TIME VALUE OF MONEY
BRIEF CONCEPT
Ø The timing of cash outflow and inflows has important economic consequences
Ø Time value is based on the belief that a dollar today is worth more than a dollar that will be received at some future date
Future Value : The value at a given future date of a present amount placed on deposit today and earning interest at a specified rate.
Present Value : The current dollar value of a future amount of money that would have to be invested today at a given interest rate over a specifies period equal to the future amount.
a) Single Amount
· Future Value
FVn = PV x (1+i)n = PV x FVIF i,n
FV = Future Value
PVn = Initial principal or present value at period n
i = Annual rate of interest paid
n = Number of period (typically years)
FVIF i,n = Future Value Interest Factor at “i” percent for “n” period
· Present Value
PV = FVn x 1 = FVn x PVIF i,n
(1+i)n
FVn = Future Value
PVn = Initial principal or present value at period n
i = Annual rate of interest paid
n = Number of period
PVIFi,n = Present Value Interest Factor at “i” percent for “n” period
b) Annuities
A streamline of equal periodic cash flow over a specified time period.
Ordinary Annuity :
An annuity for which the cash flow occurs at the end of each period.
· Future Value
FVAn = PMT x Σ (1+i)n-1 = PMT x FVIFAi,n
· Present Value
PVAn = PMT x 1 = PMT x PVIFAi,n
Σ(1+i)n-1
Annuity Due
· Future Value
FVIFAi,n ( annuity due ) = FVIFAi,n x (1+i)
· Present Value
PVIFAi,n (annuity due ) = PVIFAi,n x (1+i)
c) Mixed Stream
A stream of unequal periodic cash flows that reflect no particular pattern.
·
MMore frequent than annually
FVn = PV x ( 1 + 1/m) mxn
m = frequent in each year
n = years
e) Effective Annual Rates
The annual rate of interest actually paid or earned.
EAR = ( 1 + i/m ) m - 1
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