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1
Chapter 11
Time Value of Money
A
FEDERAL RESERVE NOTE
THE UNITED STATES OF AMERICATHE UNITED STATES OF AMERICA
L70744629F
12
1212
12
L70744629F
ONE DOLLARONE DOLLAR
WASHINGTON, D.C.
THIS NOTE IS LEGAL TENDER
FOR ALL DEBTS, PUBLIC AND PRIVATE
SERIES
1985
H 293
Adapted from Financial Accounting 4e by Porter and Norton
218
Time Value of Money
Prefer payment now vs. in future due to interest factor
Applicable to both personal and business decisions
3
Simple Interest
I = P x R x T
Princi
pal a
mount
Dollar a
mount o
f
inte
rest
per
yea
r
Time
in y
ears
Inte
rest
rate
as
a per
centa
ge
420
Example of Simple Interest
Given following data:principal amount = $ 3,000annual interest rate = 10%term of note = 2 years
Calculate interest on the note.
521
Example of Simple Interest
Given following data:principal amount = $ 3,000annual interest rate = 10%term of note = 2 years
Calculate interest on the note.
P x R x T $ 3,000 x .10 x 2 = $ 600
622
Compound Interest
Interest is calculated on principal plus previously accumulated interest
Compounding can occur annually, semi-annually, quarterly, etc.
7
Example of Compound Interest
Given following data:
principal amount = $ 3,000
annual interest rate = 10%
term of note = 2 years
semiannual compounding of interest
Calculate interest on note.
8
Compound Interest Periods
Year 1 Year 2
10% annually 10% annually
5% + 5%semiannually
5% + 5%semiannually
4 periods @ 5% semi-annual interest
9
Example of Compound Interest
Period Beginning Interest Ending Principal at 5% Balance
1 $ 3,000 $ 150 $ 3,150
2 3,150 158 3,308
3 3,308 165 3,473
4 3,473 174 3,647
10
Comparing Interest Methods
Simple annual interest: $3,000 x .10 x 2 = $ 600Semiannual compounding:
1 $ 150 2 158 3 165 4 174
Total $ 647
11
Compound Interest Computations
Present value of an
annuity
Future value of an
annuity
Present value of a
single amount
Future value of a
single amount
12
Future Value of Single Amount
Known amount of single payment or deposit Future Value
+ Interest =
13
Future Value of a Single Amount Example
If you invest $10,000 today @ 10% compound interest, what will it be worth 3 years from now?
invest
$10,000 Future Value?
+ Interest @ 10% per year
Yr. 1 Yr. 2 Yr. 3
14
Future Value of a Single Amount Example - Using Formulas
nFV = p (1 + i)
3 = $10,000 (1.10)
= $13,310
15
FV = Present Value x FV Factor = $ 10,000 X (3 periods @ 10%)
Future Value of a Single Amount Example - Using Tables
FV??$10,000 PV
Yr. 1 Yr. 2 Yr. 3
16
(n) 2% 4% 6% 8% 10% 1 1.020 1.040 1.060 1.080 1.10 2 1.040 1.082 1.124 1.166 1.210
3 1.061 1.125 1.191 1.260 1.3314 1.082 1.170 1.262 1.360 1.464
5 1.104 1.217 1.338 1.470 1.611 6 1.126 1.265 1.419 1.587 1.772 7 1.149 1.316 1.504 1.714 1.949 8 1.172 1.369 1.594 1.851 2.144
Future Value of $1
17
FV = Present Value x FV Factor = $ 10,000 X (3 periods @ 10%) = $ 10,000 X 1.331 = $ 13,310
Future Value of a Single Amount Example - Using Tables
FV = $13,310$10,000 PV
Yr. 1 Yr. 2 Yr. 3
1834
Present Value of Single Amount
Discount
Known amount of single paymentin futurePresent Value
19
Present Value of a Single Amount Example
If you will receive $10,000 in three years, what is it worth today (assuming you could invest at 10% compound interest)?
Present Value? $ 10,000
Discount @ 10%
Yr. 1 Yr. 2 Yr. 3
20
Present Value of a Single Amount Example - Using Formulas
-nPV = payment x (1 + i)
-3 = $10,000 x (1.10)
= $7,513
21
PV = Future Value x PV Factor = $ 10,000 X (3 periods @ 10%)
Present Value of a Single Amount Example - Using Tables
FV=$10,000PV ??
Yr. 1 Yr. 2 Yr. 3
22
Present Value of $1
(n) 2% 4% 6% 8% 10%
1 .9804 .9615 .9434 .9259 .9090 2 .9612 .9246 .8900 .8573 .8265 3 .9423 .8890 .8396 .7938 .7513 4 .9238 .8548 .7921 .7350 .6830 5 .9057 .8219 .7473 .6806 .6209
23
PV = Future Value x PV Factor = $ 10,000 X (3 periods @ 10%)
= $ 10,000 X .7513 = $ 7,513
Present Value of a Single Amount Example - Using Tables
FV=$10,000 PV = $7,513
Yr. 1 Yr. 2 Yr. 3
24
Periods
FutureValue?
+Interest
Future Value of an Annuity
1 2 3 4
$0 $3,000 $3,000 $3,000 $3,000
25
If we invest $3,000 each year for four years at 10% compound interest, what will it be worth 4 years from now?
Future Value of Annuity Example
$0 $3,000 $3,000 $3,000 $3,000
Yr. 1 Yr. 2 Yr. 3 Yr. 4
FV ??
26
$0 $3,000 $3,000 $3,000 $3,000
Yr. 1 Yr. 2 Yr. 3 Yr. 4
FV ??
FV = Payment x FV Factor = $ 3,000 x (4 periods @ 10%)
Future Value of Annuity Example
27
Future Value of Annuity of $1
(n) 2% 4% 6% 8% 10% 12% 1 1.000 1.000 1.000 1.000 1.000 1.000 2 2.020 2.040 2.060 2.080 2.100 2.120 3 3.060 3.122 3.184 3.246 3.310 3.374 4 4.122 4.246 4.375 4.506 4.641 4.779 5 5.204 5.416 5.637 5.867 6.105 6.353
28
FV = Payment x FV Factor = $ 3,000 x (4 periods @ 10%) = $ 3,000 x 4.641 = $ 13,923
$0 $3,000 $3,000 $3,000 $3,000
Yr. 1 Yr. 2 Yr. 3 Yr. 4
FV = $13,923
Future Value of Annuity Example
29
Present Value of an Annuity
Periods1 2 3 4
PresentValue ?
Discount$0 $500 $500 $500 $500
A
FEDERAL RESERVE NOTE
THE UNITED STATES OF AMERICATHE UNITED STATES OF AMERICA
L70744629F
12
1212
12
L70744629F
ONE DOLLARONE DOLLAR
WASHINGTON, D.C.
THIS NOTE IS LEGAL TENDER
FOR ALL DEBTS, PUBLIC AND PRIVATE
SERIES
1985
H 293
A
FEDERAL RESERVE NOTE
THE UNITED STATES OF AMERICATHE UNITED STATES OF AMERICA
L70744629F
12
1212
12
L70744629F
ONE DOLLARONE DOLLAR
WASHINGTON, D.C.
THIS NOTE IS LEGAL TENDER
FOR ALL DEBTS, PUBLIC AND PRIVATE
SERIES
1985
H 293
A
FEDERAL RESERVE NOTE
THE UNITED STATES OF AMERICATHE UNITED STATES OF AMERICA
L70744629F
12
1212
12
L70744629F
ONE DOLLARONE DOLLAR
WASHINGTON, D.C.
THIS NOTE IS LEGAL TENDER
FOR ALL DEBTS, PUBLIC AND PRIVATE
SERIES
1985
H 293
A
FEDERAL RESERVE NOTE
THE UNITED STATES OF AMERICATHE UNITED STATES OF AMERICA
L70744629F
12
1212
12
L70744629F
ONE DOLLARONE DOLLAR
WASHINGTON, D.C.
THIS NOTE IS LEGAL TENDER
FOR ALL DEBTS, PUBLIC AND PRIVATE
SERIES
1985
H 293
30
Present Value of an Annuity Example
What is the value today of receiving $4,000 at the end of the next 4 years, assuming you can invest at 10% compound annual interest?
PV ??
Yr. 1 Yr. 2 Yr. 3 Yr. 4
$0 $4,000 $4,000 $4,000 $4,000
31
Present Value of an Annuity Example
Yr. 1 Yr. 2 Yr. 3 Yr. 4
PV ??
$0 $4,000 $4,000 $4,000 $4,000
PV = Payment x PV Factor = $ 500 x (4 periods @ 10%)
32
Present Value of Annuity of $1
(n) 2% 4% 6% 8% 10%
1 0.980 0.962 0.943 0.926 0.909 2 1.942 1.886 1.833 1.783 1.735 3 2.884 2.775 2.673 2.577 2.487 4 3.808 3.630 3.465 3.312 3.170 5 4.713 4.452 4.212 3.992 3.791
33
Present Value of an Annuity Example
Yr. 1 Yr. 2 Yr. 3 Yr. 4
P.V. = $12,680
$0 $4,000 $4,000 $4,000 $4,000
PV = Payment x PV Factor = $ 4,000 x (4 periods @ 10%)
= $ 4,000 x 3.170 = $ 12,680
34
Solving for Unknowns
Assume that you have just purchased a new car for $14,420. Your bank has offered you a 5-year loan, with annual payments of $4,000 due at the end of each year. What is the interest ratebeing chargedon the loan?
35
Solving for Unknowns
Yr. 1 Yr. 2 Yr. 3 Yr. 4 Yr. 5
discount discount discount discount discount
PV = $14,420
PV = Payment x PV factor
PV factor = PV / Payment rearrange equation to solve for unknown
36
Solving for Unknowns
Yr. 1 Yr. 2 Yr. 3 Yr. 4 Yr. 5
discount discount discount discount discount
PV = $14,420
PV factor = PV / Payment = $14,420 / $4,000 = 3.605
3753
Present Value of an Annuity Table
(n) 10% 11% 12% 15% 1 0.909 0.901 0.893 0.870 2 1.736 1.713 1.690 1.626 3 2.487 2.444 2.402 2.283 4 3.170 3.102 3.037 2.855 5 3.791 3.696 3.605 3.352
PV factor of 3.605 equates to an interest rate of 12%.
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