formulae
Selected Financial Formulae
Purpose
Formula
Basic Time Value Formulae
Future Value of a Single Sum
FV = PV ( 1 + i ) N
Present Value of a Single Sum
FV PV = -----------------( 1 + i)N
Solve for N for a Single Sum
FV ln ------PV
N = --------------------ln ( 1 + i )
Solve for i for a Single Sum
i =
Present Value of an Ordinary Annuity
1 – 1 ⁄ ( 1 + i )N
PV A = Pmt ----------------------------------i
Future Value of an Ordinary Annuity
( 1 + i )N – 1
FV A = Pmt ---------------------------i
Present Value of an Annuity Due
1 – 1 ⁄ ( 1 + i )( N – 1)
PV Ad = Pmt --------------------------------------------- + Pmt i Future Value of an Annuity Due
( 1 + i )N – 1
FV Ad = Pmt ---------------------------- ( 1 + i ) i Present Value of an Annuity Growing at a
Constant Rate (g)
Pmt 1
1+g
PV GA = ------------ 1 – -----------i–g
1+i
Future Value of an Annuity Growing at a
Constant Rate (g)
Pmt 1
1+g
FV GA = ------------ 1 – -----------i–g
1+i
Holding Period Return (single period)
P 1 + Cash Flows
HPR = ----------------------------------------------- – 1
P0
N
FV
------- – 1
PV
Basic Financial Formulae © 1995-2015 by Timothy R. Mayes, Ph.D.
N
N
(1 + i)
N
1
Selected Financial Formulae
Purpose
Formula
N
Holding Period Return with Reinvestment
(for multiple sub-period returns)
HPR Reinvest =
∏ ( 1 + HPRt ) – 1
t=1
Basic Security Valuation Formulae
Dividend Discount Model (AKA, the Gordon
Model)
Two-stage Dividend Discount Model
Notes: This equation is too long for one line. g1 = Growth rate during high growth phase. g2 = Growth in constant growth phase after n. n = Length of high growth phase.
Assume g1 <> kCS and g2 < kCS
Three-stage Dividend Discount Model
Notes:
n1 = Length of high growth phase. n2 = Periods until constant growth phase. n2 = n1 + length of transistion phase.
Earnings Model
Constant Growth FCF Valuation Model
VOps = Value of Total Operations
VDebt, VPref = Value of debt and preferred stock
VNon-Ops Assets = Value of non-operating
Purpose
Formula
Basic Time Value Formulae
Future Value of a Single Sum
FV = PV ( 1 + i ) N
Present Value of a Single Sum
FV PV = -----------------( 1 + i)N
Solve for N for a Single Sum
FV ln ------PV
N = --------------------ln ( 1 + i )
Solve for i for a Single Sum
i =
Present Value of an Ordinary Annuity
1 – 1 ⁄ ( 1 + i )N
PV A = Pmt ----------------------------------i
Future Value of an Ordinary Annuity
( 1 + i )N – 1
FV A = Pmt ---------------------------i
Present Value of an Annuity Due
1 – 1 ⁄ ( 1 + i )( N – 1)
PV Ad = Pmt --------------------------------------------- + Pmt i Future Value of an Annuity Due
( 1 + i )N – 1
FV Ad = Pmt ---------------------------- ( 1 + i ) i Present Value of an Annuity Growing at a
Constant Rate (g)
Pmt 1
1+g
PV GA = ------------ 1 – -----------i–g
1+i
Future Value of an Annuity Growing at a
Constant Rate (g)
Pmt 1
1+g
FV GA = ------------ 1 – -----------i–g
1+i
Holding Period Return (single period)
P 1 + Cash Flows
HPR = ----------------------------------------------- – 1
P0
N
FV
------- – 1
PV
Basic Financial Formulae © 1995-2015 by Timothy R. Mayes, Ph.D.
N
N
(1 + i)
N
1
Selected Financial Formulae
Purpose
Formula
N
Holding Period Return with Reinvestment
(for multiple sub-period returns)
HPR Reinvest =
∏ ( 1 + HPRt ) – 1
t=1
Basic Security Valuation Formulae
Dividend Discount Model (AKA, the Gordon
Model)
Two-stage Dividend Discount Model
Notes: This equation is too long for one line. g1 = Growth rate during high growth phase. g2 = Growth in constant growth phase after n. n = Length of high growth phase.
Assume g1 <> kCS and g2 < kCS
Three-stage Dividend Discount Model
Notes:
n1 = Length of high growth phase. n2 = Periods until constant growth phase. n2 = n1 + length of transistion phase.
Earnings Model
Constant Growth FCF Valuation Model
VOps = Value of Total Operations
VDebt, VPref = Value of debt and preferred stock
VNon-Ops Assets = Value of non-operating