1. Bonds and Their Valuation 7-1 Chapter 7

2. Bond Market Bond Market Size – US : $31.2 Trillion (2009) – World : $82.2 Trillion (2009) Types of Bond: Government Bond (Treasury), Corporate Bond, and several others… Bond Market Basics Extremely large number of bond issues, but generally low daily volume in single issues Makes getting up-to-date prices difficult, particularly on a small company or municipal issues Treasury securities are an exception 7-2

3. Bond Definition A bond is a contract between the investor and the issuer (company or government) – Investor loans money to the issuer for a defined period of time at a specified interest rate. 7-3

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5. Bond Terminology Maturity Date – Final repayment date Face Value/Par Value – Notional amount used to compute the coupon payments Coupon Rate – Determines the amount of each coupon payment Coupon Payment Yield or Yield to Maturity (YTM) – Buyers of bonds earn a rate of return called the yield. 7-5

6. Bond Cash Flows, t=0 7-6 BUYERBOND ISSUER $PRICE BOND BOND ISSUANCE, t=0

7. Bond Cash Flows, t=1,…,t 7-7 BUYERBOND ISSUER $ DOLLAR RETURNS, t=1,…,T COUPONS PRINCIPAL

8. Bond Valuation Primary Principle: – Value of financial securities = PV of expected future cash flows Bond value is, therefore, determined by the present value of the coupon payments and par value. 7-8

9. Zero-Coupon Bond Zero-coupon bond (also called discount bond) – Coupon rate is =0 – Treasury Bills is a good example of zero-coupon bond. F 0 1 2 T-2 T-1 T 7-9

10. Zero Coupon Bond: Pricing Maturity (T): 5 years Face value (F): $1,000 YTM =3% annual compounding The current borrowing amount The repayment amount in 5 years 7-10

11. Coupon Bond Cash flows – Annuity component (the coupons) – Lump sum (the face value paid at maturity F) 0 1 2 T-2 T-1 T C C C C C+F Annuity 7-11 Lump sum

12. Coupon Bond: Pricing T: 5 years  YTM = 4% annual compounding  F: $1,000 Coupon rate: 5%; annual payment C= $1,000*5%=$50 Alternatively: 7-12

13. Coupon Bond: Pricing T: 5 years  F: $1,000 YTM = 4%, semi-annual compounding Coupon rate: 5%; semi-annual payment C= $1,000*5%/2 = $25 T = 5*2 = 10 periods r = YTM/2 = 4%/2= 2% 7-13

14. Exercise: Zero-coupon bond Find the value of a 15-year zero-coupon bond with a $1,000 par value and a yield to maturity (APR; semi- annually compounded) of 12%. 7-14

15. Exercise: price of zero coupon bond 7-15

16. Maturity: 30 years YTM=10% (annual compounding) Coupon: 8%, annual Face value: $1,000 What is the price of the bond today? Exercise: Coupon Bond 7-16

17. Maturity: 30 years YTM=10% (semi-annual compounding) Coupon: 8%, semi-annual Face value: $1,000 What is the price of the bond today? Exercise: Coupon Bond 7-17

18. Exercise: Coupon Bond C t = $1,000*8%/2=$40 (semi-annual) T= 30*2=60 periods r=10%/2=5% 7-18

19. Exercise: Coupon Bond A 15-year bond with a 10% coupon rate, $1,000 par value and semi-annual coupon payments was issued by Titanic Cruises Ltd seven years ago. You bought this bond two years ago when the semi-annually compounded market interest rate was 5% (YTM). – How much did you pay for the bond? 7-19

20. Exercise: Coupon Bond Remaining maturity when you bought bond two years ago: 15 – (7 – 2) = 10 years Coupon payments: YTM=5%  r six-month = 2.5% 7-20

21. Yield-to-Maturity The yield (sometimes also referred to as the yield- to-maturity or YTM) of the bond is the expected annual return on the bond if the bond is held till maturity. How to solve for YTM? – Financial Calculators – Excel 7-21

22. Maturity: 30 years Coupon: 8%, semi-annual Face value: $1,000 C t = $1,000*8%/2=$40 (semi-annual) T= 30*2=60 periods Bond Yield Example If the bond is selling at $900. What is the implied YTM? Rate=4.483%; YTM=4.483%*2=8.966% 7-22

23. Decompose YTM 7-23

24. An Example: Current and Capital Gains Yield Find the current yield and the capital gains yield in the first year for a 10-year, 9% semi-annual coupon bond that sells for $887, and has a face value of $1,000. The YTM for this bond is 10.9117%. 7-24

25. Calculating Capital Gains Yield Capital gains yield: YTM = Current yield + Capital gains yield 7-25

26. YTM, CY and CGY Grossnickle Corporation issued 20-year, 7.5% annual coupon bonds at their par value of $1,000 one year ago. Today, the market interest rate on these bonds is 5.5%. What is the yield of the bond? What is the current price of the bonds? What is the bond’s current yield? What is the bond’s capital gains yield? 7-26

27. Solution Bond Yield: 5.5% Price: CY: 75/1232.153=6.09% CGY: 5.5%-6.09%=-0.59% 7-27

28. Quick review questions: What is bond yield? How can you decompose bond yield? Where does the return (yield) come from for a zero- coupon bond? 7-28

29. Let’s return to the previous example…. T: 5 years  F: $1,000  YTM = 4% Coupon rate: 5%; semi-annual payment C= $1,000*5%/2 = $25 T = 5*2 = 10 periods r = YTM/2 = 4%/2= 2% Selling at a premium 7-29

30. YTM and Bond Price What if YTM = 5% today? r=2.5% What if YTM =6 % today? r=3% Selling at par! Selling at a discount 7-30

31. The Inverse Relationship Between Bond Prices and Yields Premium: Coupon rate>YTM 7-31

32. YTM, Coupon Rate & Bond Prices 7-32

33. What about bond price over time? This bond has a $1,000 lump sum (the par value) due at maturity (t = 10) and the bond pays annual coupon payment at 7% coupon rate. YTM equals to 10%. – What is the bond price today? – What is the bond price one year from today? – What is the bond price eight years from today? 7-33

34. Bond Price Over Time Bond price today Bond price in one year Bond price in eight years 7-34

35. Changes in Bond Value over Time What would happen to the value of these three bonds if the required rate of return remained at 10%? 7-35 Years to Maturity 1,184 1,000 816 10 13% coupon rate 7% coupon rate 10% coupon rate VBVB 50

36. Bond Values over Time At maturity, the value of any bond must equal its par value. If YTM remains constant: – The value of a premium bond would decrease over time, until it reached $1,000. – The value of a discount bond would increase over time, until it reached $1,000. – The value of a par bond stays at $1,000. 7-36

37. Quick Summary  When the yield to maturity increases, bond price must decrease  When the yield to maturity decreases, bond price must go up  Does NOT matter whether we say “yields went up” or “bond prices fell” – it means exactly the same thing  Bond price changes from time to time; as time passes by, bond prices approach par value. 7-37

38. Bond Features Call Provision – Allows the issuer to repurchase the bond at a specified call price before maturity – For the issuer, the call feature provides a means to take advantage of lower interest rates – Is this feature “free”? No –– bond buyers simply pay less for callable bonds  yields on callable bonds are higher 7-38

39. Bond Features Convertible Bonds – A convertible bond is a bond that gives the holder the right to “convert" or exchange the par amount of the bond for common shares of the issuer at some fixed “conversion” ratio 7-39

40. Bond Risks Default risk Price risk/Interest rate risk Reinvestment risk 7-40

41. Default Risk If an issuer defaults, investors receive less than the promised return. Therefore, the expected return on corporate and municipal bonds is less than the promised return. Influenced by the issuer’s financial strength and the terms of the bond contract. 7-41

42. Evaluating Default Risk: Bond Ratings Investment GradeJunk Bonds Moody’sAaa Aa A BaaBa B Caa C S & PAAA AA A BBBBB B CCC C 7-42 Bond ratings are designed to reflect the probability of a bond issue going into default.

43. Yield Spread 7-43

44. Ratings? Factors Affecting Default Risk and Bond Ratings – Financial performance – Qualitative factors: Bond contract terms – Miscellaneous qualitative factors However do not trust ratings 100%…. – There can be a lag for the bond ratings to reflect company’s situations. – OR, rating agencies are paid by the issuing firms…incentives?? https://www.youtube.com/watch?v=1u4NpD_sZy0 7-44

45. Price Risk Inverse relationship between price and yield. Price risk is the concern that rising r will cause the value of a bond to fall. An increase in a bond’s yield to maturity results will cause a price decline. – Does long-term bonds tend to be more price sensitive than short-term bonds, assuming everything else constant? 7-45

46. Price Risk (Example) Calculate the price of the following bond with $1,000 face value, 10% annual coupon – 1 year bond: YTM=5%, 10%, and 15% – 10 year bond: YTM=5%, 10%, and 15% 7-46

47. What is price risk? Does a 1-year or 10-year bond have more price risk? r 1-yearChange10-yearChange 5%$1,048$1,386 10% 1,000 1,000 15% 956 749 The 10-year bond is more sensitive to interest rate changes, and hence has more price risk. 7-47 + 4.8% – 4.4% +38.6% –25.1%

48. Illustrating Price Risk 7-48 10-Year Bond 1-Year Bond Value ($) YTM(%)

49. What is reinvestment risk? Reinvestment risk is the concern that r will fall, and future CFs will have to be reinvested at lower rates, hence reducing income. EXAMPLE: Suppose you just won $500,000 playing the lottery. You intend to invest the money and live off the interest. 7-49

50. Reinvestment Risk Example You may invest in either a 10-year bond or a series of ten 1-year bonds. Both 10-year and 1-year bonds currently yield 10%. If you choose the 1-year bond strategy: – After Year 1, you receive $50,000 in income and have $500,000 to reinvest. But, if 1-year rates fall to 3%, your annual income would fall to $15,000. If you choose the 10-year bond strategy: – You can lock in a 10% interest rate, and $50,000 annual income for 10 years, assuming the bond is not callable. 7-50

51. Conclusions about Price Risk and Reinvestment Risk CONCLUSION: Nothing is riskless! 7-51 Short-term AND/OR High-coupon Bonds Long-term AND/OR Low-coupon Bonds Price risk Low High Reinvestment risk High Low