Page - 1 - of 6

Formula Sheet FINA2222 Important Notice: Please be aware of the fact that this is not a comprehensive list of all formulas used in the lecture. Please keep in mind that all formulas used in the lecture (and corresponding textbook chapters) and the tutorials are relevant for the mid semester exam and the final exam. Market value of equity: MM Proposition I: Return on unlevered equity (RU): Unlevered Cost of Capital (pretax WACC): Unlevered Beta: Interest Tax Shield: The Interest Tax Shield and Firm Value:

Market Value of Equity

Market Value of Assets Market Value of Debt and Other Liabilities

=−

E D U A+ = =

E D U

E DR R R

E D E D+ =

+ +

Fraction of Firm Value Equity Fraction of Firm Value Debt

Financed by Equity Cost of Capital Financed by Debt Cost of Capital

wacc

E D

r

E Dr r

E D E D

≡ +

= ++ +

U E D

E D

E D E Dβ β β= +

+ +

Interest Tax Shield Corporate Tax Rate Interest Payments= ×

Cash Flows to Investors Cash Flows to Investors (Interest Tax Shield)

with Leverage without Leverage

= +

Page - 2 - of 6

MM Proposition I with Taxes: The Interest Tax Shield with Permanent Debt: Market value of debt: Interest Tax Shield with Permanent Debt (marginal tax rate constant): Weighted Average Cost of Capital with Taxes: Effective Tax Advantage of Debt: Value of the firm with leverage (with personal taxes and permanent debt):

(Interest Tax Shield)L UV V PV= +

( ) Interest(Interest Tax Shield)

c fc

f f

c

r DPV

r r

D

ττ

τ

× ××= =

= ×

Market Value of Debt (Future Interest Payments)D PV= =

(Interest Tax Shield) ( Future Interest Payments)

(Future Interest Payments)

c

c

c

PV PV

PV

D

τττ

= ×= ×= ×

(1 ) wacc E D c

E Dr r r

E D E Dτ= + −

+ +

(1 ) (1 ) (1 ) (1 ) (1 ) 1

(1 ) (1 )i c e c e

i i

τ τ τ τ τττ τ

∗ − − − − − −= = −− −

L UV V Dτ ∗= +

Page - 3 - of 6

Limits to the Tax Benefit of Debt: Growth and Debt: Levered firm (tradeoff theory): Debt Overhang (Equity holders point of view): Levered firm (Agency Costs and the Tradeoff Theory): Cum-dividend price: PCum = Current Dividend + PV (Future Dividends) Effective Dividend Tax Rate (Equilibrium condition):

(1 ) 1 0

(1 ) (1 )e e i

exi i

τ τ τττ τ

∗ − −= − = <− −

Interest Debt EBIT or Debt EBIT / D Dr r= × ≤ ≤

(Interest Tax Shield) (Financial Distress Costs)L UV V PV PV= + −

D

E

NPV β D>

I β E

(Interest Tax Shield) (Financial Distress Costs)

(Agency Costs of Debt)+ (Agency Benefits of Debt)

L UV V PV PV

PV PV

= + −−

( ) (1 ) (1 )cum ex g dP P Divτ τ− − = −

( )* 1 1 1

1 1 d

d gdcum ex

g g

P P Div Div Divτ ττ τ

τ τ −−− = × = × − = × − − −

Page - 4 - of 6

Effective dividend tax rate: Adjustment for Investor Taxes: Weighted average cost of capital: Levered value of an investment: Present value of a growing perpetuity: PV (growing perpetuity) = C/(r – g) Debt capacity: Debt capacity - VL

t calculated as: Adjusted present value (APV):

(1 ) wacc E D c

E Dr r r

E D E Dτ= + −

+ +

31 20 2 3

1 (1 ) (1 )

L

wacc wacc wacc

FCFFCF FCFV

r r r= + + +

+ + +L

Lt tD d V= ×

}Value of in year 2 and beyond

1 1

1

FCF t

LL t t

twacc

FCF VV

r

+

+ ++=+

(Interest Tax Shield) L UV APV V PV= = +

*

1 d g

dg

τ ττ

τ −

= −

( ) ( )( )

*1 1

1 1

c g

retaini

τ ττ

τ

− −= −

−

Page - 5 - of 6

Unlevered cost of capital: Valuing the interest tax shield: VL = VU + PV (interest tax shield) Flow-to-equity (FTE) method – Net borrowing at date t: Flow-to-equity (FTE) method - Free cash flow to equity: Exchange ratio: Option payoffs at expiration:

Put-Call Parity:

Pretax WACC U E D

E Dr r r

E D E D= + =

+ +

1Interest paid in year D tt r D −= ×

1Net Borrowing at Date t tt D D −= −

(1 ) (Interest Payments) (Net Borrowing)cFCFE FCF τ= − − × +

Exchange ratio A

T T

Nx T S

N A N

+ = <

Page - 6 - of 6

Replicating Portfolio in the Binomial Model:

Option Price in the Binomial Model:

Black-Scholes Formula:

Option beta – risk of an option: