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Time value of money Cheat Sheet by NatalieMoore
Variable key
Concept of future value
Future Value of Cash Flow Streams
Where:
Mixed stream
Future value
Annuity
same basic technique
Compound interest
Principal
Important to understand
Equation guide
Future value of a lump sum:
FV = CF1 x (1 +r)
(1 + r)
n
n-1
+ CF2 x (1 + r)
n-2
+ ... + CFn x
n-n
FV = PV x (1 + r)
Future Value of an Ordinary Annuity
The Power of Compound Interest
Ordinary annuity
Future Value of an Ordinary Annuity
Annuity due
Future Value of an Annuity Due
So, future value of an annuity due always greater
Future Value of Cash Flow Streams
than ordinary annuity
Present value of a lump sum in future
FV = PMT x { [ ( 1 + r ) - 1 ] / r}
n
Finding the Future Value of an Annuity Due
Present value
Present Value of a Mixed Stream
Present Value of an Ordinary Annuity
n
FV (annuity due) = PMT x { [ ( 1 + r) -1 ] / r } x (1 +
r)
Present Value of Annuity Due
Discounting
Present Value of Cash Flow Streams
Lump sum future value in excel
Perpetuity
Present Value of a Growing Perpetuity
1
1
PV = [CF1 x 1 / (1 + r) ] + [CF2 x 1 / (1 + r) ] + ... +
1
[CFn x 1 / (1 + r) ]
PV = CF1 / r - g r > g
n
n
PV = FV / (1 + r) = FV x [ 1 / (1+ r) ]
Present Value of an Ordinary Annuity
Stated Versus Effective Annual Interest Rates
The Power of Discounting
n
PV = PMT/r x [1 - 1 / (1 + r) ]
Stated annual rate
Present Value of Annuity Due
Effective annual rate (EAR)
Special applications of time value
EAR = ( 1 + r/m )
m
n
PV (annuity due) = PMT/r x [1 - 1 / (1 + r) ] x (1 + r)
-1
EAR (continuous compou-
Present Value of a Perpetuity
r
nding) = e - 1
Deposits Needed to Accumulate a Future Sum
Compounding More Frequently Than Annually
n
PV = PMT x 1/r = PMT/r
PMT = FV {[( 1 + r) - 1 ] / r}
Semiannual compounding
Loan Amortization
Quarterly compounding
m values:
Continuous Compounding
Loan amortization schedule
FV = PV x (1 + r / m)
FV (continuous compounding) =
Portion of payment representing interest declines
over the repayment period, and the portion going to
mxn
PV x ( e
rxn
)
principal repayment increases
n
PMT = PV / {1 / r x [ 1 - 1 / (1 + r) ] }
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