1. McGraw-Hill/Irwin Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved. Chapter 07 Interest Rates and Present Value

2. 1- 2 ©2012 The McGraw-Hill Companies, All Rights ReservedMcGraw-Hill/Irwin 7-2 Chapter Outline Interest Rates Present Value Future Value Kick It Up a Notch: Risk and Reward

3. 1- 3 ©2012 The McGraw-Hill Companies, All Rights ReservedMcGraw-Hill/Irwin 7-3 Interest Rates The Market for Money

4. 1- 4 ©2012 The McGraw-Hill Companies, All Rights ReservedMcGraw-Hill/Irwin 7-4 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.

5. 1- 5 ©2012 The McGraw-Hill Companies, All Rights ReservedMcGraw-Hill/Irwin 7-5 Figure 1 The Market for Money Supply Demand r* $* Interest rate (r) Money ($) Borrowed/Saved

6. 1- 6 ©2012 The McGraw-Hill Companies, All Rights ReservedMcGraw-Hill/Irwin 7-6 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

7. 1- 7 ©2012 The McGraw-Hill Companies, All Rights ReservedMcGraw-Hill/Irwin 7-7 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.

8. 1- 8 ©2012 The McGraw-Hill Companies, All Rights ReservedMcGraw-Hill/Irwin 7-8 The Amount Payable for Every Dollar Borrowed (For several interest rates and loan durations) Interest rate -> Years  20%10%5%2%1% 30237.3817.454.321.811.35 106.192.591.631.221.10 52.491.611.281.101.05 11.201.101.051.021.01

9. 1- 9 ©2012 The McGraw-Hill Companies, All Rights ReservedMcGraw-Hill/Irwin 7-9 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.

10. 1- 10 ©2012 The McGraw-Hill Companies, All Rights ReservedMcGraw-Hill/Irwin 7-10 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.

11. 1- 11 ©2012 The McGraw-Hill Companies, All Rights ReservedMcGraw-Hill/Irwin 7-11 A Multiple Year Example @ 5% YearCostBenefitPV Cost @5% PV Benefit @5% 1100100.00 210095.24 310090.70 410086.38 510082.27 610078.35 710074.62 810071.07 910067.68 1010064.46 1110061.39 1210058.47 500700454.60476.05

12. 1- 12 ©2012 The McGraw-Hill Companies, All Rights ReservedMcGraw-Hill/Irwin 7-12 A Multiple Year Example @ 8% YearCostBenefitPV Cost @8% PV Benefit @8% 1100100.00 210092.59 310085.73 410079.38 510073.50 610068.06 710063.02 810058.35 910054.03 1010050.02 1110046.32 1210042.89 500700431.21382.68

13. 1- 13 ©2012 The McGraw-Hill Companies, All Rights ReservedMcGraw-Hill/Irwin 7-13 A Multiple Year Example @ 10% YearCostBenefitPV Cost @10%PV Benefit @10% 1100100.00 210090.91 310082.64 410075.13 510068.30 610062.09 710056.45 810051.32 910046.65 1010042.41 1110038.55 1210035.05 500700416.99332.52

14. 1- 14 ©2012 The McGraw-Hill Companies, All Rights ReservedMcGraw-Hill/Irwin 7-14 Internal rate of return Internal rate of return : The interest rate where the present value of costs and benefits are equal.

15. 1- 15 ©2012 The McGraw-Hill Companies, All Rights ReservedMcGraw-Hill/Irwin 7-15 Monthly Payments Required on per $1000 of loan (For Several Interest Rates and Loan Durations) Interest rate -> Years  20%10%5%2%1% 3016.718.785.373.703.22 1019.3313.2210.619.208.76 526.4921.2518.8717.5317.09 192.6387.9285.6184.2483.79

16. 1- 16 ©2012 The McGraw-Hill Companies, All Rights ReservedMcGraw-Hill/Irwin 7-16 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.

17. 1- 17 ©2012 The McGraw-Hill Companies, All Rights ReservedMcGraw-Hill/Irwin 7-17 Future Value Future value: the interest-adjusted value of past payments.

18. 1- 18 ©2012 The McGraw-Hill Companies, All Rights ReservedMcGraw-Hill/Irwin 7-18 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

19. 1- 19 ©2012 The McGraw-Hill Companies, All Rights ReservedMcGraw-Hill/Irwin 7-19 Kick It Up A Notch: Risk and Reward

20. 1- 20 ©2012 The McGraw-Hill Companies, All Rights ReservedMcGraw-Hill/Irwin 7-20 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

21. 1- 21 ©2012 The McGraw-Hill Companies, All Rights ReservedMcGraw-Hill/Irwin 7-21 The Yield Curve Yield Curve: the relationship between reward and the time until the reward is received US Treasury Yield Curve (January 2005)