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Financial Resources Formulary (Quelltext anzeigen)
Version vom 14. Mai 2012, 11:08 Uhr
, 14. Mai 2012→Exercises
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| (12 dazwischenliegende Versionen desselben Benutzers werden nicht angezeigt) | |||
| Zeile 1: | Zeile 1: | ||
''by Clemens Werkmeister'' | ''by Clemens Werkmeister'' | ||
<html><img src="http://vg06.met.vgwort.de/na/8f870d4d147340dd92189f86b590c20c" width="1" height="1" alt=""></html> | |||
== Present values, perpetuities and annuities == | == Present values, perpetuities and annuities == | ||
'''Present value PV:''' value of a future payment C<sub>t</sub> (in year t), discounted to year 0: [[Datei: | '''Present value PV:''' value of a future payment C<sub>t</sub> (in year t), discounted to year 0: [[Datei:Form_PV.png]] | ||
'''Future value FV<sub>t</sub>:''' value of a present payment (in year 0), calculated by compounding to year t: [[Datei: | '''Future value FV<sub>t</sub>:''' value of a present payment (in year 0), calculated by compounding to year t: [[Datei:Form_FV.png]]<br/> | ||
: t year<br/> | : t year<br/> | ||
: r [[Kalkulationszinssatz|discount rate]] (interest rate)<br/> | : r [[Kalkulationszinssatz|discount rate]] (interest rate)<br/> | ||
| Zeile 38: | Zeile 38: | ||
'''Profitability index:''' ratio of NPV to investment of a project: [[Datei:Form_PI.png]] | '''Profitability index:''' ratio of NPV to investment of a project: [[Datei:Form_PI.png]] | ||
'''Equivalent annual cash flow (EAC):''' cash flow per year with the same present value as the actual cash flow of the project: [[Datei: | '''Equivalent annual cash flow (EAC):''' cash flow per year with the same present value as the actual cash flow of the project: [[Datei:cw_EAC.png]] | ||
== Interest and discount rates == | == Interest and discount rates == | ||
| Zeile 49: | Zeile 47: | ||
:- EAR for a daily rate d: EAR = (1+d)<sup>360</sup> – 1 (for 360 days per year) | :- EAR for a daily rate d: EAR = (1+d)<sup>360</sup> – 1 (for 360 days per year) | ||
Given an annual percentage rate (APR) of r, the corresponding EAR with respect to n shorter periods of equal length is: [[Datei:Form_EAR.png]] | |||
'''Effective annual rate with continuous compounding:''' effective annual rate for n → ∞ shorter periods: [[Datei:Form_EAR_cc.png]] (being r the simple annual rate) | |||
'''Annual percentage rate (APR) or simple rate:''' annualized rate of shorter period interest rates (monthly, daily rates) using simple interest. | '''Annual percentage rate (APR) or simple rate:''' annualized rate of shorter period interest rates (monthly, daily rates) using simple interest. | ||
:- APR for a monthly rate m: APR = 12 * m | :- APR for a monthly rate m: APR = 12 * m | ||
'''Real rate of return:''' rate of return adjusted for inflation: [[Datei:Form_Real_Int_1.png]] | '''Real rate of return:''' rate of return adjusted for inflation: [[Datei:Form_Real_Int_1.png]] | ||
| Zeile 65: | Zeile 63: | ||
== Valuing bonds == | == Valuing bonds == | ||
'''Price of a bond:''' [[Datei:Form_PV_Bond.png]] | '''Price of a bond:''' [[Datei:Form_PV_Bond.png]]<br/> | ||
with<br/> | with<br/> | ||
: C<sub>t</sub> annual coupon interest payment<br/> | : C<sub>t</sub> annual coupon interest payment<br/> | ||
| Zeile 84: | Zeile 80: | ||
'''(Expected) [[Wertpapierrendite|Stock return r]] (equity cost of capital):''' [[Datei:Form_Stock_Return.png]] | '''(Expected) [[Wertpapierrendite|Stock return r]] (equity cost of capital):''' [[Datei:Form_Stock_Return.png]] | ||
'''Stock price P<sub>0</sub> in the single-period case:''' [[Datei:Form_P0_einperiodig.png]] | * '''Stock price P<sub>0</sub> in the single-period case:''' [[Datei:Form_P0_einperiodig.png]] | ||
'''Dividend discount model''' for the stock price P0 in the multi-period case until time horizon H: [[Datei: | * '''Dividend discount model''' for the stock price P0 in the multi-period case until time horizon H: [[Datei:cw_DDM_v2.png]] | ||
'''Stock price P<sub>0</sub>''' with specific dividends until time horizon H and growing dividends after H: [[Datei:Form_P0_growth.png]] | * '''Stock price P<sub>0</sub>''' with specific dividends until time horizon H and growing dividends after H: [[Datei:Form_P0_growth.png]] | ||
'''Stock price for a perpetual stream of dividends:''' [[Datei:Form_P0_perpetual.png]] | * '''Stock price for a perpetual stream of dividends:''' [[Datei:Form_P0_perpetual.png]] | ||
'''Stock price for a perpetual stream of growing dividends:''' [[Datei:Form_P0_perp_growth.png]] | * '''Stock price for a perpetual stream of growing dividends:''' [[Datei:Form_P0_perp_growth.png]] | ||
* '''Stock price = Discounted earnings + growth opportunities:''' [[Datei:Cw_PVGO.png]] | |||
'''Present value of growth opportunities (PVGO):''' net present value of a firm's future investments. | |||
'''Return (Equity cost of capital) of a perpetual stream of dividends with growth:''' [[Datei:Form_RoE_growth.png]] | '''Return (Equity cost of capital) of a perpetual stream of dividends with growth:''' [[Datei:Form_RoE_growth.png]] | ||
| Zeile 101: | Zeile 102: | ||
'''Plowback ratio:''' fraction of earnings retained by the firm: [[Datei:Form_Plowback.png]] | '''Plowback ratio:''' fraction of earnings retained by the firm: [[Datei:Form_Plowback.png]] | ||
'''Sustainable growth rate:''' rate at which a firm can steadily grow: [[Datei:Form_Sustainable.png]] | '''Sustainable growth rate:''' rate at which a firm can steadily grow: [[Datei:Form_Sustainable.png]] | ||
'''Discounted cash flow (DCF):''' value of the free cash flows that are available to investors plus company value at the planning horizon, all discounted to present: [[Datei:Form_DCF.png]] | '''[[Kapitalwert|Discounted cash flow]] (DCF):''' value of the free cash flows that are available to investors plus company value at the planning horizon, all discounted to present: [[Datei:Form_DCF.png]] | ||
== Risk and return == | == Risk and return == | ||
'''Risk premium of an asset:''' asset return – return of risk-free asset | '''Risk premium of an asset:''' asset return – return of risk-free asset. | ||
'''Variance:''' expected value of squared deviations of observations from their expected value (mean): [[Datei:Form_Var.png]] (based on j observations) | |||
'''Standard deviation:''' a measure of volatility of expected stock returns: [[Datei:Form_Standard_Dev.png]] | |||
'''Expected portfolio return''' (with two assets): | '''Expected portfolio return''' (with two assets): [[Datei:Form_EV_zwei.png]] | ||
'''Expected portfolio return''' (with j = 1, …, n assets): | '''Expected portfolio return''' (with j = 1, …, n assets): [[Datei:Form_EV_n.png]] | ||
:x<sub>j</sub> weight of asset j in the portfolio<br/> | :x<sub>j</sub> weight of asset j in the portfolio<br/> | ||
| Zeile 130: | Zeile 123: | ||
:r<sub>j</sub> (expected) return of asset j<br/> | :r<sub>j</sub> (expected) return of asset j<br/> | ||
'''Variance of portfolio return (portfolio variance)''' in the case of two assets: | '''Variance of portfolio return (portfolio variance)''' in the case of two assets: [[Datei:Form_Port_Var_zwei.png]] | ||
'''Covariance''' between asset i and j with | '''Covariance''' between asset i and j with [[Datei:Form_Covariance_Formel.png]] | ||
'''Correlation coefficient''' between asset i and j: | '''Correlation coefficient''' between asset i and j: [[Datei:Form_Corr_Coeff_Formel.png]] | ||
'''Variance of portfolio return (portfolio variance)''' in the case of n assets: | '''Variance of portfolio return (portfolio variance)''' in the case of n assets: [[Datei:Form_Port_Var_n.png]] | ||
'''Sharpe-Ratio: ratio of risk premium to risk (standard deviation): [[Datei:cw_Sharpe_ratio.png]] | |||
'''Beta''' of the return of asset j to the market return (return of market portfolio m): | '''Beta''' of the return of asset j to the market return (return of market portfolio m): [[Datei:Form_Beta.png]] | ||
'''Expected return following the security market line''' equation (SML): | '''Expected return following the security market line''' equation (SML): [[Datei:Form_Expected_Return.png]] | ||
Expected return of a stock in '''event studies''': | Expected return of a stock in '''event studies''': [[Datei:Form_Normal_Return.png]] | ||
'''Abnormal return''' = actual return – expected return = | '''Abnormal return''' = actual return – expected return = [[Datei:Form_Abnormal.png]] | ||
== Capital Structure and Return == | == Capital Structure and Return == | ||
'''[[Rentabilität|Rates of return]]:''' | '''[[Rentabilität|Rates of return]]:'''<br/> | ||
[[Datei:Form_RoI.png]]<br/> | |||
[[Datei:Form_RoA.png]]<br/> | |||
[[Datei:Form_RoC.png]] | |||
'''Weighted average cost of capital (WACC):''' | '''Weighted average cost of capital (WACC):''' [[Datei:Form_WACC_after_Tax.png]] | ||
:r<sub>D</sub> interest rate on debt resp. debt cost of capital | :r<sub>D</sub> interest rate on debt resp. debt cost of capital | ||
| Zeile 165: | Zeile 157: | ||
:T<sub>c</sub> corporate tax rate | :T<sub>c</sub> corporate tax rate | ||
'''Weighted average cost of capital (WACC)''' with a zero-tax rate: | '''Weighted average cost of capital (WACC)''' with a zero-tax rate: [[Datei:Form_WACC.png]] | ||
'''Leverage-formula''' for return on equity: return on equity increases with debt/equity-ratio | '''Leverage-formula''' for return on equity: return on equity increases with debt/equity-ratio: [[Datei:Form_Leverage.png]] | ||
'''Leverage-formula''' for equity beta: risk increases with debt/equity-ratio: [[Datei:Form_Leverage_Beta.png]] | |||
== Exercises == | |||
Please try our [[Financial Exercises]] or have a look at the [[Financial Ratios]] or at our [[Investition|investment pages]].<br/> | |||