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Financial Resources Formulary (Quelltext anzeigen)
Version vom 2. Dezember 2011, 19:09 Uhr
, 2. Dezember 2011keine Bearbeitungszusammenfassung
(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…“) |
Keine Bearbeitungszusammenfassung |
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== Dynamic investment indicators == | == Dynamic investment indicators == | ||
'''Present | '''Present value PV:''' value of a future payment C<sub>t</sub> (in year t), discounted to year 0: [[Datei:Form_FV.png]] | ||
'''Future value FV<sub>t</sub>:''' value of a present payment (in year 0), calculated by compounding to year t: [[Datei:Form_PV.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]] | |||
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):[[Datei:Form_PV_Perp.png]] | ||
'''[[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]] | |||
'''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 for years 1 to n corresponding to a present value PV and discount rate r is: [[Datei:Form_Ann_PV.png]] | |||
'''Growing | '''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, …, ∞ ;g < r) and [[Datei:Form_PV_perp_growth.png]] | ||
t = 1, 2, …, n | '''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) | ||
'''Internal rate of return (IRR):''' discount rate that results in NPV = 0: | '''[[Interner Zinsfuß|Internal rate of return (IRR)]]:''' discount rate that results in NPV = 0: [[Datei:Form_NPV_zero.png]] | ||
'''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:Form_EAC.png]] | ||
| Zeile 61: | Zeile 50: | ||
:- 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) | ||
'''Annual | '''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 | ||
| Zeile 69: | Zeile 58: | ||
'''Effective annual rate with continuous compounding:''' effective annual rate for n → ∞ shorter periods | '''Effective annual rate with continuous compounding:''' effective annual rate for n → ∞ shorter periods | ||
(being r the simple annual rate) | (being r the simple annual rate) | ||
''' | |||
Real rate of return:''' rate of return adjusted for inflation | '''Real rate of return:''' rate of return adjusted for inflation | ||
→ with i = inflation rate | → with i = inflation rate | ||
== Valuing bonds | == Valuing bonds == | ||
'''Price of a bond:''' | |||
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: 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/> | ||
| Zeile 90: | Zeile 81: | ||
== Valuing stocks | == Valuing stocks == | ||
'''(Expected) Stock return r (equity cost of capital):''' | '''(Expected) [[Wertpapierrendite|Stock return r]] (equity cost of capital):''' | ||
'''Stock price P<sub>0</sub> in the single-period case:''' | '''Stock price P<sub>0</sub> in the single-period case:''' | ||
| Zeile 120: | Zeile 111: | ||
== Risk and | == 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): | '''Variance:''' expected value of squared deviations of observations from their expected value (mean): | ||
based on j observations | based on j observations | ||
'''Standard deviation:''' a measure of volatility of expected stock returns: | '''Standard deviation:''' a measure of volatility of expected stock returns: | ||
'''Expected portfolio return''' (with two assets): | '''Expected portfolio return''' (with two assets): | ||
'''Expected portfolio return''' (with j = 1, …, n assets): | '''Expected portfolio return''' (with j = 1, …, n assets): | ||
:x<sub>j</sub> weight of asset j in the portfolio | :x<sub>j</sub> weight of asset j in the portfolio<br/> | ||
:r<sub>j</sub> (expected) return of asset j | :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: | ||
| Zeile 148: | Zeile 136: | ||
'''Correlation coefficient''' between asset i and j: | '''Correlation coefficient''' between asset i and j: | ||
'''Variance of portfolio return (portfolio variance)''' in the case of n assets: | |||
'''Beta''' of the return of asset j to the market return (return of market portfolio m): | |||
'''Expected return following the security market line''' equation (SML): | |||
Expected return of a stock in '''event studies''': | |||
''' | '''Abnormal return''' = actual return – expected return = | ||
== Rates of return on capital and assets: == | == Rates of return on capital and assets: == | ||
'''[[Rentabilität|Rates of return]]:''' | |||
'''Weighted average cost of capital (WACC):''' | '''Weighted average cost of capital (WACC):''' | ||
| Zeile 168: | Zeile 168: | ||
'''Weighted average cost of capital (WACC)''' with a zero-tax rate: | '''Weighted average cost of capital (WACC)''' with a zero-tax rate: | ||
'''Leverage-formula''' for return on equity: | '''Leverage-formula''' for return on equity: return on equity increases with debt/equity-ratio | ||
'''Leverage-formula''' for equity beta: | '''Leverage-formula''' for equity beta: risk increases with debt/equity-ratio: | ||