Legend Key for TVM Formulae
Future Value - Regular Annuity
r= required rate of return, interest or discount rate per period
n= number of periods
C= periodic cash flow payment
g= periodic growth rate
FV
(1 r ) n 1
r
C
Present Value - Regular Annuity
1
(1 r ) n
r
1
Future Value Lump Sum - Simple Interest
PV
FV = PV (1+nr)
C
Present Value - Annuity Due
1
Future Value Lump Sum - Compound Interest
PVD
FV = PV (1+r)n
Present Value Lump Sum - Compound Interest
PV
Future Value - Annuity Due
FV
FVD
(1 r ) n
FVRe gularAnn(1 r )
Future Value - Annuity Due
Present Value of a Perpetual Annuity
AnnuityPayment
r
PV
C
1
(1 r ) n
(1 r )
r
FVD
(1 r ) n 1
(1 r )
r
C
Present Value of a Finite Growing Annuity
Effective Annual Rate of Interest
EAR
1
i
n
PV
n
1
C
r
g
1 g
1 r
1
n
Future Value of a Finite Growing Annuity
i= quoted annual percentage rate & n= number of compounding periods per
year.
Periodic Rate of Interest
r
1
i
m
m
Effective Annual Rate - Continuous Compounding
f
1 or r
1 EAR
1
n
1
EAR
i= quoted annual percentage rate, m=compounding frequency of quoted rate,
f= frequency of compounding of required periodic rate & n= number of
compounding periods per year.
Annual Periodic Rate of Interest
APR
Currie CFIN300
n 1 EAR
eq 1
q= quoted rate
e= 2.718281828
Price of Preferred Shares
1
n
1
P0
D
r
Price of Common Shares
Stock Price after committed new growth projects
D1
r g
P0
EPS
r
P0
NPVGO
Bond Price
Current Bond Yield
1
Annual Interest Payment
Current Bond Price
Current Yield
B
C
1
(1 r ) n
r
FaceValue
(1 r ) n
Total Dollar Return (TDR) = Dividend Income
Fisher Effect - Real Rate of Return
+ Capital Gain/(Loss)
1 R (1 r ) (1 inflation rate )
CFt
TDR
R= nominal rate of return
r= real rate of return
PE
PB
PB
CFt
PC
PB
Expected Return (in general)
Expected Portfolio Return (in general)
E ( R)
Oj
Pj
E ( RP )
j
Variance of returns (in general)
Standard Deviation of a 2 Stock Portfolio
xL2
P
2
L
xU2
2
U
x1 E( R1 ) x 2 E ( R2 ) ... x n E ( Rn )
2 xL xU
2
LU
Oj
E ( R) 2
Pj
j
Covariance of 2 Securities
Standard Deviation of a 2 Security Portfolio
CORR i , j
ij
i
j
P
Beta of a Stock
A
2
L
xU2
2
U
2 x L xU CORR L,U
L
U
Historical Variance
COV ( R A , RM )
2
x L2
( RM )
or
A
CORR L,Mkt
2
L
Mkt
(R Mkt )
2
( R1 R ) 2 ... ( RT
T 1
R )2
Capital Asset Pricing Model
E ( Ri )
rf
[ E ( RM ) r f ]
Profitabil ity Index
i
Arbitrage Pricing Theory
E ( R)
2
...
PV of CCA tax shield
Rf
1
E ( R1 ) R f
E ( R2 ) R f
n
Present value of cash inflows
Present value of cash outflows
S n dT
(d k )
CdT 1 0.5 k
(d k )
1 k
1
(1 k ) n
d= CCA rate, T= tax rate, k=cost of capital or required rate of
return & S= salvage value.
E ( Rn ) R f
Current Ratio
=
Current Assets
Current Liabilities
Total Asset
Turnover
=
Sales
Total Assets
Inventory Turnover
=
COGS
Inventory
ROE
=
Net Income
Total Equity
Currie CFIN300
Quick Ratio
= Current Assets-Inventory
Current Liabilities
ROA
=
Net Income
Total Assets
Cash Ratio
=
Cash
Current Liabilities
P/E Ratio
Receivables Turnover
=
Sales
Accounts Receivable
Dividend Payout
Ratio
=
DPS
EPS
D/E Ratio
=
Total Debt
Total Equity
Dividend Payout
Ratio
=
Cash Dividends
Net Income
Total Debt Ratio
=
Total Debt
Total Assets
Market to Book
Ratio
= Price/common share
EPS
=
Price / Common share
Book value of equity
Equity multiplier
=
Total Assets
Total Equity
Profit
Margin
=
Net Income
Sales
Net Working
Capital to Total Assets
=
Net Working Capital
Total Assets
Interval Measure
=
Current Assets
Average Daily
Operating Costs
Long Term Debt
Ratio
=
Long Term Debt
Total Equity + LT Debt
Cash Coverage
Ratio
=
EBIT + Depreciation
Interest
Days’ Sales in
Receivables
=
365 Days
Receivables Turnover
Days’ Sales in
Inventory
=
365 Days
Inventory Turnover
Internal Growth
Rate
=
ROA x R
‘Sustainable
Growth Rate
=
ROE x R
NWC
Turnover
=
Sales
NWC
‘Sustainable
Growth Rate
=
p(S/A)(1+D/E) x R
Times Interest
Earned
=
EBIT
Interest Charges
Fixed Asset
Turnover
=
Sales
Net Fixed Assets
Du Pont Identity ROE = Profit Margin x Total Asset Turnover x Equity Multiplier
Currie CFIN300