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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 estimate of βasset of division

5. βasset of division: apply divisional capital structure ( βequity of division

6. Determine Cost of Equity and Debt of division

7. Calculate WACC

2. Terminal Values

2.1 Perpetuity

2.2 Growing Perpetuity

2.3 Declining Perpetuity

2.4 Earnings Multiple

VT = Net Income * P/E

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

2.6 Book Value in Liquidation

Liquidation value

2.7 Time Horizon

|CF0 |CF1 |CF2 |CF3 |CF4 |CF5 |CF6 | |[pic] | | |[pic] | |

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

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...
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