Transcript Document

PRINCIPLES OF FINANCE
University of Management and Technology
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FIN100
Chapter 5:
The Time Value of Money
Keown, A. J., Petty, J. W., Martin, J. D., and
Scott, D.F., Foundations of Finance: The
Logic and Practice or Financial
Management (with EVA Tutor Package) (4th
Ed.) Prentice Hall © 2003.
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FIN100
Objectives
Understand and calculate compound interest
Understand the relationship between compounding and
bringing money back to the present
Annuity and future value
Annuity Due
Future value and present value of a sum with non-annual
compounding
Determine the present value of an uneven stream of
payments
Perpetuity
Understand how the international setting complicates time
value of money
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Compound Interest
When interest paid on an investment is added to the
principal, then during the next period, interest is earned on
the new sum
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FIN100
Simple Interest
Interest is earned on principal
$100 invested at 6% per year
1st year
interest is $6.00
2nd year interest is $6.00
3rd year
interest is $6.00
Total interest earned:$18
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FIN100
Compound Interest
Interest is earned on previously earned interest
$100 invested at 6% with annual compounding
1st year
interest is $6.00
Principal is $106
2nd year interest is $6.36
Principal is $112.36
3rd year
interest is $6.74
Principal is $119.11
Total interest earned: $19.10
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FIN100
Future Value (1)
How much a sum will grow in a certain number of years
when compounded at a specific rate.
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Future Value (2)
What will an investment be worth in a year?
$100 invested at 7%
FV = PV(1+i)
$100 (1+.07)
$100 (1.07) = $107
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Future Value (3)
Future Value can be increased by:
Increasing number of years of compounding
Increasing the interest or discount rate
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FIN100
Future Value (4)
What is the future value of $1,000 invested at 12% for 3
years? (Assume annual compounding)
Using the tables, look at 12% column, 3 time periods. What
is the factor?
$1,000 X 1.4049 = 1,404.90
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FIN100
Present Value (1)
What is the value in today’s dollars of a sum of money to be
received in the future ?
or
The current value of a future payment
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FIN100
Present Value (2)
What is the present value of $1,000 to be received in 5 years
if the discount rate is 10%?
Using the present value of $1 table, 10% column, 5 time
periods
$1,000 X .621 = $621
$621 today equals $1,000 in 5 years
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FIN100
Annuity
Series of equal dollar payments for a specified number of
years.
Ordinary annuity payments occur at the end of each period
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FIN100
Compound Annuity
Depositing or investing an equal sum of money at the end of
each year for a certain number of years and allowing it to
grow.
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FIN100
Compounding Annuity
What will $1,000 deposited every year for eight years at 10%
be worth?
Use the future value of an annuity table, 10% column, eight
time periods
$1,000 X 11.436 = $11,436
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FIN100
Future Value of an Annuity
If we need $8,000 in 6 years (and the discount rate is 10%),
how much should be deposited each year?
Use the Future Value of an Annuity table, 10% column, six
time periods.
$8,000 / 7.716 = $1036.81 per year
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FIN100
Present Value of an Annuity (1)
Pensions, insurance obligations, and interest received from
bonds are all annuities. These items all have a present
value.
Calculate the present value of an annuity using the present
value of annuity table.
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FIN100
Present Value of an Annuity (2)
Calculate the present value of a $100 annuity received
annually for 10 years when the discount rate is 6%.
$100 X 7.360 = $736
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FIN100
Present Value of an Annuity (3)
Would you rather receive $450 dollars today or $100 a year
for the next five years?
Discount rate is 6%.
To compare these options, use present value.
The present value of $450 today is $450.
The present value of a $100 annuity for 5 years at 6% is
XXX?
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FIN100
Present Value of an Annuity (4)
Present Value table, five time periods, 6% column factor is
4.2124
$100 X 4.2124 = 421.24
Which option will you choose?
$450 today or $100 a year for five years
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FIN100
Annuities Due
Ordinary annuities in which all payments have been shifted
forward by one time period.
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FIN100
Amortized Loans
Loans paid off in equal installments over time
Typically Home Mortgages
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FIN100
Payments and Annuities
If you want to finance a new motorcycle with a purchase
price of $25,000 at an interest rate of 8% over 5 years, what
will your payments be?
Use the present value of an annuity table, five time periods,
8% column – factor is 3.993
$25,000 / 3.993 = 6,260.96
Five annual payments of $6,260.96
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FIN100
Amortization of a Loan
Reducing the balance of a loan via annuity payments is
called amortizing.
A typical amortization schedule looks at payment, interest,
principal payment and balance.
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FIN100
Amortization Schedule
Amortize the payments on a 5-year loan for $10,000 at 6% interest.
N
1
2
3
4
5
PaymentInterest
$2,373.96
$2,373.96
$2,373.96
$2,373.96
$2,373.99
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$493.56
$380.74
$261.15
$134.38
Prin. Pay
New Balance
(PxRxT)
(Payment Interest)
(Principal – Prin Pay)
$600
$1,880.40
$1,993.22
$2,112.81
$2239.61
$1,773.96
$6,345.64
$4352.42
$2,239.61
-----------
$8,226.04
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FIN100
Mortgage Payments
How much principal is paid on the first payment of a $70,000
mortgage with 10% interest, on a 30 year loan (with monthly
payments)
Payment is $614
How much of this payment goes to principal and how much
goes to interest?
$70,000 x .10 x 1/12 = $583
Payment of $614, $583 is interest, $31 is applied toward
principal
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FIN100
Compounding Interest with Nonannual periods
If using the tables, divide the percentage by the number of
compounding periods in a year, and multiply the time periods
by the number of compounding periods in a year.
Example:
10% a year, with semi annual compounding for 5 years.
10% / 2 = 5% column on the tables
N = 5 years, with semi annual compounding or 10
Use 10 for Number of periods, 5% each
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FIN100
Non-annual Compounding
What factors should be used to calculate 5 years at 12%
compounded quarterly
N = 5 x 4 = 20
% = 12% / 4 = 3%
Use 3% column, 20 time periods
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Perpetuity
An annuity that continues forever is called perpetuity
The present value of a perpetuity is
PV = PP/i
PV = present value
PP = Constant dollar amount of perpetuity
i = Annuity discount rate
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FIN100
Future Value of $1 Table
N
1
2
3
4
5
6
7
8
9
10
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6%
1.06
1.1236
1.1910
1.2625
1.3382
1.4185
1.5036
1.5938
1.6895
1.7908
8%
1.0800
1.1664
1.2597
1.3605
1.4693
1.5869
1.7138
1.8509
1.9990
2.1589
10%
1.1000
1.2100
1.3310
1.4641
1.6105
1.7716
1.9487
2.1436
2.3579
2.5937
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12%
1.1200
1.2544
1.4049
1.5735
1.7623
1.9738
2.2107
2.4760
2.7731
3.1058
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Present Value of $1
N
1
2
3
4
5
6
7
8
9
10
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6%
.9434
.8900
.8396
.7921
.7473
.7050
.6651
.6274
.5919
.5584
8%
.9259
.8573
.7938
.7350
.6806
.6302
.5835
.5403
.5002
.4632
10%
.9091
.8264
.7513
.6830
.6209
.5645
.5132
.4665
.4241
.3855
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12%
.8929
.7972
.7118
.6355
.5674
.5066
.4523
.4039
.3606
.3220
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Future Value of Annuity
N
1
2
3
4
5
6
7
8
9
10
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6%
8%
10%
12%
1.000
1.0000
1.000
1.000
2.060
2.0800
2.100
2.1200
3.1836
3.2464
3.310
3.3744
4.3746
4.5061
4.6410
4.7793
5.6371
5.8666
6.1051
6.3528
6.9753
7.3359
7.7156
8.1152
8.3938
8.9228
9.4872
10.8090
9.8975
10.6366
11.435912.2997
11.491312.4876
13.5795
14.7757
13.1808
14.4866
15.9374
17.5487
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Present Value of an Annuity
N
1
2
3
4
5
6
7
8
9
10
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6%
.9434
1.8334
2.6730
3.4651
4.2124
4.9173
5.5824
6.2098
6.8017
7.3601
8%
.9259
1.7833
2.5771
3.3121
3.9927
4.6229
5.2064
5.7466
6.2469
6.7101
10%
.9091
1.7355
2.4869
3.1699
3.7908
4.3553
4.8684
5.3349
5.7590
6.1446
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12%
.8929
1.6901
2.4018
3.0373
3.6048
4.1114
4.5638
4.9676
5.3282
5.6502
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