Finance Basic Formulae

 

where r is interest rates, n number of compounding period in one year, and T number of years

where r is interest rates, n number of compounding period in one year, and T number of years

where EAR is the Equivalent Annual Rate, APR is Annual Percentage Rate, and n is the number of compounding period in a year

where r is interest rates and T number of years in continuous compounding

where r is interest rates and T number of years in continuous compounding

EAR and APR in continuous compounding

 

 

where PVA is the Present Value of Annuity, CF is Cash Flow of a compounding period, r is the annual interest rate (opportunity cost of capital, required rate of return), n is the number of compounding period in a year, and T is number of years (lifetime of cash flows)

where FVA is the Futuret Value of Annuity, CF is Cash Flow of a compounding period, r is the annual interest rate (opportunity cost of capital, required rate of return), n is the number of compounding period in a year, and T is number of years (lifetime of cash flows)

 

where Coupon is Coupon Dollar amount semiannually, YTM is the Yield-to-Maturity (opportunity cost of capital, required rate of return or interest rate), and T is number of years (lifetime of cash flows). AF stands for Annuity Factor, DF stands for Discount Factor

CF is Cash Flow of a compounding period, r is compounding period's interest rate (opportunity cost of capital, required rate of return)

Bond Pricing General Equation

P0 is price of bond, Couponi is semiannual coupon at time i, and YTMi is Yield-to-Maturity for maturity I, Par is face value of bond, and T is years to maturity.

 

where Coupon is Coupon Dollar amount Annually, and Price is the Market Price of the Bond (given by aforementioned equation)

HPR is Holding Period Return calculated over one compounding period, Interim Cash is any cash received during the period e.g. for bonds Interim Cash is Coupon, for Stock Interim Cash is Dividend

Stock Pricing General Equation

Pt is price of stock at time t, Divt+i is dividend at time t+i, and r is required rate return of stock (opportunity cost of equity)

Stock Pricing Constant Growth

Pt is price of stock at time t, Divt+1 is dividend at time t+1, r is required rate return of stock (opportunity cost of equity), and g is the growth rate of dividends

BRR is book rate of return, B.V. stand for book value

 

EAC is equivalent annual cost, r is opportunity cost, and T is life of project

 

BE is Break even point, FC is fixed cost, and DEP is Depreciation, and %VC is percentage variable cost

DOL is degree of operating leverage, FC is fixed cost, and DEP is Depreciation, and Profits is before-tax profits

Statistics in State Space

rAi is return of asset A in state i, pi is probability of state i, and S is total number of states

Time-Series Statistics

Portfolio Statistics

For a portfolio of N assets, with return asset i equal to ri

CAPM

E(ri ) is the expected return of asset i, bi is beta of stock i, rf is return of risk free asset, E(ri) is expected return of the market, and MRP is the market risk premium

Portfolio Beta

bP is beta of the portfolio, bi is the beta of asset i, wi is the weight of asset i

WACC (general)

wL is the weight of loans with cost of rL, wD is the weight of debt with cost of rD, wP is the weight of preferred stocks with cost of rP, wE is the weight of common stocks with cost of rE, and t is the marginal tax rate

Pricing Preferred Stock

P is price of preferred stock, Div is dividend, and r is required rate return of stock (opportunity cost of equity)

Assets' Beta

bA is beta of assets, bD is beta of debt, bE is beta of equity, D is value of debt, E value of equity and V is firm's value

WACC (reduced)

wD is the weight of debt with cost of rD, wE is the weight of equity with cost of rE, and t is the marginal tax rate