Transcript Ross Template

Chapter 9
The Time Value
of Money
PPT 9-1
TABLE 9-1
Future value of $1 (FVIF)
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FIGURE 9-1
Relationship of present value
and future value
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PPT 9-2
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PPT 9-3
TABLE 9-2
Present value of $1 (PVIF)
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FIGURE 9-2
Compounding process for annuity
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PPT 9-4
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PPT 9-5
TABLE 9-3
Future value of an
annuity of $1 (FVIFA)
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PPT 9-7
TABLE 9-5
Relationship of present
value to annuity
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PPT 9-8
TABLE 9-6
Payoff table for loan
(amortization table)
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PPT 9-9
Determining the Yield on an Investment
Formula
Table Appendix
Future value – single amount
(9-1)
FV = PV x FVIF
9-1
A
Present value – single amount
(9-2)
PV = FV x PVIF
9-2
B
Future value – annuity
(9-3)
FVA = A x FVIFA
9-3
C
Present value – annuity
(9-4)
9-4
D
Annuity equaling a future value
(9-5)
PVA = A x PVIFA
FVA
A=
FVIFA
PVA
A=
PVIFA
9-3
C
9-4
D
Annuity equaling a present value (9-6)
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PPT 9-10
Finding Present Value (first part)
A1
A2
A3
A4
A5
$1,000 $1,000 $1,000 $1,000 $1,000
Present
value
0
1
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2
3
4
5
6
7
8
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PPT 9-10
Finding Present Value (second part)
End of third period—Beginning of fourth period
$3,993
A1
A2
A3
A4
A5
$1,000$1,000$1,000$1,000$1,000
Present
value
0
1
2
3
4
5
6
7
8
Each number represents the end of the period; that is, 4 represents the
end of the fourth period.
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PPT 9-10
Finding Present Value (final part)
End of third period—Beginning of fourth period
$3,170
Present
value
0
$3,993 A1
A2
A3
A4
A5
(single amount) $1,000$1,000$1,000$1,000$1,000
1
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2
3
4
5
6
7
8
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Chapter 9 - Outline
LT 9-1
 Time
Value of Money
 Future Value and Present Value
 Annuity
 2 Questions to Ask in Time Value of Money
Problems
 Adjusting for Non-Annual Compounding
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Time Value of Money
LT 9-2
The basic idea behind the concept of time value of money is:
– $1 received today is worth more than $1 in the future
OR
– $1 received in the future is worth less than $1 today
Why?
– because interest can be earned on the money
The connecting piece or link between present (today) and
future is the interest rate
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Future Value and Present Value
LT 9-3
Future Value (FV) is what money today will be worth at
some point in the future
FV = PV x FVIF
FVIF is the future value interest factor (Appendix A)
Present Value (PV) is what money at some point in the
future is worth today
PV = FV x PVIF
PVIF is the present value interest factor (Appendix B)
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Annuity
LT 9-4
Annuity:
– a stream or series of equal payments to be received in the
future

The payments are assumed to be received at the end of
each period

A good example of an annuity is a lottery, where the
winner is paid over a number of years
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2 Questions to Ask in Time Value
of Money Problems
LT 9-5
Future Value or Present Value?
Future Value: Present (Now)  Future
Present Value: Future  Present (Now)
Single amount or Annuity?
Single amount: one-time (or lump) sum
Annuity: same amount per year for a number of
years
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Adjusting for Non-Annual
Compounding
LT 9-6
 Interest
is often compounded quarterly, monthly,
or semiannually in the real world
 Since the time value of money tables assume
annual compounding, an adjustment must be
made:
– the number of years is multiplied by the number of
compounding periods
– the annual interest rate is divided by the number of
compounding periods
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