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