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TIME VALUE OF MONEY
Time line
important tool used in time value of money analysis; it is a graphical representation used to show the timing of cash flows
Time :
0 1 2 3 4 5
Outflow cash deposit ,cost , or amount paid
has a minus sign
Inflow cash receipt
Time:
Cash flows: ?
5%0 1 2 3
100
Time:
10%
?100
1 25%
0
Compounding
arithmetic process of determining the final value of a cash flow or series of cash flow when compound interest is applied
PV = present value, beginning amounti = interest rateINT= interest earned during the year
(PVxi)= future value, ending
amountn = number of periods
= PV + INT = PV + PV(i) = PV (n+i) = $100 (1+0.05) = $100 (1.05) = $105
Future value (FV) amount to which a cash flow or a series of cash flows will grow over a given period of time when compounded at a given interest rate
Initial deposit:
Interest earned:
Amount at the end of each
period = 127.63
121.55115.76
110.25105.00
6.085.795.515.00
=?=?=?=?=?100
543210
:
5.25
i
N = the number of periodsI = interest rate of periodsPV = present valuePMT = paymentFV = future value
Relationship among Future Value, Growth, Interest Rates, and Time
0 2 4 6 8 100
1
2
3
4
5
i = 0%I =5%i = 10%i = 15%
Periods
Future Value of $1
Opportunity Cost Rate rate of return on the best available alternative investment of equal risks
Present Value (PV) value of today of a future cash flow or series of cash flow
Fair(Equilibrium)Value price at which investors are indifferent between buying or selling a security
Discounting
process of finding the present value of a cash flow or a series of cash flows; discounting is the reverse of compounding
PV =
0 1 2 3 4 55%
PV=? 127.63
0 1 2 3 4 55%
127.63
÷1.05
121.25115.76110.25105.00100
÷1.05 ÷1.05 ÷1.05 ÷1.05
Relationship among Present Value, Interest Rates, and Time
0 2 4 6 8 100
0.25
0.5
0.75
1
i = 0%i = 5%i = 10%i = 15%
i= i=
0 1 2 3 4 5?
78.35 100
n= n=
05%
78.35 100
n=?
Annuity
series of payment of an equal amount at fixed intervals for a specified number of periods
Ordinary (Deferred) Annuity annuity whose payment occur at the end of each period
Annuity Due
annuity whose payment occur at the beginning of each period
future value of an annuity over n periods
Perpetuity
stream of equal payments expected to continue forever
CONSOL
perpetual bond issued by the British government to consolidated past debts; in general, any perpetual bond
Uneven Cash Flow Stream series of cash flow in which the amount varies from one period to the next
Payment (PMT)
term designates equal cash flows coming at regular intervals
Cash Flows (CF)
term designates uneven cash flows
Terminal Value
future value of an uneven cash flows stream
Annual compounding arithmetic process of
determining the final value of a cash flow or series of cash flows when interest is added once a year
Semiannual Compounding arithmetic process of determining the final value of a cash flow or series of cash flows when interest is added twice a year
Nominal (Quoted, or Stated, or APR) Interest Rate contracted, or quoted, or
stated, interest rate
Effective (Equivalent)Annual Rate (EFF% or EAR) annual rate of interest
actually being earned, as opposed to the quoted rate
“equivalent annual rate”
Annual Percentage Rate (APR)
periodic rate X the number of periods per year
Amortized Loan
loan that is repaid in equal payments over its life
Amortization schedule
table showing precisely how a loan will be repaid
gives the required payment on each payment date and a breakdown of the payment, showing how much is interest and how much is repayment of principal