Finance

FORMULAE

Mid-Term 1

Cost of capital and capital structure

 S 

 B 

k

 ke  

 k (1   c )

 B  S

 B  S d

EBIT 1   c 



VL

 B

k e       k d  1   c   

 S

VL  VU   c B

VU 

S

EBIT 1   c 



 EBIT  k B1  

d

c

ke

 1   c 1   e  

B

V L  VU  1 

1  d  





Notation:

k

ke

kd



c

e

d

=

=

=

=

=

=

=

weighted average cost of capital

cost of equity capital

cost of debt capital

cost of capital for an unlevered firm

corporate tax rate

personal tax rate on equity income

personal tax rate on debt income

EBIT = earnings before interest and taxes

B = market value of debt

S = market value of equity

VU = value of an unlevered firm

VL = value of a levered firm

Security Market Line (CAPM)



E ( Ri )  R f   i E ( Rm )  R f



E  Ri  = expected return on security i

Rf

= risk free rate

E ( Rm ) = expected return on the market portfolio

i

= beta coefficient of security i

Net Present Value

n

NPV 



t 1

h =

k =

Io =

CFt =

n =

CFt

Io

t 

1 h

(1  k )

weighted average floatation cost

cost of capital

initial outlay

cash flow from project in period t

life of project (periods)

Gordon Model

Po = D1/(ke - br)

Notation:

Po

D1

ke

b

r

=

=

=

=

=

time 0 share price

period 1 dividend

share yield

retention rate

return on investment

Cost of debt (approximation)

kd 

Ct   F  P N

 P  F 2

Notation:

k d = cost of debt capital

Ct = coupon in period t

P = market price

F = face value

N = number of periods to maturity

Financial leverage and the CAPM



 

k e  R f   u E  Rm   R f   e   u



e  u 1  1  c   B / S 

 E R   R 

m



Notation:

= cost of equity capital

= risk-free rate

= unlevered (asset) beta

= expected return on the market

= equity beta

= corporate tax rate

Effect of...