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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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
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
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 )