risk 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  rWACC   rD (1 T)   rE  D  E   D  E 

 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  rWACC 2.2 Growing Perpetuity

CF VT  rWACC  g 2.3 Declining Perpetuity CF VT  rWACC  (g) 2.4 Earnings Multiple

VT = Net Income * P/E 1 P / E  rWACC 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 V  * sales T sales

marketvalue V  *bookvalue T bookvalue 2.6 Book Value in Liquidation Liquidation value

2.7 Time Horizon

CF0 CF1 CF2 CF3 CF4 CF5 CF6 TV CF TV 5 6 0  5 TV5  (1 rWACC ) rWACC

3. Investment Calculation

3.1 NPV “normal” NPV, incremental NPV Formulas for CorpFin Midterm page 4/5

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 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 Formulas for CorpFin Midterm page 5/5

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