8/12/2019 Finance Equations

1/1

ice of CPN bonds= PV(coupons) + PV(par value)ice = Cpn/(1+YTM) + Cpn/(1+YTM) ++ Cpn/(1+YTM) n +

ar/(1+YTM) n PN in $s= (CPN rate/m)*Face value

etention rate = 1 dividend payout rate (or payout ratio) = fraction of arms earnings that is retained in the company OE = return on equityeturn on retained earnings = retention rate * RoE= retention rate * RoE= (1 payout ratio)*RoEock price at time N (after Div N is received:

ap gains = r div yieldultiple growth rates:ice of stock= PV of D1, D2, D3 + PV [Div*(1+g1) 3*(1+g2)] / [(r-g2)]orporate Valuation/ Discounted FCF Model:ock price: lue of the company = PV of FCFs

ompany value = FCF 1/(1+WACC) + FCF 2/(1+WACC)2 ...

iscount rate = WACC

alue of stockholders equity = Value of the company value of debtd preferred.ice per stock = Stockholders equity/ shares outstanding

aluation based on Comparable Firms:E based comparable method:

Estimated firm1 price= PE Comparable * EPS of firm1ice to sales based method:(firm1 sales)*(firm2 P/S ratio)= mkt value of equityprice per share = (firm1 price or mkt value of equity) / (firm1 shares

utstanding or number of shares)

ayback period = # of years + (Unrecovered cost at start of year prior to

full recovery ) / Cash flow during full recovery yeardifferent IRR= IRR of project A IRR of project Bxpected return = p i.R i = p 1R 1 + p 2R 2 easuring average return:

E(R)=easuring risk: Variance = Var(R) = p i.(R i - E(R))

2

Standard deviation (or SD) = [Var(R)] 1/2 Weight of any asset i =

i = (Value invested in asset i)/Total portfolio valueotal portfolio value = Sum of value of all assets in the portfolio

Return on portfolio:Portfolio E(R P ) = w 1E(R 1) + w 2E(R 2) .. w nE(R n)Portfolio SD = [(w 1)

2 (sd(R 1))2 + (w 2)

2 (sd(R 2))2 +

2w1w2 sd(R 1) sd(R 2) ]

1/2 Value of portfolio= (Invested amount)(1+R P )

Risk premium= R r fCapital Asset Pricing Model (CAPM), also required return

also: E(R i) r f = i[E(R m) r f ]Market risk premium= E(R m) r f Risk premium of stock I= E(R i) r f

Portfolio Beta:Cost of preferred Stock:

Price: P p = Div p/r pr p = Div p/P p = Cost of Preferred Stock

Cost of Debt: After tax cost of debt = r D(1 - T C).TC = Corporate tax rate

Cost of equity:

a) CAPM: b) Dividend discount model:

WACC = r = w e r e + w dr d(1-t) + w pr p we = (Mkt value of equity)/(Total mkt value of assets)wd = (Mkt value of debt)/(Total mkt value of assets)wp = (Mkt value of preferred stock)/(Total mkt value ofassets)

Market Value of Equity + Market value of PreferredStock + Market Value of Debt = Total Market Value

of Assets

VC = V A + V B + Synergy CashTotal price paid for the target = P B Premium = P B VB -> Gains to the target shareholdersGain Acq. shares = (Synergy Premium) ->Gains to Acq. shareholdersn = # of old shares of Acq.m = # of shares issued for the acquisitionP C = price per share of the Acq. after theannouncement or the hypothetical price per share ofthe merged firm.

P C = V C = V A + V B + Synergy Cash

m + n m + nm= (exchange ratio) x (# old shares of target)P B = m x P C Gains on Per share basis:- Target: Premium / #old shares Targ- Acq: (Synergy Premium) / # old shares AcqBreak-even synergy P C = P A

Synergy = PremiumP B = m x P C + cash

= m x P A + cashSo Premium = mP A + Cash VB = Break-even synergy

1

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Divr g

1

0 E

Divr g

P 1 10 1 E

Div P P

r

1 01 1 1

0 0 0

Dividend Yield Capital Gain Rate

1 P P Div P Div

P P P

EarningsDividend Payout Rate

Shares Outstandingt

t t t

t

Eps

v

1 N N

E

Div

r g

N N N

N

N N

N N

r g r

Divr Divr Divr Div

r P r Divr Divr Div

)1(1

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)1/()1/(.......)1/()1/(

122

11

22

11

1 2

1( ... )T

T R R R R

2 2 21 21( ) ( ) ( ) ... ( )1 T Var R R R R R R RT

1 1 2 2 ... P n n R w R w R w R

Risk Premium for Security

[ ] [ ]i f i Mkt f i

E R r E R r

1 1 2 2 ... P n nw w w