# Fairfax

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Fairfax
Formulas Midterm

Cost of Capital

1.1 Basic Formula

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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:

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The Equity-Beta is a function of the risk of a firm’s assets (operating risk) and the amount of financial leverage.

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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)

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Debt-Beta for Investment Grade firms is statistically not relevant and can be dropped.

1.4 Financial/Operating/Market Risk

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βasset = operating risk

Rest of term = financial risk (drops out when debt = 0)

Βdebt = 0 if debt carries no market risk

1.5 Cost of Debt

rD = rf + Credit Spread

1.6 Cost of Equity

CAPM: rE = rf + βE(rm-rf)

1.7 Cost of Capital (WACC)

• 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) ( βequity of comparable

3. βequity of comparable: remove effects of capital structure ( βasset of comparable

4. Assume βasset of comparable = best

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Carlson M, Fisher A, Giammarino R (2004): "Corporate Investment and Asset Price Dynamics: Implications for the Cross-section of Returns." J. Financ., 59: 2577-2603. Campbell, John Y and Tuomo Vuolteenaho (2004). Bad beta, good beta. Am. Econ. Rev., 94: 1249-1275. Campbell J, Polk C, Vuolteenaho T (2007). Growth or Glamour? Fundamentals and Systematic Risk in Stock Returns. NBER Working Paper, No. 11389. Graham JR, Harvey CR (2001): "The Theory and Practice of Corporate Finance: Evidence from the ?ed," J. Financ. Econ., 60: 187-243 Heinkel R (1982). “A Theory of Capital Structure Relevance under Imperfect Information.” J. Financ., 12: 1141-1150. Huffman A (1983). Inter-industry differences and the impact of operating and financial leverages on equity risk. Rev. Financ. Econ., 4(2): 141155. Hamada R (1972). The Effect of Firm’s Capital Structure on the Systematic Risk of Common Stocks. J. Financ., 435-452. Harris Milton, Artur Raviv. (1991). “The Theory of Capital Structure.” J. Financ., 3: 297-355. Kaplan PD, Peterson JD (1998). "Full-information Industry Betas." Financ., Manage., 27: 85-94.…

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