1. McGraw-Hill/Irwin ©2001 The McGraw-Hill Companies All Rights Reserved 5.0 Chapter 5 Discounte d Cash Flow Valuation

2. McGraw-Hill/Irwin ©2001 The McGraw-Hill Companies All Rights Reserved 5.1 5.3 Comparing Rates: The Effect of Compounding Periods

3. McGraw-Hill/Irwin ©2001 The McGraw-Hill Companies All Rights Reserved 5.2 Comparing Rates: The effect of Compounding Periods Interest Rates are quoted in many different ways: Tradition Legislation Mislead borrowers and investors

4. McGraw-Hill/Irwin ©2001 The McGraw-Hill Companies All Rights Reserved 5.3 Effective Annual Rates and Compounding If a rate is quoted as 10% compounded semiannually: The investment pays 5% every six months. 10 / 2 = 5

5. McGraw-Hill/Irwin ©2001 The McGraw-Hill Companies All Rights Reserved 5.4 Effective Annual Rates and Compounding Is 10% compounded semiannually (5% every six months) = 10% per year? No! $1 at 10% per year = 1(1.10) = 1.10.10 / 1.00 = 10% $1 at 5% every six months = 1(1.05) = 105 + 105(1.05) = 1.1025 = 1(1.05) 2 = 1.1025.1025 / 1.00 = 10.25% You earned interest on interest (compounding) 10% compounded semiannually = 10.25% compounded annually

6. McGraw-Hill/Irwin ©2001 The McGraw-Hill Companies All Rights Reserved 5.5 Effective Annual Rates and Compounding Anytime we have compounding during the year, we need to be concerned about what the rate really is?

7. McGraw-Hill/Irwin ©2001 The McGraw-Hill Companies All Rights Reserved 5.6 Effective Annual Rates and Compounding Stated Interest Rate (Quoted Interest Rate): The interest rate expressed in terms of the interest payment made each period. 10% compounded semiannually - in the previous example Effective Annual Rate (EAR): The interest rate expressed as if it were compounded once per year. The rate you will actually earn! 10.25% in the previous example

8. McGraw-Hill/Irwin ©2001 The McGraw-Hill Companies All Rights Reserved 5.7 Calculating and Comparing Effective Annual Rates Example: Pg 127 Suppose you’ve shopped around and come up with the following three rates: Bank A: 15 percent, compounded daily Bank B: 15.5 percent, compounded quarterly Bank C: 16 percent, compounded annually Which of these is best if you are thinking of opening a savings account? We want to find: Effective Annual Rate (EAR): The interest rate expressed as if it were compounded once per year. The rate you will actually earn!

9. McGraw-Hill/Irwin ©2001 The McGraw-Hill Companies All Rights Reserved 5.8 Calculating and Comparing Effective Annual Rates Example: Pg 127 Bank A: 15 percent, compounded daily Using our FV Formula: FV = PV (1 + r) t $1 x (1 +.15/365) 365 $1 x (1.000411) 365 = $1.1618.1618 / $1 =.1618 EAR Formula on page 128 EAR = (1 + Quoted rate/m) m – 1 m = the number of times the interest is compounded during the year EAR = (1 +.15/365) 365 – 1 EAR = (1 +.000411) 365 – 1 EAR =.1618

10. McGraw-Hill/Irwin ©2001 The McGraw-Hill Companies All Rights Reserved 5.9 Calculating and Comparing Effective Annual Rates Example: Pg 127 Bank B: 15.5 percent, compounded quarterly EAR = (1 + Quoted rate/m) m – 1 m = the number of times the interest is compounded during the year EAR = (1 +.155/4) 4 - 1 EAR = (1 +.03875) 4 - 1 EAR =.1642 Bank C: 16 percent, compounded annually The EAR = the Annual % Rate =.16

11. McGraw-Hill/Irwin ©2001 The McGraw-Hill Companies All Rights Reserved 5.10 Calculating and Comparing Effective Annual Rates Example: Pg 127 Results: Bank A: 15 percent, compounded daily EAR =.1618 Bank B: 15.5 percent, compounded quarterly EAR =.1642 Bank C: 16 percent, compounded annually EAR =.1600 The highest quoted rate is not necessarily the best. Compounding during the year can lead to a significant difference between the quoted rate the the effective rate.