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