Some Useful Formulas 1

Some Useful Formulas1 Some Financial Ratios Market-to-Book Ratio = Return on Equity = Return on Assets = EPS = Market Value of Equity Book Value of...
Author: Roy Washington
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Some Useful Formulas1 Some Financial Ratios Market-to-Book Ratio =

Return on Equity =

Return on Assets = EPS =

Market Value of Equity Book Value of Equity

Net Income Book Value of Equity

Net Income + Interest Expense Total Assets

Net Income Shares Outstanding

P / E Ratio =

Market Capitalization Share Price = Net Income Earnings per Share

Debt-to-Capital Ratio =

Total Debt Total Equity + Total Debt

Financial Planning A = Assets ROE = Return on equity

Sustainable Growth Rate:

g = Plowback ratio * ROE

Internal Growth Rate:

IGR = Plowback ratio * ROE * E/A

Bokföringslagen 15§ “Har värdet på anläggningstillgång varaktigt gått ned, skall nedskrivning ske med det engångsbelopp som kan anses erforderligt enligt god redovisningssed”.

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Denna formelsamling är avsedd som ett komplement och stöd till inhämtade kunskaper och inte en ersättning för dessa. Den gör inte heller anspråk på att vara en fullständig förteckning av alla för examinationen nödvändiga samband och uttryck! I händelse av tryckfel eller andra felaktigheter så är det användarens ansvar att använda sig utav korrekt samband alt. uttryck.

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Time Value of Money r = ränta, avkastningskrav / -möjlighet n = tid, antal perioder PMT = Payment per period CF = Cash Flow, kassaflöde i = årlig inflationstakt T = skattesats APR = Annual Percentage Rate N

CFn n n =1 (1 + rn )

PV = ∑

Basic Formulas:

N

CFn n n =1 (1 + rn )

NPV = −Cost + ∑ Future Value (Slutvärde)

FVn = PV (1 + r)n

Present Value (Nuvärde)

PV = FVn (1 + r)n =FVn

1 (1 + r ) n

1 1 AF(r,n) = PVA(r,n) = 1 − r  (1 + r ) n (1 + r )t − 1 FVA(r , t ) = r

Annuity factor (Nusumma) (Slutsumma) PV of a perpetuity:

  

PV = PMT / r r  FV = PV 1 +   m FV = PV e r n

Interest r per year compounded m times a year for n years Continuous compounding

mn

m

APR   EAR = 1 +  −1 m  

Effective Annual Rate and m compounding periods per year N

CFn n n =1 (1 + IRR )

0 = CF0 + ∑

Internal Rate of Return, IRR:

N

∑ CF (1 + r )

N −n

n

Modified Internal Rate of Return, MIRR:

(nominell) ränta r

CF0 =

n =1

(1 + MIRR) N

real ränta: rr =



1+ r -1 1+ i

↕ ränta efter skatt: rT = r (1-T)↔

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real ränta efter skatt: rrT =

2

1 + rT −1 1+ i

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Bond and Stock Valuation Div, CPN = Utdelning, kupong P = Marknadsvärde, börskurs. FV = Maturity (par / face) value of a bond rE = Avkastning(-skrav) för en aktie/eget kapital rD = Avkastning (-skrav) för lån y ( =YTM) =Avkastningskrav för en obligation Vn = Enterprice value on date n FCFn = Free cash flow on date n

d  d   d   1 + y1 1  = 1 + y 2 2 1 + y3 3  360   360  360  

Penningmarknadens fundamentalsamband: (Law of one Price tillämpad)

N

CPN n FV N + n (1 + y ) N n =1 (1 + y )

P=∑

(Present) Value of a bond: P = (ev.) upplupen kupong + FV * kurs Rate of Return2 on a security held for period n:

RoRn =

(Present) Value of a common stock:

P0 = ∑

… with Constant Long-Term Growth

P0 = ∑

Divn + ( Pn − Pn−1 ) Pn−1

N

Divn PN + n (1 + rE ) N n =1 (1 + rE ) Div n 1 + n (1 + r ) N n =1 (1 + r ) N

 Div N +1     r−g 

If the initial dividend is paid in year 1 and the dividend grows thereafter at a constant rate of g, the present value of the dividend stream is: Div1 Constant growth case P0 = rE − g N

FCFn = E + D − Cash n n =1 (1 + rWACC )

V0 = ∑

Enterprice value

2

Även: Total Return

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Risk and Return E(R) = Expected return (Mean) σ2 = Variance σ Μ= Standard deviation of market retun σij = Kov ij = Cov ij = Covariance between the returns on security i and j. ρ ij = Korr ij = Corr ij = Correlation between the returns on security i and j. Xj = Vikten av värdepapper j RM = Rm = Rate of return on the market portfolio rf = rRF = rrf = Rate of return on a risk-free security n

R p = ∑ X j rj

Return on a portfolio of n securities:

j =1

2

Variance for a security of N observations:

1 N σ = ∑ Rn − R N − 1 n=1

Covariance

1 N ∑ ( Ri,n − Ri )( R j ,n − R j ) N − 1 n=1

(

2

Cov( Ri , R j ) =

)

Mean and Variance of a portfolio with Xi in i and Xj in j (i.e. two assets)

[ ]

Mean

E R p = X i Ri + X j R j

Variance

Varp = X i σ i2 + X j σ 2j + 2 X i X j Cov( Ri , R j )

2

2

σij = σι σj ρij n

n

i =1

j

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