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BCOR 2200 Chapter 6

BCOR 2200 Chapter 6. Interest Rates and Bond Valuation. Chapter 6 Outline: Bonds and Bond Valuation More on Bond Features Bond Ratings Some Different Types of Bonds Bond Markets Inflation and Interest Rates Determinants of Bond Yields. Key Concepts and Skills:

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BCOR 2200 Chapter 6

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  1. BCOR 2200Chapter 6 Interest Rates and Bond Valuation

  2. Chapter 6 Outline: • Bonds and Bond Valuation • More on Bond Features • Bond Ratings • Some Different Types of Bonds • Bond Markets • Inflation and Interest Rates • Determinants of Bond Yields

  3. Key Concepts and Skills: • Know the important bond features and bond types • Understand how to calculate bond prices • Understand why prices fluctuate • Understand bond ratings • Understand the impact of inflation on interest rates • Understand the Term Structure of Interest Rates and the determinants of bond yields • Understand the determinants of bond yields

  4. 6.1 Bonds and Bond Valuation First some terminology: A 30 year $1,000 bond pays $100per year (Annual payments) and repays the $1,000 in thirty years. The market requires a 9% return on loans to this company. • COUPON = $100 • COUPON RATE = Coupon/Face = $100/$1,000= 10% • COUPON PERIOD = Annual • FACE VALUE or PAR VALUE= $1,000 • TIME (or TERM) TO MATURITY = 30 years • YIELD TO MATURITY (YTM) = required rate = 9%

  5. A Bond is Defined (or Identified) by: • Issuer (the borrower) • A Corporation (corps): GE, GM… • A Municipality (Munis): Boulder, New York State, E470 Public Highway Authority… • The Federal Government (Govies): Issued to finance the deficit and debt • Maturity (when the loan is repaid) • Usually a date (but in this class we’ll use a time to maturity) • A ten year bond is a 2024 but we’ll call it a ten year. • Structure (how the money is repaid) • Coupon, Zero, Amortizing

  6. A Bond is Defined (or Identified) by: • Coupon Rate (if applicable) • 7% Semi-Annual, 10% Annual, or “Zero-Coupon” • Bond Features • Callable, Convertible... (we’ll talk about this later) • Rating • Rating agencies (S&P, Moodys, Fitch…) issue public rating. • BBB or higher are Investment Grade • BB or lower are Non-Investment Grade(junk) Example: GE 5.125 of 2028 (“five and an eighth of 28”) • GE corp bond. Matures in 2028. Pays a 5.125% S-A coupon. AAA rated

  7. Calculate the price of the bond: • 30year $1,000 Face or Par Value, 10% annual coupon and 10%required rate (so YTM = 10%) Two Components: • Thirty payments of $100, discounted at 10%: PV = 100/(1.1)+ 100/(1.1)2 + 100/(1.1)3 + … + 100/(1.1)30 = $942.69 N = 30 I/YR = 10 PMT = 100 PV = -942.69 • One payment of $1,000 in thirty years PV = 1,000/(1.1)30 = $57.31 N = 30 I/YR = 10 FV = 1000 PV = -57.31 Or both at the same time: Total Price: = $942.69 + $57.31 = $1,000 N = 30 I/YR = 10 PMT = 100 FV = 1000 PV = -1000 Equal to the Face Value or Par Value

  8. Calculate the price of the bond: Same bond with different YTMs: • Why might the bond’s YTM change? • The issuer’s credit rating has changed • All rates have changed 30 year $1,000 Face or Par Value, 10% annual coupon 8% required rate (YTM = 8%) N = 30 I/YR = 8 PMT = 100 FV = 1000 PV = -1225 • Price = $1,225 > $1,000 • Great than the Face Value or Par Value (Premium) 30 year $1,000 Face or Par Value, 10% annual coupon 12% required rate (YTM = 12%) N = 30 I/YR = 12 PMT = 100 FV = 1000 PV = -839 • Price = $839 < $1,000 • Less than the Face Value or Par Value (Discount)

  9. Clicker Question: • A 20 year, $1,000 face-value bond pays an 7% annual coupon and has a discount rate of 9%. • Calculate the bond’s price • Is it priced at par, a discount or a premium? • $217 (Discount) • $234 (Discount) • $817 (Discount) • $1,000 (Par) • $1,196 (Premium)

  10. Clicker Answer: • 20 year, $1,000 face-value bond pays an 7% annual coupon and has a discount rate of 9%: • PMT = $1,000 x 0.07 = $70 N = 20 I/YR = 9% PMT = 70 FV = 1,000 PV = -817 The price is $817. The answer is C.

  11. Important thing about a bond’s price: • If YTM = Coupon Rate Price = Par N = 30 I/YR = 10 PMT = 100 FV = 1000 PV = -1000 • If YTM > Coupon Rate Price < Par • Priced at a “discount” N = 30 I/YR = 12 PMT = 100 FV = 1000 PV = -839 • If YTM < Coupon Rate Price > Par • Priced at a “premium” N = 30 I/YR = 8 PMT = 100 FV = 1000 PV = -1225 Why?

  12. Price-YTM Relationship At YTM = 10%, Price = Par = $1,000

  13. Clicker Question: • A 20 year, $1,000 face-value bond pays an 5.50% annual coupon and is priced at par. • Calculate the yield to maturity. • 3.50% • 5.50% • 7.50% • 9.50% • Not enough information to calculate YTM

  14. Clicker Answer: • A 20 year, $1,000 face-value bond pays an 5.50% annual coupon and is priced at par. • If the price equals par, then the YTM equals the coupon rate. The Answer is B.

  15. Bonds are Generally Issued at Par • By tradition, a bond is issued at par • This means the YTM equals the Coupon Rate • A company that wants to borrow money, goes to the market to determine what rate of return lenders (bond buyers) require on the company’s bonds • Call this is the Required Return • Or the Required Yield • Or the Yield to Maturity (YTM) • The company then sets the coupon rate of the bond equal to the YTM • And then the bond is issued at par.

  16. Changes in Price as Time Changes Back to the $1,000, 30 year, 10% coupon, 10% YTM bond N = 30 I/YR = 10 PMT = $100 FV = $1,000 PV = -1,000 Now one year has passed. Recalculate the Bonds value: N = 29 I/YR = 10 PMT = $100 FV = $1,000 PV = -1,000 So still $1,000 since Coupon Rate = YTM! Examine two components: • Twenty-nine $100 payments discounted at 10% (No FV) N = 29 I/YR = 10 PMT = $100 PV = -936.96 • One $1,000 payment in twenty-nine years (No PMTs) N = 29 I/YR = 10 FV = $1,000 PV = -63.04 29 yrs Total Value = $936.96+ $63.04 = $1,000 30 yrs Total Value = $942.69 + $57.31 = $1,000 One fewer annuity payment but $1,000 FV received one year sooner.

  17. Changes in Price as the YTM Changes Back to the 30 years to maturity. But required rate is now 11%. Why? N = 30 I/YR = 11PMT = $100 FV = $1,000 PV = -913.06 So less than $1,000 since denominator (the rate) has increased Examine two components: • Thirty $100 payments discounted at 11% N = 30 I/YR = 11PMT = $100 PV = -869.38 • One $1,000 payment in thirty years N = 30 I/YR = 11FV = $1,000 PV = -43.68 • 11% YTM Total Value = $869.38+ $43.68 = $913.06 • 10% YTM Total Value = $942.69 + $57.31 = $1,000 Why is price lower?

  18. Changes in Price as the YTM Changes • Call this Interest Rate Risk • It is the Volatility of the bond’s value caused by changes in rates The Price function: PV = C/(1 + r)1 + C/(1 + r)2 + C/(1 + r)3 + … + (C + FV)/(1 + r)t C = Coupon (Fixed) FV = Face Value (Fixed) t = Time to Maturity (slow and can see that one coming) r = YTM or the discount rate • So what will change the price of the bond by tomorrow? • Changes in the YTM (aka changes in Rates)! • So bond holders incur Interest Rate Risk

  19. Determinants of Interest Rate Risk • What causes Interest Rate Risk? • Or what characteristics of a bond increase Interest Rate Risk? • We will see there are three factors that increase Interest Rate Risk: • Interest rate risk Increases as Time to MaturityINCREASES • Longer Maturity, higher interest rate risk • Interest rate risk Increases as the Coupon RateDECREASES • Lower coupon, higher interest rate risk • Interest rate risk Increases as the Starting YTMDECREASES • Lower YTM, higher interest rate risk

  20. Time to Maturity • The longer the term to maturity (ceteris paribus), the greater the Interest Rate Risk • The % change in price increases as maturity increases. The % change in price for the 30 year bond is 10.27%

  21. Starting YTM • The Lower the Starting YTM, The higher the interest rate risk • The % change in price increases as the starting YTM decreases The % change in price when YTM starts at 5% is 15.20%

  22. Starting YTM • Compare the SLOPE of the line at the Red, Blue and Green dots. • The slope is steepest at the Red dot • Steeper slope means greater a change in price (Rise) for given change in rates (Run) • Interest Rate Risk is measured by the slope

  23. Figure 6.2 from the text Table and Chart of the Price-Yield Relationship: Red is a 30 Year Bond Blue is a 1 Year Bond (The 30 Year Bond has a steeper slope)

  24. Fig 6.2 • Compare the slope of the RED LINE at 5% and 20% - • It is much steeper at 5% (greater slope) • Steeper means greater change in Price (Rise) for given change in rates (Run) • Interest Rate Risk is measured by the slope

  25. Coupon Rate • The lower the coupon rate, the greater the Interest Rate Risk • The % change in price is increases as the coupon rate decreases The % change in price for the 5% coupon bond is 11.43%

  26. Interest Rate Risk Factors Recap: • Interest rate risk Increases as the Time to Maturity INCREASES • Longer Maturity, higher interest rate risk • Interest rate risk Increases as the Starting YTMDECREASES • Lower YTM, higher interest rate risk • Interest rate risk Increases as the Coupon RateDECREASES • Lower coupon, higher interest rate risk

  27. Clicker Question: • Consider Bonds 1 and 2: Bond 1: 10 year bond, 10% annual coupon, 10% YTM Bond 2: 20 year bond, 10% annual coupon, 10% YTM • Consider Bonds 3 and 4: Bond 3: 10 year bond, 5% annual coupon, 5% YTM Bond 4: 10 year bond, 10% annual coupon, 5% YTM Which of the following is true about interest rate risk? • Bond 1 > Bond 2 and Bond 3 > Bond 4 • Bond 2 > Bond 1 and Bond 3 > Bond 4 • Bond 1 > Bond 2 and Bond 4 > Bond 3 • Bond 2 > Bond 1 and Bond 4 > Bond 3

  28. Clicker Answer: Bond 1: 10 year bond, 10% annual coupon, 10% YTM Bond 2: 20 year bond, 10% annual coupon, 10% YTM Longer Maturity  Greater Interest Rate Risk  2 > 1 Bond 3: 10 year bond, 5% annual coupon, 5% YTM Bond 4: 10 year bond, 10% annual coupon, 5% YTM Lower Coupon  Greater Interest Rate Risk  3 > 4 Which of the following is true about interest rate risk? • Bond 1 > Bond 2 and Bond 3 > Bond 4 • Bond 2 > Bond 1 and Bond 3 > Bond 4 • Bond 1 > Bond 2 and Bond 4 > Bond 3 • Bond 2 > Bond 1 and Bond 4 > Bond 3

  29. Is Interest Rate Risk Bad? • Not Necessarily! • Interest Rate Risk is: Change in the price for a change in yield • If RATES go up, bond PRICES go down • A big down-change in price is bad • If RATES go down, bond PRICES go up • A big up-change in price is good! • So if you think rates will decrease… then more interest rate risk is good!

  30. Semi-Annual Coupon Bonds There are special “rules” for bonds that pay Semi-Annual coupons: • Example: 21 year, 5.125% S-A bond. YTM = 5.88% Calculate the price: • Coupon Rate = 5.125% means 0.05125/2 = 0.025625 NOT 0.03 or 0.026 or 0.0256 or… Use FULL PRECISSION!! Coupon payment = 0.025625 x $1,000 = $25.625 • YTM = 5.88% means 0.0588/2 = 0.0294 NOT 0.03 or 0.029 (or 3 or 2.9 entered into the calculator) • Number of Semi-Annual Periods = 21 x 2 = 42 N = 42 I/YR = 2.94 PMT = 25.625 FV = 1000 PV = ? (Greater or less than $1,000?) PV = -909.62

  31. Clicker Question: • A 15 year, $1,000 face-value bond pays an 8.25% SEMI-ANNUAL coupon and has a YTM of 10%. • Calculate the bond’s price • Note: Both the Coupon Rate and the YTM are quoted at twice the periodic rate (Always! Always! Always!) • $850 • $865 • $950 • $1,000 • $1,200

  32. Clicker Answer: • A 15 year, $1,000 face-value bond pays an 8.25% SEMI-ANNUAL coupon and has a YTM of 10%. • Calculate the bond’s price • Note: Both the Coupon Rate and the YTM are quoted at twice the periodic rate (Always! Always! Always!) N = 15 x 2 = 30 I/YR = 10/2 = 5 PMT = (0.0825/2)1,000 = 41.25 FV = 1,000 PV = -865 (so the answer is B)

  33. Debt Not an ownership interest No voting rights Interest is a “cost of doing business” and is tax-deductible Creditors have legal recourse if interest or principal payments are missed Excess debt can lead to financial distress and bankruptcy Equity Ownership interest Common stockholders vote to elect the board of directors and on other issues Dividends are not considered a cost of doing business and are not tax deductible Dividends are not a liability of the firm until declared. Stockholders have no legal recourse if dividends are not declared An all-equity firm cannot go bankrupt (although it can go “out of business”) 6.2 More on Corporate Bond FeaturesDifferences between Debt and Equity:

  34. A Bond is Formally called a Bond Indenture It is a contract between the issuer and the lender Contract Terms Includes: • The Basic Terms of the Bonds • Interest rate, Payment Structure, Repayment Schedule (or Amortization)… • Total Amount of Bonds Issued • Assets used to collateralize the bond • Debentures – unsecured • Collateralized – secured by financial securities • Mortgage bonds – secured by real property (land or buildings) • Notes – unsecured debt with original maturity less than 10 years • Seniority • Which bonds gets paid first? • “Senior Debt” gets paid first • “Subordinate Debt” get paid next Some More Terms

  35. More Terms of a Bond Contract: • Sinking Fund Provisions • Money set aside to repay the bond is called a sinking provision • How much money is set aside and when • Call Provisions • Price and time when the company can “buy back” or “call” the bond (if it wants) • Conversion Provisions • Price and time when the bond holders can convert the bond to shares of stock (if they want) • Details of Restrictive Covenants • Must maintain a D/E ratio below a certain level • May not sell certain assets (the company can’t sell its trucks) • May not issue new debt senior to this issue • Must limit dividends (payments to stockholders) Why?

  36. 6.3 Bond Ratings • Bonds that are sold to the public are rated by one of the major credit-rating agencies (S&P, Moody’s, Fitch…) • The agencies are private companies that are paid by the issuer to produce ratings • Many investment funds (mutual funds, insurance companies, endowments…) will not buy unrated debt • Unrated or bonds rated BB or below are called… Non-Investment Grade or “Junk Bonds” • Some low quality bond issuers will buy “bond insurance” • The issuer pays 6% to the bond owners and 5% to the insurance company • The net of 11% is less than the issuer would have paid without the insurance • If not insured, the issuer probably would not have been able to sell bonds at all

  37. 6.4 Types of bonds Bonds are Defined by: • The type of issuer • Government, Municipality, Corporation • How is the interest paid? • Is there a coupon? Annual? Semi-Annual? • Is the coupon rate fixed or does it float? • Do you buy it at a discount today and receive all the interest (along with principal) at the end? (Zero-Coupon) • How is the principal paid? • All at the end? (Bullet Maturity) • A little each period? (Self-Amortizing)

  38. Government Bonds Called Treasury Securities (Treasury Site) • T-Bills • Pure discount bonds • Original maturity of one year or less • T-Notes • Coupon debt • Original maturity between one and ten years • T-Bonds • Coupon debt • Original maturity greater than ten years • TIPS • Treasury Inflation Protection Securities • The Principaladjusts with CPI • Pays a fixed rate on an adjusted principal amount • TIPS Rates & Terms; TIPS in Depth

  39. Municipal Bonds • Issued by state and local governments and Authorities, School Districts, Special Districts… • It is how they borrow money to build bridges, schools, airports, buy open space… • Interest earned by the bond owners is tax-exempt at the federal level Example: A corporate bond pays 8% and a Muni bond pays 5%. • If your marginal tax bracket is 30%, which bond to you prefer? You keep 1 - 0.30 of the corporate coupon (1-0.30)(0.08) = 0.056 = 5.6% so the 8% corporate bond is better • If your marginal tax bracket is 40%, which bond to you prefer? (1-0.40)(0.08) = 0.048 = 4.8% so the 5% muni bond is better • At what tax bracket are you indifferent between the bonds? (1 - T)(0.08) = 0.05  T = 1 - (0.05/0.08) = 0.375 = 37.5%

  40. More on Munis Either General Obligationor Revenue Bonds • GO bonds are backed by the “full faith and credit” of the issuer • All a city’s or state’s taxes and revenue sources are committed to paying the coupons and principal • Revenue bonds (Revs) are backed by revenue from a specific project • E470 Tolls • DIA Landing and gate fees

  41. Floating Rate Bonds (Floaters) • Coupons set at an “Index rate” plus a spread • Index rates: T-bill rate, T-bonds rate, LIBOR • If the coupon is T-bills + 200 bps • And the T-bill rate is 4.75% • Then the Floater pays 6.75% Price of a Floater is usually close to Par • A company’s default risk premium is 200 bps above T-bills • So coupon rate is set to T-bills + 200 • Then the Coupon Rate = Discount Rate (a.k.a. YTM) • If Coupon Rate = YTM  Price = Par • As TVM changes, T-bill rate changes and coupon rate changes • But coupon rate and discount rate are still equal  Price = Par • Unless default risk changes. • Say default risk increase to 300 bps • Then Coupon Rate (T-bill + 200) < YTM (T-Bill + 300)  Price < Par

  42. LIBOR London Inter-Bank Offered Rate • The average rate charged by London banks for off-shore dollar loans • Off-shore dollars are called “eurodollars” • So LIBOR is also called the eurodollar rate • Eurodollars are not the same as euros • Why London bank rates and not US bank rates? • London banks are less regulated • US banks charge the Fed Funds rate “plus” • LIBOR is determined more by “natural” supply and demand • But is also affected by the Fed Funds rate

  43. 6.5 Bond Markets • Dealers at securities firms stand ready to buy and sell certain bonds • They are linked electronically and by phone • This is called an Over-the-Counter market (OTC) • Distinguish this from a big room full of traders called an exchange • There are an extremely large number of bond issues • Multiple bonds from each company • Generally illiquidity (low volume) in any single bond issue • Most recent treasury at each maturity is an exception • Only one Federal government • The most recent treasury at each maturity is called the “on-the-run” treasury Read about bond quotes on pages 187 to 191 There is a HW question on this.

  44. 6.6 Interest Rates and Inflation • Inflation decreases purchasing power • Nominal return is amount paid • Real Return factors out inflation • Measures increase in purchasing power • Let Nominal Return = 10%, Inflation = 3% • $100(1.10) = $110 only buys (1.10/1.03) -1 = 6.80% more stuff • Not 10% more stuff

  45. Interest Rates and Inflation Before the year: • Given Ex Ante or ExpectedInflation (h) • Calculate the Required Nominal Return After the year: • Given Ex Post or MeasuredInflation (i) • Calculate the realized real return

  46. Ex-Ante (or before you hold the bond) Use EXPECTED INFLATION = h Example: • You will hold a bond for one year. • The Required real return is 5% • ExpectedInflationis 3% • Calculate the Required Nominal Return on a bond R = Nominal Return r = Required Real Return = 5% h = expected inflation = 3% R = (1 + r)(1 + h) - 1 R = (1.05)(1.03) -1 = 8.15%

  47. Clicker Question: • You require a real return of 10% on a bond. • You expect inflation to be 5% • Calculate the nominal return on the bond. • 5.0% • 5.5% • 10.5% • 15.0% • 15.5%

  48. Clicker Answer: r = required return = 10% h = expected inflation = 5% R = Nominal Return = (1 + r)(1 + h) - 1 = (1.10)(1.05) -1 = 15.5% The Answer is E What is the ESTIMATED Nominal Return? 10% + 5% = 15%

  49. Ex-Post (or after you have held the bond) Use REALIZED or MEASURED INFLAITON= i Example: • The nominal return was 8.15% • Measured Inflationwas 2% • Calculate the Realized Real Return R = Nominal Return = 8.15% r = Required Real Return i = measured inflation = 2% r = (1 + R)/(1 + i) - 1 r = (1.0815)/(1.02) – 1 = 6.03% > 5%

  50. Clicker Question • You have earned 12% nominal return on a bond. • Over the period you held the bond, measured inflation was 4% • Calculate the realizedREAL return on the bond • 4.00% • 7.69% • 8.00% • 8.69% • 12.00%

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