1. PowerPoint to accompany Chapter 6 Bonds

2. Copyright © 2011 Pearson Australia (a division of Pearson Australia Group Ltd) – 9781442502000 / Berk/DeMarzo/Harford / Fundamentals of Corporate Finance / 1 st edition 6.1 Bond Terminology  A bond is a security sold by governments and corporations to raise money from investors today in exchange for promised future payments.  Payments on the bond are made until a final repayment date, called the maturity date of the bond.  The time remaining until the repayment date is known as the term of the bond. 2

3. Copyright © 2011 Pearson Australia (a division of Pearson Australia Group Ltd) – 9781442502000 / Berk/DeMarzo/Harford / Fundamentals of Corporate Finance / 1 st edition 6.1 Bond Terminology  Two types of payments  The principal or face value (par value) of a bond is the notional amount we use to calculate the interest payments, which gets repaid at maturity.  Bonds also promise additional payments called coupons, which are paid periodically (for example, six-monthly) until the maturity date of the bond. 3

4. Copyright © 2011 Pearson Australia (a division of Pearson Australia Group Ltd) – 9781442502000 / Berk/DeMarzo/Harford / Fundamentals of Corporate Finance / 1 st edition  Coupon payment  The amount of each coupon payment is determined by the coupon rate of the bond.  The coupon rate is expressed as an APR, so the amount of each coupon payment, CPN, is: (Eq. 6.1) 4 6.1 Bond Terminology FORMULA!

5. Copyright © 2011 Pearson Australia (a division of Pearson Australia Group Ltd) – 9781442502000 / Berk/DeMarzo/Harford / Fundamentals of Corporate Finance / 1 st edition  Example:  A $1,000 bond with a 10% coupon rate and six-monthly payments will pay coupon payments of: 5 6.1 Bond Terminology CPN = $1,000 x 10% = $50 every six months 2

6. Copyright © 2011 Pearson Australia (a division of Pearson Australia Group Ltd) – 9781442502000 / Berk/DeMarzo/Harford / Fundamentals of Corporate Finance / 1 st edition 6 Table 6.1 Review of Bond Terminology

7. Copyright © 2011 Pearson Australia (a division of Pearson Australia Group Ltd) – 9781442502000 / Berk/DeMarzo/Harford / Fundamentals of Corporate Finance / 1 st edition 6.2 Zero-Coupon Bonds  Bonds without coupons are called zero-coupon bonds and are commonly known as Bills  Zero-coupon bonds have only two cash flows— the payment for the bond at current market price and the face value at maturity.  Example:  A one-year zero-coupon bond with a $100,000 face value has an initial price of $96,618.36.  If you purchased this bond and held it to maturity, you would have the following cash flows: 7 Period: 0 1 Cash Flow: ($96,618.36) $100,000

8. Copyright © 2011 Pearson Australia (a division of Pearson Australia Group Ltd) – 9781442502000 / Berk/DeMarzo/Harford / Fundamentals of Corporate Finance / 1 st edition 6.2 Zero-Coupon Bonds  Although zero coupon bonds pay no direct interest, investors are compensated for the time value of money by purchasing the bond at a discount to its face value.  Prior to its maturity date, the price of a zero- coupon bond is always less than its face value.  That is, zero-coupon bonds always trade at a discount (a price lower than the face value), so they are also called pure discount bonds. 8

9. Copyright © 2011 Pearson Australia (a division of Pearson Australia Group Ltd) – 9781442502000 / Berk/DeMarzo/Harford / Fundamentals of Corporate Finance / 1 st edition 6.2 Zero-Coupon Bonds  Yield to maturity of a zero-coupon bond  The Internal Rate of Return of an investment in a bond is called the yield to maturity (YTM).  Yield to maturity of an n-year zero-coupon bond: (Eq. 6.2) 9 FORMULA! The yield to maturity of a bond is the discount rate that sets the PV of the promised bond payments equal to the current market price of the bond.

10. Copyright © 2011 Pearson Australia (a division of Pearson Australia Group Ltd) – 9781442502000 / Berk/DeMarzo/Harford / Fundamentals of Corporate Finance / 1 st edition Example 6.1 Yields for Different Maturities (p.161) Problem:  Suppose the following zero-coupon bonds are trading at the prices shown below per $100 face value.  Determine the corresponding yield to maturity for each bond. Plan:  We can use Eq. 6.2 to solve for the YTM of the bonds. Maturity1 year2 years3 years4 years Price$96.62$92.45$87.63$83.06 10

11. Copyright © 2011 Pearson Australia (a division of Pearson Australia Group Ltd) – 9781442502000 / Berk/DeMarzo/Harford / Fundamentals of Corporate Finance / 1 st edition Execute: 11 Example 6.1 Yields for Different Maturities (p.161)

12. Copyright © 2011 Pearson Australia (a division of Pearson Australia Group Ltd) – 9781442502000 / Berk/DeMarzo/Harford / Fundamentals of Corporate Finance / 1 st edition 6.2 Zero-Coupon Bonds  Risk-free interest rates  The Law of One Price implies that all one-year risk-free investments must earn this same return, the competitive market risk-free interest rate.  A default-free zero-coupon bond that matures on date n provides a risk-free return, which equals the yield to maturity on such a bond.  Consequently, we will often refer to the yield of such a zero-coupon risk-free bond as the risk-free interest rate.  These default-free, zero-coupon yields are also called spot interest rates, because these rates are offered ‘on the spot’ at that point in time. 12

13. Copyright © 2011 Pearson Australia (a division of Pearson Australia Group Ltd) – 9781442502000 / Berk/DeMarzo/Harford / Fundamentals of Corporate Finance / 1 st edition Figure 6.1 Zero-Coupon Yield Curve Consistent with the Bond Prices in Example 6.1 13

14. Copyright © 2011 Pearson Australia (a division of Pearson Australia Group Ltd) – 9781442502000 / Berk/DeMarzo/Harford / Fundamentals of Corporate Finance / 1 st edition Example 6.2 Calculating the Price of a Zero-Coupon Bond (p.162) Problem:  Given the yield curve in Figure 6.1, what is the price of a 5-year risk-free zero-coupon bond with a face value of $100? Plan & Execute:  We can use the bond’s yield to maturity to calculate the bond’s price as the PV of its face value. From the yield curve, the yield to maturity is 5.0%: 14

15. Copyright © 2011 Pearson Australia (a division of Pearson Australia Group Ltd) – 9781442502000 / Berk/DeMarzo/Harford / Fundamentals of Corporate Finance / 1 st edition Evaluate:  We can calculate the price of a zero-coupon bond simply by calculating the present value of the face value using the bond’s yield to maturity.  Note that the price of the 5-year zero-coupon bond is even lower than the price of the other zero-coupon bonds in Example 6.1, because the face value is the same, but we must wait longer to receive it. 15 Example 6.2 Calculating the Price of a Zero-Coupon Bond (p.162)

16. Copyright © 2011 Pearson Australia (a division of Pearson Australia Group Ltd) – 9781442502000 / Berk/DeMarzo/Harford / Fundamentals of Corporate Finance / 1 st edition 6.3 Coupon Bonds  Coupon bonds  Pay investors their face value at maturity and make regular coupon interest payments.  The Government issues Treasury bonds into the capital markets to meet its budgetary needs, usually with maturities that range between three to thirty years.  The original maturity is the term of the bond at the time it was originally issued. 16

17. Copyright © 2011 Pearson Australia (a division of Pearson Australia Group Ltd) – 9781442502000 / Berk/DeMarzo/Harford / Fundamentals of Corporate Finance / 1 st edition  Coupon bond cash flows  Return on a coupon bond comes from two sources:  the difference between purchase price and principal value  periodic coupon payments.  In the following example, we take a bond description and translate it into the bond’s cash flows. 17 6.3 Coupon Bonds

18. Copyright © 2011 Pearson Australia (a division of Pearson Australia Group Ltd) – 9781442502000 / Berk/DeMarzo/Harford / Fundamentals of Corporate Finance / 1 st edition Example 6.3 The Cash Flows of a Coupon Bond (p.163) Problem:  Assume that it is 15 May 2013 and the Australian Office of Financial Management has just issued Treasury bonds with a May 2015 maturity, $1000 par value and a 5% coupon rate with six-monthly coupons.  The first coupon payment will be paid on 15 November 2013.  What cash flows will you receive if you hold this note until maturity? 18

19. Copyright © 2011 Pearson Australia (a division of Pearson Australia Group Ltd) – 9781442502000 / Berk/DeMarzo/Harford / Fundamentals of Corporate Finance / 1 st edition Solution: Plan:  The phrase ‘May 2015 maturity, $1000 par value’ tells us that this is a bond with a face value of $1000 and five years to maturity.  The phrase ‘5% coupon rate with six-monthly coupons’ tells us that the bond pays a total of 5% of its face value each year in two equal six- monthly instalments.  Finally, we know that the first coupon is paid on 15 November 2013. 19 Example 6.3 The Cash Flows of a Coupon Bond (p.163)

20. Copyright © 2011 Pearson Australia (a division of Pearson Australia Group Ltd) – 9781442502000 / Berk/DeMarzo/Harford / Fundamentals of Corporate Finance / 1 st edition Execute:  The face value of this note is $1000; with six-monthly coupons you will receive: CPN=$1,000 x (5%/2)=$25.  Note that the last payment occurs in two years (4 six-month periods) from now and is composed of both a coupon payment of $25 and the face value payment of $1000. 20 Example 6.3 The Cash Flows of a Coupon Bond (p.163) Timeline May 2013 Nov 2013 May 2014 Nov 2014 May 2015 $25 $25 $25 $25 + $1,000

21. Copyright © 2011 Pearson Australia (a division of Pearson Australia Group Ltd) – 9781442502000 / Berk/DeMarzo/Harford / Fundamentals of Corporate Finance / 1 st edition Evaluate:  Since a bond is just a package of cash flows, we need to know those cash flows in order to value the bond.  That is why the description of the bond contains all of the information we would need to construct its cash flow timeline. 21 Example 6.3 The Cash Flows of a Coupon Bond (p.163)

22. Copyright © 2011 Pearson Australia (a division of Pearson Australia Group Ltd) – 9781442502000 / Berk/DeMarzo/Harford / Fundamentals of Corporate Finance / 1 st edition  Price of a coupon bond  The Price of a coupon bond is the present value of all its future cash flows 22 6.3 Coupon Bonds FORMULA!

23. Copyright © 2011 Pearson Australia (a division of Pearson Australia Group Ltd) – 9781442502000 / Berk/DeMarzo/Harford / Fundamentals of Corporate Finance / 1 st edition  Yield to maturity of a coupon bond  The yield to maturity for a bond is the IRR of investing in the bond and holding it to maturity:  From the timeline we see that the coupon payments represent an annuity, so the yield to maturity is the interest rate y that solves the following equation: 23 6.3 Coupon Bonds

24. Copyright © 2011 Pearson Australia (a division of Pearson Australia Group Ltd) – 9781442502000 / Berk/DeMarzo/Harford / Fundamentals of Corporate Finance / 1 st edition (Eq. 6.3) 24  Yield to maturity of a coupon bond 6.3 Coupon Bonds FORMULA!

25. Copyright © 2011 Pearson Australia (a division of Pearson Australia Group Ltd) – 9781442502000 / Berk/DeMarzo/Harford / Fundamentals of Corporate Finance / 1 st edition Example 6.4 Calculating the Yield to Maturity of a Coupon Bond (p.165) Problem:  Consider a five-year, $1000 bond with a 5% coupon rate and semi-annual coupons with a yield to maturity of 6%  What is the current price of the bond? 25

26. Copyright © 2011 Pearson Australia (a division of Pearson Australia Group Ltd) – 9781442502000 / Berk/DeMarzo/Harford / Fundamentals of Corporate Finance / 1 st edition Solution: Plan:  From a cash flow timeline, we can see that the bond consists of an annuity of 10 payments of $25, paid every 6 months, and one lump-sum payment of $1000 in 5 years (ten six-month periods).  We can use Eq. 6.3 to solve for the price. However, we must use six-month intervals consistently throughout the equation. 26 Example 6.4 Calculating the Yield to Maturity of a Coupon Bond (p.165)

27. Copyright © 2011 Pearson Australia (a division of Pearson Australia Group Ltd) – 9781442502000 / Berk/DeMarzo/Harford / Fundamentals of Corporate Finance / 1 st edition Execute: 27 Example 6.4 Calculating the Yield to Maturity of a Coupon Bond (p.165)

28. Copyright © 2011 Pearson Australia (a division of Pearson Australia Group Ltd) – 9781442502000 / Berk/DeMarzo/Harford / Fundamentals of Corporate Finance / 1 st edition Example 6.5 Calculating a Bond Price from its Yield to Maturity (p.165) Problem:  Consider again the five-year $1000 bond with a 5% coupon rate and semi-annual coupons in Example 6.4.  Suppose interest rates drop and the bond’s yield to maturity decreases to 4.50% (expressed as an APR with semi-annual compounding).  What price is the bond trading for now? 28

29. Copyright © 2011 Pearson Australia (a division of Pearson Australia Group Ltd) – 9781442502000 / Berk/DeMarzo/Harford / Fundamentals of Corporate Finance / 1 st edition Solution: Plan:  Given the yield, we can calculate the price using Eq.6.3.  Note that a 4.50% APR is equivalent to a semi- annual rate of 2.25%.  Also, recall that the cash flows of this bond are an annuity of 10 payments of $25, paid every six months, and one lump-sum cash flow of $1000 (the face value) paid in five years (10 six-month periods). 29 Example 6.5 Calculating a Bond Price from its Yield to Maturity (p.165)

30. Copyright © 2011 Pearson Australia (a division of Pearson Australia Group Ltd) – 9781442502000 / Berk/DeMarzo/Harford / Fundamentals of Corporate Finance / 1 st edition Execute: 30 Example 6.5 Calculating a Bond Price from its Yield to Maturity (p.165)

31. Copyright © 2011 Pearson Australia (a division of Pearson Australia Group Ltd) – 9781442502000 / Berk/DeMarzo/Harford / Fundamentals of Corporate Finance / 1 st edition 6.4 Why Bond Prices Change  Zero-coupon bonds always trade for a discount— that is, prior to maturity, their price is less than their face value.  But coupon bonds may trade at a discount, or at a premium (a price greater than their face value).  Most issuers of coupon bonds choose a coupon rate so that the bonds will initially trade at, or very close to, par (that is, at the bond’s face value).  After the issue date, the market price of a bond generally changes over time. 31

32. Copyright © 2011 Pearson Australia (a division of Pearson Australia Group Ltd) – 9781442502000 / Berk/DeMarzo/Harford / Fundamentals of Corporate Finance / 1 st edition 6.4 Why Bond Prices Change  Interest rate changes and bond prices  If a bond sells at par, the only return investors will earn is from the coupons that the bond pays.  The bond’s coupon rate will exactly equal its yield to maturity.  As interest rates in the economy fluctuate, the yields that investors demand to invest in bonds will also change.  As interest rates and bond yields rise, bond prices will fall, and vice versa, so that bond prices and interest rates always move in the opposite direction. 32

33. Copyright © 2011 Pearson Australia (a division of Pearson Australia Group Ltd) – 9781442502000 / Berk/DeMarzo/Harford / Fundamentals of Corporate Finance / 1 st edition Figure 6.2 A Bond’s Price versus its Yield to Maturity 33

34. Copyright © 2011 Pearson Australia (a division of Pearson Australia Group Ltd) – 9781442502000 / Berk/DeMarzo/Harford / Fundamentals of Corporate Finance / 1 st edition Table 6.2 Bond Prices Immediately After a Coupon Payment 34

35. Copyright © 2011 Pearson Australia (a division of Pearson Australia Group Ltd) – 9781442502000 / Berk/DeMarzo/Harford / Fundamentals of Corporate Finance / 1 st edition Example 6.6 Determining the Discount or Premium of a Coupon Bond (p.169) Problem:  Consider three 30-year bonds with annual coupon payments.  One bond has a 10% coupon rate, one has a 5% coupon rate, and one has a 3% coupon rate.  If the yield to maturity of each bond is 5%, what is the price of each bond per $100 face value?  Which bond trades at a premium, which trades at a discount, and which trades at par? 35

36. Copyright © 2011 Pearson Australia (a division of Pearson Australia Group Ltd) – 9781442502000 / Berk/DeMarzo/Harford / Fundamentals of Corporate Finance / 1 st edition Solution: Plan:  Each bond has 30 years to maturity and pays its coupons annually. Therefore, each bond has an annuity of coupon payments, paid annually for 30 years, and then the face value paid as a lump sum in 30 years.  They are all priced so that their yield to maturity is 5%.  Therefore, we can use Eq. 6.3 to calculate the price of each bond as the PV of its cash flows, discounted at 5%. 36 Example 6.6 Determining the Discount or Premium of a Coupon Bond (p.169)

37. Copyright © 2011 Pearson Australia (a division of Pearson Australia Group Ltd) – 9781442502000 / Berk/DeMarzo/Harford / Fundamentals of Corporate Finance / 1 st edition Execute: 37 Example 6.6 Determining the Discount or Premium of a Coupon Bond (p.169)

38. Copyright © 2011 Pearson Australia (a division of Pearson Australia Group Ltd) – 9781442502000 / Berk/DeMarzo/Harford / Fundamentals of Corporate Finance / 1 st edition Evaluate:  The prices reveal that when the coupon rate of the bond is higher than its yield to maturity, it trades at a premium.  When its coupon rate equals its yield to maturity, it trades at par.  When its coupon rate is lower than its yield to maturity, it trades at a discount. 38 Example 6.6 Determining the Discount or Premium of a Coupon Bond (p.169)

39. Copyright © 2011 Pearson Australia (a division of Pearson Australia Group Ltd) – 9781442502000 / Berk/DeMarzo/Harford / Fundamentals of Corporate Finance / 1 st edition Example 6.7 The Effect of Time on the Price of a Bond (pp.170-1) Problem:  Suppose you purchase a 30-year, zero-coupon bond with a yield to maturity of 5%. For a face value of $100, the bond will initially trade for:  If the bond’s yield to maturity remains at 5%, what will its price be five years later?  If you purchased the bond at $23.14 and sold it five years later, what would the IRR of your investment be? 39

40. Copyright © 2011 Pearson Australia (a division of Pearson Australia Group Ltd) – 9781442502000 / Berk/DeMarzo/Harford / Fundamentals of Corporate Finance / 1 st edition Plan:  If the bond was originally a 30-year bond and five years have passed, then it has 25 years left to maturity.  If the yield to maturity does not change, then you can calculate the price of the bond with 25 years left exactly as we did for 30 years, but using 25 years of discounting instead of 30.  Once you have the price in five years, you can calculate the IRR of your investment.  The FV is the price in 5 years, the PV is the initial price ($23.14), and the number of years is 5. 40 Example 6.7 The Effect of Time on the Price of a Bond (pp.170-1)

41. Copyright © 2011 Pearson Australia (a division of Pearson Australia Group Ltd) – 9781442502000 / Berk/DeMarzo/Harford / Fundamentals of Corporate Finance / 1 st edition Execute: 41 Example 6.7 The Effect of Time on the Price of a Bond (pp.170-1)

42. Copyright © 2011 Pearson Australia (a division of Pearson Australia Group Ltd) – 9781442502000 / Berk/DeMarzo/Harford / Fundamentals of Corporate Finance / 1 st edition Evaluate:  Note that the bond price is higher, and hence the discount from its face value is smaller, when there is less time to maturity.  The discount shrinks because the yield has not changed, but there is less time until the face value will be received.  If a bond’s yield to maturity does not change, then the IRR of an investment in the bond equals its yield to maturity even if you sell the bond early. 42 Example 6.7 The Effect of Time on the Price of a Bond (pp.170-1)

43. Copyright © 2011 Pearson Australia (a division of Pearson Australia Group Ltd) – 9781442502000 / Berk/DeMarzo/Harford / Fundamentals of Corporate Finance / 1 st edition Figure 6.3 The Effect of Time on Bond Prices 43

44. Copyright © 2011 Pearson Australia (a division of Pearson Australia Group Ltd) – 9781442502000 / Berk/DeMarzo/Harford / Fundamentals of Corporate Finance / 1 st edition 6.4 Why Bond Prices Change  Interest rate risk and bond prices  While the effect of time on bond prices is predictable, unpredictable changes in interest rates will also affect bond prices—and some bonds will react more strongly than others.  Investors view long-term loans to be riskier than short-term loans; the same is true of short- versus long-term bonds: 44

45. Copyright © 2011 Pearson Australia (a division of Pearson Australia Group Ltd) – 9781442502000 / Berk/DeMarzo/Harford / Fundamentals of Corporate Finance / 1 st edition Example 6.8 The Interest Rate Sensitivity of Bonds (p.172) Problem:  Consider a 10-year coupon bond and a 30-year coupon bond, both with 10% annual coupons.  By what percentage will the price of each bond change if its yield to maturity increases from 5% to 6%? 45

46. Copyright © 2011 Pearson Australia (a division of Pearson Australia Group Ltd) – 9781442502000 / Berk/DeMarzo/Harford / Fundamentals of Corporate Finance / 1 st edition Solution: Plan:  We need to calculate the price of each bond for each yield to maturity and then calculate the percentage change in the prices.  For both bonds, the cash flows are $10 per year for $100 in face value and then the $100 face value repaid at maturity.  The only difference is the maturity: 10 years and 30 years. With those cash flows, we can use Eq. 6.3 to calculate the prices. 46 Example 6.8 The Interest Rate Sensitivity of Bonds (p.172)

47. Copyright © 2011 Pearson Australia (a division of Pearson Australia Group Ltd) – 9781442502000 / Berk/DeMarzo/Harford / Fundamentals of Corporate Finance / 1 st edition 47 Example 6.8 The Interest Rate Sensitivity of Bonds (p.172) Execution:

48. Copyright © 2011 Pearson Australia (a division of Pearson Australia Group Ltd) – 9781442502000 / Berk/DeMarzo/Harford / Fundamentals of Corporate Finance / 1 st edition Evaluate:  The 30-year bond is twice as sensitive to a change in the yield than is the 10-year bond. 48 Example 6.8 The Interest Rate Sensitivity of Bonds (p.172)