84
Business Finance
Lecture 15
Review of the Previous Lecture
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Time Value of Money
{
Future Value Concept
{
Present Value Concept
{
Multiple Cash Flow
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Future Value
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Present Value
Topics under Discussion
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Annuities cash Flows
{
Present Value
{
Future Value
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Annuities Due
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Perpetuities
Annuities
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We will frequently encounter situations where we have multiple cash flows that are all the
same amount.
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Series of equal installments for a loan-repayment
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A series of constant, or level, cash flows that occur at the end of each period for some fixed
number of periods is called an ordinary
Annuity.
Present Value for Annuity cash flows
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For annuity calculation, we use a variation of present value equation.
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The present value of an annuity of
C
dollars per period for t periods when interest rate is r is:
PV=C ° (1 - Present value factor)/r = C ° [1 - 1/(1 + r)
t
]/r
Where
C = Periodic payment or annuity
r = rate of interest
t = number of periods
The term in the parenthesis is called present value interest factor of an annuity (PVIFA
r,t
).

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85
Present Value Interest Factor of an Annuity (PVIFA)
Interest Rates
Number of
Periods
5%
10%
15%
20%
1
0.9524
0.9091
0.8696
0.8333
2
1.8594
1.7255
1.6257
1.5278
3
2.7232
2.4869
2.2832
2.1065
4
3.5460
3.1699
2.8550
2.5887

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