Transcript 8-1 Chapter F8 The Time Value of Money Electronic Presentation by Douglas Cloud Pepperdine University 8-2 Objectives 1.

8-1
Chapter F8
The Time Value
of Money
Electronic Presentation
by Douglas Cloud
Pepperdine University
8-2
Objectives
1. Define futureOnce
and present
value.
you have
2. Determine
the futurethis
value
of a single
completed
chapter,
amount invested
at the
you should
be present
able to:time.
3. Determine the future value of an annuity.
4. Determine the present value of a single
amount to be received in the future.
5. Determine the present value of an annuity.
6. Determine investment values and interest
expense or revenue for various periods.
8-3
Objective
1
Determine future
and present value.
8-4
Future Value
The future value
of an amount is
the value of that
amount at a
particular time in
the future.
8-5
Present Value
The present value of
an amount is the
value of that amount
on a particular date
prior to the time the
amount is paid or
received.
8-6
Future Value
Future Value = Present Value (1 + R)
If $1,000 is invested on January 1, 2004, at
Interest Rate
5% interest, what will be the future value
(the amount that will accumulate) by
December 31, 2004?
Future Value = $1,000(1.05)
Future Value = $1,050
8-7
Objective
2
Determine the future
value of a single
amount invested at the
present time.
8-8
Compound Interest
Earning interest in one period
on interest earned in an earlier
period is known as compound
interest.
8-9
Compound Interest
If the accumulated amount ($1,050
from Slide 6) is left in the savings
account for a second year, until
December 31, 2005, how much would
the investment be worth at that time?
$1,050(1.05) = $1,102.50
8-10
Compound Interest
Assume you invest $500 for three
years at 8% interest. How much
would your investment be worth at
the end of three years?
FV = PV(1 + R) t
FV = $500(1.08)³
FV = $629.86
8-11
Compound Interest
Recall that the future value
of an amount is the value of
that amount at a particular
time in the future.
8-12
Compound Interest
You can use Excel to
determine the future
value of $500 that earns
8% interest compounded
annually for three years.
8-13
Compound Interest
Insert =500*(1.08^3)
in a cell and press
Enter.
8-14
Compound Interest
629.856
The amount shown in the
cell represents the future
value, which is $629.86.
8-15
Compound Interest
Excel also contains builtin functions for
calculating present and
future values.
8-16
Compound Interest
When you see USING
EXCEL in the margin of the
textbook, follow the
instructions to learn how to
use the built-in function.
8-17
Compound Interest
To calculating a future
value, a future value of a
single amount table, such
as the one in the next
slide, can be used.
8-18
Compound Interest
Period
Interest Rate
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
1
2
3
1.010 1.020 1.030 1.040 1.050 1.060 1.070 1.080 1.090
1.020 1.040 1.061 1.082 1.103 1.224 1.145 1.664 1.188
1.030 1.061 1.093 1.125 1.158 1.191 1.225 1.260 1.295
8-19
Compound Interest
Period
Interest Rate
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
1
2
3
1.010 1.020 1.030 1.040 1.050 1.060 1.070 1.080 1.090
1.020 1.040 1.061 1.082 1.103 1.224 1.145 1.664 1.188
1.030 1.061 1.093 1.125 1.158 1.191 1.225 1.260 1.295
8-20
Compound Interest
Period
Interest Rate
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
1
2
3
1.010 1.020 1.030 1.040 1.050 1.060 1.070 1.080 1.090
1.020 1.040 1.061 1.082 1.103 1.224 1.145 1.664 1.188
1.030 1.061 1.093 1.125 1.158 1.191 1.225 1.260 1.295
FV = $500 x 1.260 = $630 (rounded)
8-21
Exhibit 1
A
Interest Table for an Investment
of $500 for Three Years at 8%
Year
B
Value at
Beginning of Year
1
2
3
500.00
540.00
583.20
Total
C
Interest Earned
(B x Interest Paid)
40.00
43.20
46.66
129.86
D
FV at End
(B + C)
540.00
583.20
629.86
8-22
Objective
3
Determine the
future value of an
annuity.
8-23
Future Value of an Annuity
An annuity is a series of
equal amounts received or
paid over a specified number
of equal time periods.
8-24
Future Value of an Annuity
If $500 is invested at the end of
each year for three years, how much
would the investment be worth at
the end of three years if the interest
earned is 8% per year?
8-25
Future Value of an Annuity
Period
Interest Rate
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
1
2
3
1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
2.010 2.020 2.030 2.040 2.050 2.060 2.070 2.080 2.090
3.030 3.060 3.091 3.122 3.153 3.184 3.215 3.246 3.278
FVA = Amount invested (A) x Interest factor (IF)
FVA = $500 x 3.246 (rounded to three decimal places)
FVA = $1,623 (rounded)
8-26
Exhibit 2
A
Year
1
2
3
Total
Interest Table for an Annuity
of $500 at End of Each Year
for Three Years at 8%
B
C
Value
Interest Earned
at Beginning (Column B x
of Year
Interest Rate)
0.00
500.00
1,040.00
0.00
40.00
83.20
123.20
D
Amount
Invested at
End of Year
500.00
500.00
500.00
1,500.00
E
FV at
End of
Year
500.00
1,040.00
1,623.20
8-27
Future Value of an Annuity
How much would you
need to invest each year
to accumulate $1,000 at
the end of three years to
take a trip to Mexico
after you graduate from
college? Assume you
can earn 6% on your
investment.
8-28
Future Value of an Annuity
Period
Interest Rate
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
1
2
3
1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
2.010 2.020 2.030 2.040 2.050 2.060 2.070 2.080 2.090
3.030 3.060 3.091
3.184 1.225
3.215 3.246
3.091 3.122 3.153
3.153 3.184
1.191
1.260 3.278
1.295
FVA = Amount invested (A) x Interest factor (IF)
$1,000 = A x 3.184 (rounded to three decimal places)
A = $1,000 ÷ 3.184
A = $314 (rounded)
8-29
Future Value of an Annuity
We can calculate the amount of the
payment in Excel using the payment
function. Insert =PMT(0.06,3,,1000) in
a cell and press Enter.
8-30
Objective
4
Determine the present
value of a single
amount to be received
in the future.
8-31
Present Value of a Single Amount
Using Excel, the present value of an investment
that pays $3,000 at the end of three years at 8% can
be calculated by inserting =3000*(1/(1.08^3)) in a
cell and pressing Enter.
8-32
Present Value of a Single Amount
The present value of a single
amount table also could be used
to determine the present value
of the $3,000.
8-33
Present Value of a Single Amount
Period
Interest Rate
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
1
2
3
0.990 0.980 0.971 0.962 0.952 0.943 0.935 0.926 0.917
0.980 0.961 0.943 0.925 0.907 0.890 0.873 0.857 0.842
0.971 0.942 0.915 0.889 0.864 0.840 0.816 0.794 0.772
PV = FV x IF
PV = $3,000 x 0.794 (rounded to three decimal places)
PV = $2,382 (rounded)
8-34
Exhibit 3
A
Year
1
2
3
Interest Table for a Present
Value of $2,381.49 for Three
Years at 8%
B
Present Value at
Beginning of Year
2,381.49
2,572.01
2,777.77
Total
*Adjusted due to rounding
C
D
Interest Earned Value at End
(B x Interest Rate)
(B + C)
190.52
205.76
222.23*
618.51
2,572.01
2,777.77
3,000.00
8-35
Objective
5
Determine the
present value of an
annuity.
8-36
Present Value of an Annuity
Assume that you are considering
How much
the purchase of an investment
that
you of
have
would pay $1,000would
at the end
investThe
now?
each year for threetoyears.
investment is expected to earn a
return of 8%.
8-37
Present Value of an Annuity
Present Value at
Beginning of Year 1
$ 925.93 = $1.000 x (1.08)¹ (table value of 0.92593)
8-38
Present Value of an Annuity
Present Value at
Beginning of Year 1
$ 925.93
857.34 = $1,000 ÷ (1.08)² (table value of .= 0.85734)
8-39
Present Value of an Annuity
Present Value at
Beginning of Year 1
$ 925.93
857.34
793.83 = $1,000 ÷ (1.08)³ (table value of 0.79373)
8-40
Present Value of an Annuity
Present Value at
Beginning of Year 1
$ 925.93
857.34
793.83
$2,577.10 Required investment now
8-41
Present Value of an Annuity
Present Value at
Beginning of Year 1
$ 925.93
857.34
793.83
$2,577.10 Required investment now
$3,000.00 Total amount received over three years
2,577.10 Present value of total investment
$ 422.90 Interest earned over three years
8-42
Present Value of an Annuity
The PV function in Excel
can be used to calculate the
present value of an annuity.
The function can be entered
in the pop-up box or directly
into the cell.
8-43
Present Value of an Annuity
If you purchase an
investment that paid $1,000
each year for three years at
8% interest, insert
=PV(0.08,3,–1000) in a cell
and press Enter.
8-44
Present Value of an Annuity
Or, you can use the
present value of an
annuity table.
8-45
Present Value of an Annuity
Period
Interest Rate
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
1
2
3
0.990 0.980 0.971 0.962 0.952 0.943 0.935 0.926 0.917
1.970 1.942 1.913 1.886 1.860 1.833 1.808 1.783 1.759
2.941 2.884 2.829 2.775 2.723 2.673 2.624 2.577 2.531
PVA = FV x IF
PVA = $1,000 x 2.577 (table value read to three decimal
places)
PVA = $2,577 (rounded)
8-46
Exhibit 4
Interest Table for an Annuity
of $1,000 Each Year for
Three Years at 8%
A
B
C
Present Value Interest Earned
at Beginning (Column B x
Year
of Year
Interest Rate)
1
2,577.10
206.17
D
E
Total Amount Value at
Invested
End of
(B + C)
Year
2,783.27
1,783.27
$2,783.27 – $1,000.00
8-47
Exhibit 4
Interest Table for an Annuity
of $1,000 at the End of Each
Year for Three Years at 8%
A
B
C
Present Value Interest Earned
at Beginning (Column B x
Year
of Year
Interest Rate)
1
2
2,577.10
1,783.27
206.17
142.66
D
E
Total Amount Value at
Invested
End of
(B + C)
Year
2,783.27
1,925.93
1,783.27
925.93
$1,925.93 – $1,000.00
8-48
Exhibit 4
Interest Table for an Annuity
of $1,000 at the End of Each
Year for Three Years at 8%
A
B
C
Present Value Interest Earned
at Beginning (Column B x
Year
of Year
Interest Rate)
1
2
3
Total
2,577.10
1,783.27
925.93
206.17
142.66
74.07
422.90
D
E
Total Amount Value at
Invested
End of
(B + C)
Year
2,783.27
1,925.93
1,000.00
1,783.27
925.93
0.00
8-49
Objective
6
Determine
investment values
and interest
expense or revenue
for various periods.
8-50
Loan Payments and Amortization
You negotiate with a
dealer to purchase a
car for $5,000, which
you arrange to borrow
from a local bank.
8-51
Loan Payments and Amortization
What
approach
should I use?
The bank charges
12% interest on the
loan, which is to be
repaid in two years in
equal monthly
payments.
8-52
Loan Payments and Amortization
Of course, the present
value of an annuity.
How much
will the
payment be
each month?
8-53
Loan Payments and Amortization
If the annual interest rate is 12 percent,
then interest is 1 percent per month.
Interest Rate
Period
0.01
0.01
0.01
0.02
0.03
0.04
0.05
1
2
0.990
10
0.99010
1.97040
0.98039
1.94156
0.97087
1.91347
0.96154
1.88609
0.95238
1.85941
3
2.94099
2.88388
2.82861
2.77509
2.72325
24
21.24339 18.91393 16.93554 15.24696 13.79864
8-54
Loan Payments and Amortization
If the annual interest rate is 12 percent,
then interest is 1 percent per month.
Interest Rate
Period
0.01
0.01
0.01
0.02
0.03
0.04
0.05
1
2
0.990
10
0.99010
1.97040
0.98039
1.94156
0.97087
1.91347
0.96154
1.88609
0.95238
1.85941
3
2.94099
2.88388
2.82861
2.77509
2.72325
24
21.24339 18.91393 16.93554 15.24696 13.79864
8-55
Loan Payments and Amortization
There are 24 monthly
periods in two years.
Interest Rate
Period
0.01
0.01
0.01
0.02
0.03
0.04
0.05
1
2
0.990
10
0.99010
1.97040
0.98039
1.94156
0.97087
1.91347
0.96154
1.88609
0.95238
1.85941
3
2.94099
2.88388
2.82861
2.77509
2.72325
24
21.24339
21.24339 18.91393 16.93554 15.24696 13.79864
8-56
Loan Payments and Amortization
PVA = A x IF
$5,000 = A x 21.24339
A = $5,000 ÷ 21.24339
A = $235.37
Interest Rate
Period
0.01
0.01
0.01
0.02
0.03
0.04
0.05
1
2
0.990
10
0.99010
1.97040
0.98039
1.94156
0.97087
1.91347
0.96154
1.88609
0.95238
1.85941
3
2.94099
2.88388
2.82861
2.77509
2.72325
24
21.24339
21.24339 18.91393 16.93554 15.24696 13.79864
8-57
Loan Payments and Amortization
Insert =PMT(.01,24,5000)
How do I determineinthe
the cell
and press
Enter. by
monthly
car payment
using the payment
function in Excel?
8-58
Exhibit 5
A
Amortization Table for
Automobile Loan of $5,000 for
24 Months at 1% per Month
B
Present Value
at Beginning
Month
of Year
1
5,000.00
C
Interest Incurred
(Column B x
Interest Rate)
D
Amount
Paid)
E
Value at
End of
Month
50.00
235.37
4,814.63
$5,000.00 – ($235.37 – $50.00)
8-59
Exhibit 5
A
Amortization Table for
Automobile Loan of $5,000 for
24 Months at 1% per Month
B
Present Value
at Beginning
Month
of Year
1
2
5,000.00
4,814.63
C
Interest Incurred
(Column B x
Interest Rate)
D
Amount
Paid)
E
Value at
End of
Month
50.00
48.15
235.37
235.37
4,814.63
4,627.41
$4,814.63 – ($235.37 – $48.15)
8-60
Exhibit 5
Amortization Table for
Automobile Loan of $5,000 for
24 Months at 1% per Month
8-61
Loan Payments and Amortization
On April 1, 2004, you
borrow the necessary
$5,000 from the bank
by issuing a note
payable.
8-62
Loan Payments and Amortization
ASSETS
Date
Accounts
4/1 Notes Receivable
Cash
Cash
= LIABILITIES
Other
Assets
5,000
-5,000
Bank’s Books
+ OWNERS’ EQUITY
Contributed Retained
Capital
Earnings
8-63
Loan Payments and Amortization
ASSETS
Date
Accounts
4/1 Cash
Notes Payable
Cash
= LIABILITIES
+ OWNERS’ EQUITY
Contributed Retained
Capital
Earnings
Other
Assets
5,000
5,000
Customer’s Books
8-64
Loan Payments and Amortization
On April 30, 2004, the
first payment of $235.37
is made. Interest of $50
is included ($5,000 x
1%) in the payment.
8-65
Loan Payments and Amortization
ASSETS
Date
Accounts
Cash
= LIABILITIES
Other
Assets
4/30 Cash
235.37
Notes Receivable
–185.37
Interest Revenue
Bank’s Books
+ OWNERS’ EQUITY
Contributed Retained
Capital
Earnings
50.00
8-66
Loan Payments and Amortization
ASSETS
Date
Accounts
Cash
4/30 Notes Payable
Interest Expense
Cash
–235.37
= LIABILITIES
+ OWNERS’ EQUITY
Contributed Retained
Capital
Earnings
Other
Assets
–185.37
Customer’s Books
–50.00
8-67
Loan Payments and Amortization
In the last month of the
loan (March 2006), the
bank records would reflect
that the note has been fully
paid by the customer.
8-68
Loan Payments and Amortization
ASSETS
Date
Accounts
Cash
= LIABILITIES
Other
Assets
3/31 Cash
235.30
Notes Receivable
–232.97
Interest Revenue
+ OWNERS’ EQUITY
Contributed Retained
Capital
Earnings
2.33
Bank’s Books
Click this button to review the amortization table.
8-69
Loan Payments and Amortization
ASSETS
Date
Accounts
Cash
3/31 Cash
–235.30
Notes Payable
Interest Expense
= LIABILITIES
+ OWNERS’ EQUITY
Contributed Retained
Capital
Earnings
Other
Assets
–232.97
Customer’s Books
–2.33
8-70
Unequal Payments
How
much
The
Jill Johnson
amounts
would
her
she
invested
invested
a
investments
portion
in
thoseof
years
her
be
worth
at
salary
were $700,
at the
the
end
of
four
beginning
$800, $900,
of
years
if
she
each
and $1,000,
year for
earned
6%
per
respectively.
four years.
year?
8-71
Unequal Payments
$700
x 1.19102
Four
(6%,
Years
3 periods)
$800
$ 833.71
x 1.12360
(6%,
2 periods)
Three
Years
898.88
1 period)
$900 x 1.0600
Two(6%,
Years
954.00
$1,000
One
Year
x 1.0000
Total
1,000.00
$3,686.59
8-72
Unequal Payments
How much would
she have to invest
to receive $200,
$300, and $400 at
the end of the
next three years if
she earned 7%?
8-73
Unequal Payments
PV at
Beginning
of Year
$186.92
xOne
0.93458
Year
Two
Years
x 0.87344
262.03
326.52
$775.47
Amounts Received
at End of Each Year
$200
Years
xThree
0.81630
Total
$300
$400
8-74
Exhibit 6
Future and Present
Value Concepts
8-75
CHAPTER F8
THE END
8-76
8-77
8-78
Exhibit 5
A
Amortization Table for
Automobile Loan of $5,000 for
24 Months at 1% per Month
B
Present Value
at Beginning
Month
of Year
1
2
3
23
24
5,000.00
4,814.63
4,627.41
463,70
232.97
C
Interest Incurred
(Column B x
Interest Rate)
D
Amount
Paid)
E
Value at
End of
Month
50.00
48.15
46.27
4.64
2.33
235.37
235.37
235.37
235.37
235.30
4,814.63
4,627.41
4,438.32
232.97
0.00
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