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
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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
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
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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
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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
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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