Financial Resources Formulary: Unterschied zwischen den Versionen

Zur Navigation springen Zur Suche springen

Financial Resources Formulary (Quelltext anzeigen)

Version vom 14. Mai 2012, 11:08 Uhr

2.224 Bytes hinzugefügt ,  14. Mai 2012
→‎Exercises
(Die Seite wurde neu angelegt: „''by Clemens Werkmeister'' == Dynamic investment indicators == '''Present Value PV:''' value of a future payment C<sub>t</sub> (in year t), discounted to year…“)
 
 
(14 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 ==


== Dynamic investment indicators ==
'''Present value PV:''' value of a future payment C<sub>t</sub> (in year t), discounted to year 0: [[Datei:Form_PV.png]]


'''Present Value PV:''' value of a future payment C<sub>t</sub> (in year t), discounted to year 0:
'''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/>
: r [[Kalkulationszinssatz|discount rate]] (interest rate)<br/>
: [[Datei:Form_Disc_Fact.png]] discount factor with discount rate (interest rate) r for t years<br/>
: C<sub>t</sub> cash flow in year t<br/>
: C<sub>0</sub> initial investment of a project (for normal investment projects: C<sub>0</sub>  < 0)<br/>
: T number of years of the project<br/> 


 
The sum of several present values is a PV, too '''(additivity of present values)''':[[Datei:Form_PV_Sum.png]]
'''Future Value FV<sub>t</sub>:''' value of a present payment (in year 0), calculated by compounding to year t:
 
with t year
r discount rate (interest rate)
discount factor with discount rate (interest rate) r for t years
C<sub>t</sub> Cash flow in year t
C<sub>0</sub> initial investment of a project (for normal investment projects: C<sub>0</sub>  < 0)
T number of years of the project
The sum of several present values is a PV, too (additivity of present values):


'''Net present value NPV:''' PV of future payments (of a project or a company) plus the - usually negative - initial investment C<sub>0</sub>:
'''[[Kapitalwert|Net present value NPV]]:''' PV of future payments (of a project or a company) plus the - usually negative - initial investment C<sub>0</sub>: [[Datei:Form_NPV.png]]
 
 
'''Perpetuity (console):''' a periodic (annual) payment C that is received or paid forever (beginning with the first payment at the end of year 1):
 
 
'''Annuity:''' a payment of a level cash flow C during a specified number of years (from year 1 to n). Its present value can be calculated as difference between two perpetuities:
 
'''Annuity (recovery) factor:''' average payment at the end of n periods, corresponding to a present value PV and considering for interest rate r:


(Wiedergewinnungsfaktor WGFr,n)
'''Perpetuity (console):''' a periodic (annual) payment C that is received or paid forever (beginning with the first payment at the end of year 1):[[Datei:Form_PV_Perp.png]]


'''Annuity present value factor:''' factor for the PV of n equal payments at the end of years 1 to n.
'''[[Annuität|Annuity]]:''' a payment of a level cash flow C during a specified number of years (from year 1 to n). Its present value can be calculated as difference between two perpetuities: [[Datei:Form_PV_Ann.png]]


(Rentenbarwertfaktor RBFr,n)
'''Annuity (recovery) factor:''' average payment at the end of n periods, corresponding to a present value PV and considering for interest rate r:[[Datei:Form_Recov_factor.png]]


'''Annuity present value factor:''' factor for the PV of n equal payments at the end of years 1 to n: [[Datei:Form_Ann_PV_factor.png]]


The annuity C over years 1 to n corresponding to a present value PV and discount rate r is:
The annuity C for years 1 to n corresponding to a present value PV and discount rate r is: [[Datei:Form_Ann_PV.png]]


'''Growing perpetuity:''' a perpetuity starting with cash flow C<sub>1</sub> in year 1 and increasing by the annual growth rate g forever:
'''Growing perpetuity:''' a perpetuity starting with cash flow C<sub>1</sub> in year 1 and increasing by the annual growth rate g forever:[[Datei:Form_C_growth.png]] (for t = 1, 2, …, &#8734; ;g < r) and [[Datei:Form_PV_perp_growth.png]]
t = 1, 2, …, &#8734; (g < r)


'''Growing annuity:''' an annuity starting with cash flow C<sub>1</sub> in year 1 and increasing by the annual growth rate g for n years:
'''Growing annuity:''' an annuity starting with cash flow C<sub>1</sub> in year 1 and increasing by the annual growth rate g for n years: [[Datei:Form_PV_ann_growth.png]] (with t = 1, 2, …, n)


t = 1, 2, …, n
'''[[Interner Zinsfuß|Internal rate of return (IRR)]]:''' discount rate that results in NPV = 0: [[Datei:Form_NPV_zero.png]]
 
'''Internal rate of return (IRR):''' discount rate that results in NPV = 0:
'''Profitability index:''' ratio of NPV to investment of a project:
'''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:


'''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 60: 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 → &#8734; 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
Given an annual percentage rate (APR) of r, the corresponding EAR with respect to n shorter periods of equal length is:
'''Effective annual rate with continuous compounding:''' effective annual rate for n → &#8734; shorter periods
(being r the simple annual rate)
'''
Real rate of return:''' rate of return adjusted for inflation
→  with i = inflation rate


'''Real rate of return:''' rate of return adjusted for inflation: [[Datei:Form_Real_Int_1.png]]
→ [[Datei:Form_Real_Int_2.png]]  (being i the inflation rate)




== Valuing bonds: ==


== Valuing bonds ==


'''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/>
: F face value (or principal)<br/>
: F face value (or principal)<br/>
: r discount rate (yield to maturity)<br/>
: r discount rate ([[Wertpapierrendite|yield to maturity]])<br/>
: N maturity<br/>
: N maturity<br/>


'''Duration of a bond with maturity N:''' weighted average period of bond payments.  
'''Duration of a bond with maturity N:''' weighted average period of bond payments: [[Datei:Form_Duration.png]]


'''Modified duration:''' a measure of volatility (elasticity) of bond prices:
'''Modified duration:''' a measure of volatility (elasticity) of bond prices: [[Datei:Form_Mod_Duration.png]]
   
   




== Valuing stocks: ==
== Valuing stocks ==


'''(Expected) Stock return r (equity cost of capital):'''
'''(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:'''
* '''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:
* '''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:
* '''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:'''
* '''Stock price for a perpetual stream of dividends:''' [[Datei:Form_P0_perpetual.png]]
'''Stock price for a perpetual stream of growing dividends:'''
* '''Stock price for a perpetual stream of growing dividends:''' [[Datei:Form_P0_perp_growth.png]]
 
'''Return (Equity cost of capital) of a perpetual stream of dividends with growth:'''
* '''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 on Equity with market values:'''
'''Return (Equity cost of capital) of a perpetual stream of dividends with growth:''' [[Datei:Form_RoE_growth.png]]
'''Payout ratio:''' fraction of earnings paid out as dividends:  
'''Return on Equity with market values:''' [[Datei:Form_RoE.png]]
'''Plowback ratio:''' fraction of earnings retained by the firm:
'''Payout ratio:''' fraction of earnings paid out as dividends: [[Datei:Form_Payout.png]]
'''Present value of growth opportunities (PVGO):''' net present value of a firm's future investments
'''Plowback ratio:''' fraction of earnings retained by the firm: [[Datei:Form_Plowback.png]]


'''Sustainable growth rate:''' rate at which a firm can steadily grow:
'''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:
'''[[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)


'''Variance:''' expected value of squared deviations of observations from their expected value (mean):
'''Standard deviation:''' a measure of volatility of expected stock returns: [[Datei:Form_Standard_Dev.png]]
based on j observations


'''Standard deviation:''' a measure of volatility of expected stock returns:
'''Expected portfolio return''' (with two assets): [[Datei:Form_EV_zwei.png]]
'''Expected portfolio return''' (with two assets):
'''Expected portfolio return''' (with j = 1, …, n assets): [[Datei:Form_EV_n.png]]
'''Expected portfolio return''' (with j = 1, …, n assets):
:x<sub>j</sub> weight of asset j in the portfolio<br/>
 
:x<sub>j</sub> weight of asset j in the portfolio
:r<sub>j</sub> (expected) return of asset j<br/>


:r<sub>j</sub> (expected) return of asset j
'''Variance of portfolio return (portfolio variance)''' in the case of two assets: [[Datei:Form_Port_Var_zwei.png]]


'''Expected return following the security market line''' equation (SML):
'''Covariance''' between asset i and j with [[Datei:Form_Covariance_Formel.png]]
Expected return in event studies:
'''Correlation coefficient''' between asset i and j: [[Datei:Form_Corr_Coeff_Formel.png]]
'''Abnormal return''' = actual return – expected return =
'''Variance of portfolio return (portfolio variance)''' in the case of n assets: [[Datei:Form_Port_Var_n.png]]


'''Variance of portfolio return (portfolio variance)''' in the case of two assets:
'''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): [[Datei:Form_Beta.png]]


'''Covariance''' between asset i and j with
'''Correlation coefficient''' between asset i and j:


'''Expected return following the security market line''' equation (SML): [[Datei:Form_Expected_Return.png]]
Expected return of a stock in '''event studies''': [[Datei:Form_Normal_Return.png]]
'''Variance of portfolio return (portfolio variance)''' in the case of n assets:
'''Abnormal return''' = actual return – expected return = [[Datei:Form_Abnormal.png]]


'''Beta''' of the return of asset j to the market return (return of market portfolio m):
== Capital Structure and 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):''' [[Datei:Form_WACC_after_Tax.png]]
== Rates of return on capital and assets: ==
 
'''Weighted average cost of capital (WACC):'''
 
 
: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 166: 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]]
 


'''Leverage-formula''' for equity beta: Risk increases with debt/equity-ratio:
== Exercises ==
Please try our [[Financial Exercises]] or have a look at the [[Financial Ratios]] or at our [[Investition|investment pages]].<br/>
Wikimeister
ConfirmedUser, Student, Bürokraten, Administratoren
589

Bearbeitungen

Abgerufen von „https://controwiki.de/index.php/Spezial:Mobiler_Unterschied/311...562“

Navigationsmenü