Isues in economics today 6th by guell chapter07

Chapter 07 Interest Rates and Present Value McGraw-Hill/Irwin Copyright © 2012 by The McGraw-Hill Companies, Inc All rights reserved Chapter Outline • Interest Rates • Present Value • Future Value • Kick It Up a Notch: Risk and Reward McGraw-Hill/Irwin ©2012 The McGraw-Hill Companies, All Rights Reserved 7-2 1-2 Interest Rates The Market for Money McGraw-Hill/Irwin ©2012 The McGraw-Hill Companies, All Rights Reserved 7-3 1-3 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 McGraw-Hill/Irwin ©2012 The McGraw-Hill Companies, All Rights Reserved 7-4 1-4 Figure The Market for Money Interest rate (r) Supply r* Demand $* McGraw-Hill/Irwin Money ($) Borrowed/Saved ©2012 The McGraw-Hill Companies, All Rights Reserved 7-5 1-5 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 McGraw-Hill/Irwin ©2012 The McGraw-Hill Companies, All Rights Reserved 7-6 1-6 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 rate n is the number of years until the payment is received/made McGraw-Hill/Irwin ©2012 The McGraw-Hill Companies, All Rights Reserved 7-7 1-7 The Amount Payable for Every Dollar Borrowed (For several interest rates and loan durations) Interest rate -> Years ↓ 30 20% 10% 5% 2% 1% 10 237 17.4 4.32 1.81 1.35 38 6.19 2.59 1.63 1.22 1.10 2.49 1.61 1.28 1.10 1.05 1.20 1.10 1.05 1.02 1.01 McGraw-Hill/Irwin ©2012 The McGraw-Hill Companies, All Rights Reserved 7-8 1-8 Examples From This Table • If you borrow $1 and promise to pay it back in 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 McGraw-Hill/Irwin ©2012 The McGraw-Hill Companies, All Rights Reserved 7-9 1-9 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 McGraw-Hill/Irwin ©2012 The McGraw-Hill Companies, All Rights Reserved 7-10 1-10 A Multiple Year Example @ 5% Year Cost Benefit PV Cost @5% 100 100.00 100 95.24 100 90.70 100 86.38 100 82.27 PV Benefit @5% 100 78.35 100 74.62 100 71.07 100 67.68 10 100 64.46 11 100 61.39 12 100 58.47 500 McGraw-Hill/Irwin 700 454.60 476.05 ©2012 The McGraw-Hill Companies, All Rights Reserved 7-11 1-11 A Multiple Year Example @ 8% Year Cost PV Cost @8% Benefit 100 100.00 100 92.59 100 85.73 100 79.38 100 73.50 PV Benefit @8% 100 68.06 100 63.02 100 58.35 100 54.03 10 100 50.02 11 100 46.32 12 100 42.89 500 McGraw-Hill/Irwin 700 431.21 382.68 ©2012 The McGraw-Hill Companies, All Rights Reserved 7-12 1-12 A Multiple Year Example @ 10% Year Cost PV Cost @10% Benefit 100 100.00 100 90.91 100 82.64 100 75.13 100 68.30 PV Benefit @10% 100 62.09 100 56.45 100 51.32 100 46.65 10 100 42.41 11 100 38.55 12 100 35.05 500 McGraw-Hill/Irwin 700 416.99 332.52 ©2012 The McGraw-Hill Companies, All Rights Reserved 7-13 1-13 Internal rate of return • Internal rate of return : The interest rate where the present value of costs and benefits are equal McGraw-Hill/Irwin ©2012 The McGraw-Hill Companies, All Rights Reserved 7-14 1-14 Monthly Payments Required on per $1000 of loan (For Several Interest Rates and Loan Durations) Intere st rate -> Years ↓ 20% 10% 5% 2% 1% 30 16.7 19.3 8.78 5.37 3.70 3.22 13.2 10.6 9.20 8.76 10 McGraw-Hill/Irwin ©2012 The McGraw-Hill Companies, All Rights Reserved 7-15 1-15 Examples From This Table • If you borrow $1000 and promise to pay it back monthly over 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 McGraw-Hill/Irwin ©2012 The McGraw-Hill Companies, All Rights Reserved 7-16 1-16 Future Value • Future value: the interest-adjusted value of past payments Future Value = payment × (1 + r ) McGraw-Hill/Irwin ©2012 The McGraw-Hill Companies, All Rights Reserved n 7-17 1-17 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 McGraw-Hill/Irwin ©2012 The McGraw-Hill Companies, All Rights Reserved 7-18 1-18 Kick It Up A Notch: Risk and Reward McGraw-Hill/Irwin ©2012 The McGraw-Hill Companies, All Rights Reserved 7-19 1-19 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 McGraw-Hill/Irwin ©2012 The McGraw-Hill Companies, All Rights Reserved 7-20 1-20 The Yield Curve • Yield Curve: the relationship between reward and the time until the reward is received US Treasury Yield Curve (January 2005) McGraw-Hill/Irwin ©2012 The McGraw-Hill Companies, All Rights Reserved 7-21 1-21 ... 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 $236.38 in interest McGraw-Hill/Irwin... McGraw-Hill/Irwin Money ($) Borrowed/Saved ©2012 The McGraw-Hill Companies, All Rights Reserved 7-5 1-5 Nominal vs Real Interest Rates • Nominal Interest Rate: the advertised rate of interest • Real Interest... McGraw-Hill/Irwin ©2012 The McGraw-Hill Companies, All Rights Reserved 7-3 1-3 Interest Rate • The interest rate is the percentage, usually expressed in annual terms, of a balance that is paid by a borrower