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Introduction to Finance

Formula Sheet

(2.1)

Accounting identity:

assets ≡liabilities+ owners' equity

(2.2)

Net working capital:

NWC =current assets - current liabilities

(2.3)

Net income:

net income = revenues - expenses

(2.4)

Earnings before interest and taxes:

EBIT =revenues - operating expenses

(2.5)

Operating cash flow:

OCF = EBIT + depreciation - taxes

(2.6)

Change in retained earnings:

ΔRE = net income - distributed earnings

(2.7)

Cash flow from assets:

CF from assets ≡ CF to creditors + CF to owners

(3.2)

Future value of a lump sum:

FV =PV × ( 1+r )

(3.3)

Present value of a lump sum:

PV =FV ×

(3.4)

Interest rate:

(3.5)

Number of periods:

(4.3)

Future value of an annuity:

( )

n

FV 1 = n n ( 1+r ) ( 1+r )

1/n

r=

FV PV

n=

ln ( FV / PV ) ln( 1+r )

−1

n ( 1+r ) −1 ] [ FV =PMT ×

r

(4.4)

Present value of an annuity:

PV =PMT ×

[1−1 / ( 1+r )n] r

PMT r

(4.8)

Present value of a perpetuity:

PV =

(4.9)

Annuity payment:

PMT =

FV

=

PV

[ (1 +r ) −1] /r [1−1/ ( 1+r )n ] /r

(4.10)

Number of periods:

n

(

)

(

FV ×r PV ×r ln 1− PMT PMT n= =− ln ( 1+ r) ln ( 1+r ) ln 1+

APR m

(5.1)

Periodic interest rate:

(5.2)

Effective annual rate:

(5.4)

Fisher effect:

( 1+r ) =( 1+r )× (1+ h )

(5.6)

Nominal interest rate:

r=r ¿ +h+ ( r ¿×h )

(5.11)

Nominal interest rate:

r=r ¿ +h+dp + mp

r=

(

EAR= 1+

APR m −1 m

)

¿

1

)

Introduction to Finance (6.1)

Formula Sheet

Bond value:

1− bond price= par value ×

1 +coupon × n ( 1+r )

1 ( 1+r ) n r

(6.2)

Zero-coupon bond value:

(7.2)

Value of preferred stock:

(7.5)

Value of common stock (infinite horizon):

pric e 0=

Di v 0 × ( 1+g ) r−g

(7.6)

Value of common stock (infinite horizon):

pric e 0=

Di v 1 r−g

(7.8)

Value of common stock (finite horizon):

price 0=

(7.9)

Expected rate of return for common stock:

r=

Expected rate of return for preferred stock:

r=

(8.1)

Profit:

profit =ending value+ distributions −original cost

(8.2)

Return:

(8.3)

Holding period return:

(8.4)

Simple annual return:

(8.5)

Effective annual rate:

(8.6)

Variance:

(7.10)

bond price= par value ×

price=

1 n ( 1+r )

dividend r

[ ( )]

pricen Div 0 × ( 1+g ) 1+g × 1− + n r−g 1+r ( 1+r )

Di v 0 × ( 1+g ) price 0

n

+g

dividend price

return=

loss profit or orginal cost original cost

HPR=

profit/ (loss ) original cost

APR=

HPR n

HPR =

profit cost

variance ( X )=

∑ ( X i−average )2 =σ 2 n−1

(8.7)

Standard deviation:

2 standard deviation= √ variance= √ σ =σ

(8.8)

Expected payoff:

expected payoff=∑ payof f i ×probabilit y i

(8.9)

Variance:

σ 2 =∑ ( payoff i −expected payoff)2 ׿ probability i ¿

(8.10)

Portfolio beta:

n

β p=∑ wi × β i i=1

2

Introduction to Finance (8.11) (9.1)

CAPM: Net present value:

(9.2)

Equivalent annual annuity:

(9.3)

Internal rate of return:

(9.4)

(11.1)

Formula Sheet E ( ri ) =r f + [ E ( rm )−r f ]×β i

NPV =−CF0 +

EAA=

CF1

( 1+ r )

1

CF 2

+

( 1+r )

+

2

+

CF 3

( 1+r)

3

+. ..+

CF n

(1+r )

n

NPV PVIFA

$ 0=−C F 0 +

C F1

( 1+r)

1

+

C F2

(1+r )

C F3

(1+r )

3

+...+

C Fn

(1+r )n

present value of benefits present value of costs

Profitability index:

PI =

Net present value:

NPV =−investment +∑

n

t=1

(11.2)

2

cash flow t

(1+WACC )t

Cost of debt:

1− net price= par value ×

1 +coupon × n ( 1+R d )

(11.3)

Net price of preferred stock:

(11.4)

Cost of preferred stock:

R ps=

(11.5)

Cost of equity:

Re =E ( r i ) =r f + [ E ( r m ) −r f ] ×β i

net price=

1 (1+R d )n Rd

dividend R ps

dividend price

r (¿¿ i)=r f + β( E ( r m )−r f ) Re =E ¿ Div 0 × ( 1+ g) +g P0

(11.6)

Cost of retained earnings:

(11.7)

Cost of new equity:

(11.8)

After-tax cost of debt:

after-tax cost of debt=R d × ( 1−T c )

(11.9)

Weighted average cost of capital:

WAC C adj =

Re =

Re =

3

Di v 0 × (1+ g ) +g P0 × ( 1−F)

E D PS × R ps + × Rd × ( 1−T c) × Re + V V V...