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McGraw-Hill/Irwin Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.
Chapter 07 Interest
Rates and Present Value
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Chapter Outline
• Interest Rates• Present Value• Future Value• Kick It Up a Notch: Risk and
Reward
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Interest Rates
The Market for Money
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Interest Rate
• The interest rate is the percentage, usually expressed in annual terms, of a balance that is paid by a borrower to a lender that is in addition to the original amount borrowed or lent.
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Figure 1 The Market for Money
Supply
Demand
r*
$*
Interest rate (r)
Money ($) Borrowed/Saved
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Nominal vs. Real Interest Rates
• Nominal Interest Rate: the advertised rate of interest
• Real Interest Rate: the rate of interest after inflation expectations are accounted for; the compensation for waiting on consumption
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Present Value• Present Value is the interest
adjusted value of future payment streams.
• Mathematically, the present value of a payment is =(payment)/(1+r)n Where
r is the interest raten is the number of years until the payment is received/made.
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The Amount Payable for Every Dollar Borrowed (For several interest rates
and loan durations)
Interest rate -> Years
20% 10% 5% 2% 1%
30 237.38
17.45
4.32 1.81 1.35
10 6.19 2.59 1.63 1.22 1.10
5 2.49 1.61 1.28 1.10 1.05
1 1.20 1.10 1.05 1.02 1.01
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Examples From This Table• If you borrow $1 and promise to pay
it back in 5 years at 5% interest you will owe $1.28 which is the original $1 plus 28 cents in interest.
• If you borrow $1 and promise to pay it back in 30 years at 20% interest you will owe $237.38 which is the original $1 plus $236.38 in interest.
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Mortgages, Car Payments, and other Multiple-Payment Examples• Mortgages are loans taken out to
buy homes. Typically you borrow a large sum of money and promise to pay it back in even amounts each month for 10, 15, or 30 years.
• Car loans are similar to mortgages in that you borrow a large sum but the loan duration is usually two to six years.
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A Multiple Year Example @ 5%Year Cost Benefit PV Cost
@5%PV Benefit @5%
1 100 100.00
2 100 95.24
3 100 90.70
4 100 86.38
5 100 82.27
6 100 78.35
7 100 74.62
8 100 71.07
9 100 67.68
10 100 64.46
11 100 61.39
12 100 58.47
500 700 454.60 476.05
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A Multiple Year Example @ 8%Year Cost Benefit
PV Cost @8%
PV Benefit @8%
1 100 100.00
2 100 92.59
3 100 85.73
4 100 79.38
5 100 73.50
6 100 68.06
7 100 63.02
8 100 58.35
9 100 54.03
10 100 50.02
11 100 46.32
12 100 42.89
500 700 431.21 382.68
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A Multiple Year Example @ 10%Year Cost Benefit
PV Cost @10%
PV Benefit @10%
1 100 100.00
2 100 90.91
3 100 82.64
4 100 75.13
5 100 68.30
6 100 62.09
7 100 56.45
8 100 51.32
9 100 46.65
10 100 42.41
11 100 38.55
12 100 35.05
500 700 416.99 332.52
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Internal rate of return
• Internal rate of return : The interest rate where the present value of costs and benefits are equal.
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Monthly Payments Required on per $1000 of loan (For Several Interest
Rates and Loan Durations)
Interest
rate ->
Years
20% 10% 5% 2% 1%
30 16.71
8.78 5.37 3.70 3.22
10 19.33
13.22
10.61
9.20 8.76
5 26.49
21.25
18.87
17.53
17.09
1 92.63
87.92
85.61
84.24
83.79
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Examples From This Table• If you borrow $1000 and
promise to pay it back monthly over 5 years at 5% interest you will owe $18.87 per month.
• If you borrow $1000 and promise to pay it back monthly over 10 years at 20% interest you will owe $19.33 per month.
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Future Value
• Future value: the interest-adjusted value of past payments.
nrpaymentValueFuture 1
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Rule of 72
• Rule of 72: A short cut that allows you to estimate the time it would take for an investment to double by dividing 72 by the annual interest rate.• For example: How long would it take to
double your money ($10,000) at 4% interest?• FV formula: $10,000x(1.04)^18=$20,258.17 (so
a little less than 18 years is the answer).• Rule of 72: 72/4=18 years
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Kick It Up A Notch:
Risk and Reward
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Kick It Up A Notch: Risk and Reward
• Risk: the possibility that the investor will not get those anticipated payoffs• Default Risk: the risk to the investor that
the borrower will not pay • Market Risk: the risk that the market
value of an asset will change in an unanticipated manner
• Reward• Risk Premium the reward investors
receive for taking greater risk
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The Yield Curve• Yield Curve: the relationship between reward and
the time until the reward is received
2.00
2.50
3.00
3.50
4.00
4.50
5.00
Year
Inte
rest
Rat
e
US Treasury Yield Curve (January 2005)