1. 6-1 July 16 Outline EAR versus APR Interest Rates and Bond Valuation

2. 6-2 Effective Annual Rate (EAR) This is the actual rate paid (or received) after accounting for compounding that occurs during the year If you want to compare two alternative investments with different compounding periods, you need to compute the EAR and use that for comparison.

3. 6-3 Annual Percentage Rate (APR) This is the annual rate that is quoted by law on all loans. By definition: APR = period rate times the number of periods per year

4. 6-4 Computing EARs Example Suppose you can earn 1% per month on $1 invested today. What is the APR? 1(12) = 12% How much are you effectively earning? FV = 1(1.01) 12 = 1.1268 Rate = (1.1268 – 1) / 1 =.1268 = 12.68%

5. 6-5 Computing EARs Example (continued) Suppose you put it in another account and earn 3% per quarter. What is the APR? 3(4) = 12% How much are you effectively earning? FV = 1(1.03) 4 = 1.1255 Rate = (1.1255 – 1) / 1 =.1255 = 12.55%

6. 6-6 EAR - Formula Remember that the APR is the quoted rate, and “m” is the number of compounding periods per year

7. 6-7 EAR and Frequency of Compounding

8. Interest Rates and Bond Valuation 8

9. 9 Chapter Outline Bond Definition Bond Features Bond Valuation Inflation and Interest Rates Determinants of Bond Yields Bond Ratings Bond Markets

10. A bond is a contract between two parties: one is the investor (you) and the other is a company or a government agency (like a municipal bond) Bond Definition 10

11. A bond contains three key items: 1.The par value (typically $1,000) 2. Term of the contract (e.g., maturities ranging from 2-30 years) 3. A coupon interest rate Bond Features 11

12. You lend money to the borrower with the expectation that you will get back your original investment plus interest. The interest is determined by the coupon interest rate. 12 Bond Features

13. For example: A 6% coupon interest rate yields: (the coupon interest rate) x ( the par value) (6%) x ($1,000) = $60 per year for each year of the bond. 13

14. Let’s look at this visually using the time line: 12345 $60 14

15. Let’s look at this visually using the time line: Now let’s add the maturity value… 12345 $60 $1,000 15

16. So the investor receives the principal ($1,000) and earned interest ($60 per year) as payment for loaning the company money. 16

17. Types of Bonds 17 1.Government Bonds 2.Zero Coupon Bonds 3.Floating-Rate Bonds 4.Catastrophe (Cat) Bonds 5.Convertible Bonds

18. Let’s look at this visually using the time line: 1.The annuity 2.The single payment (lump sum) $60 $1,000 123450 18

19. Now bring each back into present value terms: First the annuity… Secondly, the lump sum… $60 $1,000 123450 19

20. The Bond Pricing Equation 20 Notice that r = the discount rate used to bring back the future dollars. This discount rate has a name in bonds: The Yield to Maturity (YTM).

21. A bond valuation example: 5 year bond 14% as the discount rate (YTM) 6% coupon interest rate $1,000 maturity value 21

22. 22 5 years = N 14% = Discount rate (YTM) $60 = Payment (PMT) $1,000 = FV PV = ? -725.35 1st 2nd TI BA II Plus

23. 23 Excel

24. Key concepts: If the coupon interest rate exactly equals the discount rate, then the bond value today will ALWAYS = the par value ($1,000) If the coupon interest rate is less (more) than the discount rate, then the bond value today will be greater (less) than the par value ($1,000). Bond prices are inversely related to discount rates. 24 Bond Valuation

25. 25 Bond Valuation

26. 26 See http://www.bloomberg.com/markets/rates-bonds/government- bonds/us for the current US Treasury Yield Curve.http://www.bloomberg.com/markets/rates-bonds/government- bonds/us