Chapter 7 Interest Rates and Present ValueChapter OutlineYou Are HereInterest RatesInterest RateFigure 1 The Market for MoneyNominal vs. Real Interest RatesPresent ValueThe Amount Payable for Every Dollar Borrowed (For several interest rates and loan durations)Examples From This TableMortgages, Car Payments, and other Multiple-Payment ExamplesA Multiple Year Example @ 5%A Multiple Year Example @ 8%A Multiple Year Example @ 10%Internal rate of returnMonthly Payments Required on per $1000 of loan (For Several Interest Rates and Loan Durations)Slide 17Future ValueRule of 72Kick It Up A Notch:Kick It Up A Notch: Risk and RewardThe Yield CurveChapter 7 Interest Rates and Present ValueCopyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill/Irwin7-2Chapter Outline•Interest Rates•Present Value7-3You Are Here7-4Interest RatesThe Market for Money7-5Interest Rate•The interest rate is the percentage, usually expressed in annual terms, of a balance that is paid by a borrower to a lender that is in addition to the original amount borrowed or lent.7-6Figure 1 The Market for MoneySupplyDemandr*$*Interest rate (r) Money ($) Borrowed/Saved7-7Nominal 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 consumption7-8Present 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.7-9The Amount Payable for Every Dollar Borrowed (For several interest rates and loan durations)Interest rate -> Years 20% 10% 5% 2% 1%30 237.3817.454.32 1.81 1.3510 6.19 2.59 1.63 1.22 1.105 2.49 1.61 1.28 1.10 1.051 1.20 1.10 1.05 1.02 1.017-10Examples 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.7-11Mortgages, 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.7-12A Multiple Year Example @ 5%Year Cost Benefit PV Cost @5% PV Benefit @5%1 100 100.002 100 95.243 100 90.704 100 86.385 100 82.276 100 78.357 100 74.628 100 71.079 100 67.6810 100 64.4611 100 61.3912 100 58.47500 700 454.60 476.057-13A Multiple Year Example @ 8%Year Cost Benefit PV Cost @8%PV Benefit @8%1 100 100.002 100 92.593 100 85.734 100 79.385 100 73.506 100 68.067 100 63.028 100 58.359 100 54.0310 100 50.0211 100 46.3212 100 42.89500 700 431.21 382.687-14A Multiple Year Example @ 10%Year Cost Benefit PV Cost @10%PV Benefit @10%1 100 100.002 100 90.913 100 82.644 100 75.135 100 68.306 100 62.097 100 56.458 100 51.329 100 46.6510 100 42.4111 100 38.5512 100 35.05500 700 416.99 332.527-15Internal rate of return•Internal rate of return : The interest rate where the present value of costs and benefits are equal.7-16Monthly Payments Required on per $1000 of loan (For Several Interest Rates and Loan Durations)Interest rate -> Years 20% 10% 5% 2% 1%30 16.718.78 5.37 3.70 3.2210 19.3313.2210.619.20 8.765 26.4921.2518.8717.5317.091 92.6387.9285.6184.2483.797-17Examples 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.7-18Future Value•Future value: the interest-adjusted value of past payments. nrpaymentValueFuture  17-19Rule 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 years7-20Kick It Up A Notch:Risk and Reward7-21Kick 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 risk7-22The Yield Curve•Yield Curve: the relationship between reward and the time until the reward is receivedUS Treasury Yield Curve (January