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Chapter 5

Chapter 5. Bonds, Bond Valuation, and Interest Rates. Topics in Chapter. Key features of bonds Bond valuation Measuring yield Assessing risk. Determinants of Intrinsic Value: The Cost of Debt. Net operating profit after taxes. Required investments in operating capital. −.

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Chapter 5

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  1. Chapter 5 Bonds, Bond Valuation, and Interest Rates

  2. Topics in Chapter • Key features of bonds • Bond valuation • Measuring yield • Assessing risk

  3. Determinants of Intrinsic Value: The Cost of Debt Net operating profit after taxes Required investments in operating capital − Free cash flow (FCF) = FCF1 FCF2 FCF∞ ... Value = + + + (1 + WACC)1 (1 + WACC)2 (1 + WACC)∞ Weighted average cost of capital (WACC) Market interest rates Firm’s debt/equity mix Cost of debt Cost of equity Market risk aversion Firm’s business risk

  4. Interest Rates & Interest-Bearing Securities • Interest rates: • Based on supply & demand for money • Driven by risk factors • Role of Federal Reserve • Basis Point • .01% or .0001

  5. rd = r* + IP + DRP + LP + MRP rd = Required rate of return on a debt security. r* = Real risk-free rate. IP = Inflation premium. DRP = Default risk premium. LP = Liquidity premium. MRP = Maturity risk premium. Risk & Term Structure of Interest Rates

  6. Risk & Term Structure • r = r* + IP + DRP + LP + MRP • r = nominal interest rate of a particular security (or required rate of return) • r* = real risk-free interest ratetypically 1-4% depending on monetary policyassumes expected inflation = zero • IP = Inflation premiumAve. inflation over life of bond • DRP = Default risk premiumCompensation for possible defaultFunction of bond ratings

  7. Risk & Term Structure • r = r* + IP + DRP + LP + MRP • LP = Liquidity Premium Compensation for possible difficulty selling bond quickly at fair market value • MRP = Maturity Risk PremiumCompensation for possible loss in value due to increase in interest rates over maturity of bond. Affects longer maturities more than shorter.

  8. Premiums Added to r* (real risk-free rate) for Different Types of Debt • ST Treasury: • only IP for ST inflation • LT Treasury: • IP for LT inflation, MRP • ST corporate: • ST IP, DRP, LP • LT corporate: • IP, DRP, MRP, LP

  9. Inflation & Interest Rates • Nominal Interest= 12% - Inflation -1% = Real Int. % =11% If inflation = & req’d real return = Then Nominal rate =? = 12% • 8% =4% • 8% 11% =19%

  10. Relationship b/w Nominal & Real Interest Rates, & Inflation • Nom = Real + Inflation • But, inflation not additive, it grows or compounds, so multiply • Nom = (Real) x (Infl) • And (1+Nom) = (1 + real) x (1 + infl) • Is better determinant; known as Fisher effect

  11. Estimating Inflation Premium (IP) • Treasury Inflation-Protected Securities (TIPS) are indexed to inflation. • IP for a particular length maturity can be approximated as the difference between the yield on a non-indexed Treasury security of that maturity minus the yield on a TIPS of that maturity.

  12. Bond Spreads, the DRP, and the LP • A “bond spread” is often calculated as the difference between a corporate bond’s yield and a Treasury security’s yield of the same maturity. Therefore: • Spread = DRP + LP. • Bond’s of large, strong companies often have very small LPs. Bond’s of small companies often have LPs as high as 2%.

  13. Term Structure Yield Curve • Term structure of interest rates: the relationship between interest rates (or yields) and maturities. • A graph of the term structure is called the yield curve.

  14. Hypothetical Treasury Yield Curve

  15. What factors can explain shape of this yield curve? • Upward slope due to: • Increasing expected inflation • Increasing maturity risk premium • What about liquidity & default risk?

  16. Treasury vs. Corporate Yield Curves relationships • Corp yield curves are higher than Treasuries, but not necessarily parallel. • Spread b/w the two yield curves widens as corporate bond rating decreases due to: • DRP & LP

  17. Computing Yields • Estimate the inflation premium (IP) for each future year. This is the estimated average inflation over that time period. • Step 2: Estimate the maturity risk premium (MRP) for each future year.

  18. Assume investors expect inflation to be 5% next year, 6% the following year, and 8% per year thereafter. • Step 1: Find the average expected inflation rate over years 1 to n: IP1 = 5%/1.0 = 5.00%. IP10 = [5 + 6 + 8(8)]/10 = 7.5%. IP20 = [5 + 6 + 8(18)]/20 = 7.75%. Must earn these IPs to break even versus inflation; that is, these IPs would permit you to earn r* (before taxes).

  19. Step 2: Find MRP based on this equation: Assume the MRP is zero for Year 1 and increases by 0.1% each year. MRPt = 0.1%(t - 1). MRP1 = 0.1% x 0 = 0.0%. MRP10 = 0.1% x 9 = 0.9%. MRP20 = 0.1% x 19 = 1.9%.

  20. Step 3: Add the IPs and MRPs to r*: rRFt = r* + IPt + MRPt . rRF = Quoted market interest rate on treasury securities. Assume r* = 3%: rRF1 = 3% + 5% + 0.0% = 8.0%. rRF10 = 3% + 7.5% + 0.9% = 11.4%. rRF20 = 3% + 7.75% + 1.9% = 12.65%.

  21. Upward vs. Downward sloping yield curves due to? • Real risk-free rate = 3% • Expected inflation for • Year 1 =7%, Yr 2 = 5%; Yr 3 = 3% • What are interest rates for 1, 2, & 3 yr borrowings?

  22. Interest Rates & MRP problem • Assume the real risk-free rate (r*) is 4% and inflation is expected to be 7 percent in Year1; 4% in yr 2; and 3% thereafter. Assume all Treasury Bonds are highly liquid and free of default risk. If 2-yr and 5-yr T-Bonds both yield 11%, what is the difference in the maturity risk premiums (MRPs) on the two bonds; that is, what is MRP5 – MRP2?

  23. Interest Rates & Inflation Problem • Due to the recession, the rate of inflation expected for the coming year is only 3.5%. However, the rate of inflation in Yr 2 and thereafter is expected to be constant at some level above 3.5%. Assume the real risk-free rate (r*) = 2% for all maturities, and there are no maturity premiums. If 3-year T-Bonds yield 3% (0.03) more than the 1-year T-Bonds, what rate of inflation is expected after year 1?

  24. Coupon Bonds • Bond = Debt = Borrowing • Fixed Maturity (Maturity Date) = N • Par Value=Face Value=Maturity Value=$1000=FV • Coupon Rate=Stated Rate (locked in in bond contract) • Coupon payment= Coupon rate x face value=PMT • Market Rate of interest = Yield to Maturity = rate used to discount bond CF’s = I • **PV cash flow of bonds always opposite sign of PMT & FV!!!

  25. Bond Perspectives Debt Asset Has $ Lender Buyer or Investor Bondholder Creditor Requires return to invest $ in bonds based on risk Interest Received (earned) (Revenue) - pay tax on it Capital Appreciation • Needs $ • Borrower • Issuer or seller • Debtholder • Cost of borrowing • Interest Paid (Expense) – generates tax benefit (Svgs) • Cost of Debt • = Rd or Kd; • After-tax cost = Rd (1-t)

  26. Key Features of a Bond • Par value: Face amount; paid at maturity. Assume $1,000. • Coupon interest rate: Stated interest rate. Multiply by par value to get dollars of interest. Generally fixed. (More…)

  27. Key Features of a Bond • Maturity: Years until bond must be repaid. Declines. • Issue date: Date when bond was issued. • Default risk: Risk that issuer will not make interest or principal payments.

  28. Value of Financial Security • Value of any asset based on the net present value of the expected future cash flows discounted by the interest (discount) rate that reflects risk factors • Discount (interest rate) depends on: • Riskiness of CFs reflected by DRP, MRP, LP • General level of interest rates, which reflects inflation, supply & demand for $, production opportunities, time preferences for consumption

  29. 0 1 2 10 Value of a 10-year, 10% coupon bond if rd = 10% 10% ... V = ? 100 100 100 + 1,000 $100 $100 $1,000 V = . . . + + + B (1 + rd)1 (1 + rd)N (1 + rd)N = $90.91 + . . . + $38.55 + $385.54 = $1,000.

  30. PV annuity PV maturity value Value of bond $ 614.46 385.54 $1,000.00 = = = INPUTS 10 10 100 1000 N I/YR PV PMT FV -1,000 OUTPUT The bond consists of a 10-year, 10% annuity of $100/year plus a $1,000 lump sum at t = 10:

  31. INPUTS 10 13 100 1000 N I/YR PV PMT FV -837.21 OUTPUT What would happen if expected inflation rose by 3%, causing r = 13%? When market interest rate (rd)rises above coupon rate, bond’s value (PV or price) falls below par, so sells @ discount.

  32. INPUTS 9 13 100 1000 N I/YR PV PMT FV -846.05 OUTPUT What happens if one year passes but the market i stays at 13%?

  33. INPUTS 8 13 100 1000 N I/YR PV PMT FV -856.04 OUTPUT What happens if a second year passes but the market i stays at 13%?

  34. INPUTS 1 13 100 1000 N I/YR PV PMT FV -973.45 OUTPUT What happens if 9 years pass but the market i stays at 13%? As a bond approaches maturity, it’s price approaches the face or maturity value of $1000

  35. Bond Pricing in Excel

  36. INPUTS 10 7 100 1000 N I/YR PV PMT FV -1,210.71 OUTPUT What would happen if inflation fell, and rd declined to 7%? If coupon rate > mrkt i% (rd), price rises above par, and bond sells at a premium.

  37. Bond Pricing in Excel • PV = ? $1210.71

  38. Summary of Bond price and interest rate relationships • If market rate of interest increases above the stated (coupon) rate, then bond’s price falls and sells at discount • If market rate of interest drops below the stated (coupon) rate, then bond’s price increases and sells at a premium • **INVERSE RELATIONSHIP b/w Market i% and Bond’s PRICE!***

  39. Bond prices & changing interest rates • Suppose the bond was issued 20 years ago and now has 10 years to maturity. What would happen to its value over time if required rate of return remained at 10%, or at 13%, or at 7%?

  40. Bond Value ($) vs Years remaining to Maturity rd = 7%. 1,372 1,211 rd = 10%. M 1,000 837 rd= 13%. 775 30 25 20 15 10 5 0

  41. Bond Price Movements over time • At maturity, value of any bond must equal its par value. • Value of a premium bond decreases to $1,000. • Value of a discount bond increases to $1,000. • A par bond stays at $1,000 if mrkt i% (rd)remains constant.

  42. INPUTS 10 7 100 1000 N I/YR PV PMT FV ? OUTPUT What’s market value of 10 year 10% coupon bond when market = 7%? Bond sells at a premium:: Price today = $1,210.71.

  43. INPUTS 10 (1210.71) 100 1000 N I/YR PV PMT FV ? OUTPUT If you buy a 10%, 10 year bond today for $1,210.71, and hold it to maturity, what’s your rate of return? Solve for i% = 7% = Yield to maturity (YTM)

  44. What’s “yield to maturity”? • YTM is rate of return earned on a bond held to maturity. Also called “promised yield.” • It assumes bond will not default. • Includes both interest pmt component & cap gains over bond’s life • Interest rate equating bond’s price today to NPV of PMTs & FV. (Think market rate of interest) • Vs. Annualized Return which reflects only a one-year holding period

  45. 0 1 9 10 rd=? ... 90 90 90 1,000 PV1 . . . PV10 PVM Find i % (rd) that “works”! 887 YTM on a 10-year, 9% annual coupon, $1,000 par value bond selling for $887

  46. Find YTM (i % or rd) INT INT M ...  V = + + + B      (1 + rd)N (1 + rd)1 (1 + rd)N 1,000 90 90 ... 887 = + + +       (1 + rd)1 (1 + rd)N (1 + rd)N INPUTS 10 -887 90 1000 N I/YR PV PMT FV 10.91 OUTPUT

  47. YTM in Excel

  48. Bond Prices & Int. Rates • If coupon rate < mrkt i % (rd), bond sells at a discount. • If coupon rate = i %, bond sells at its par value. • If coupon rate > i%, bond sells at a premium. • If market i% rises, price falls. • Price = par at maturity.

  49. INPUTS 10 -1134.2 90 1000 N I/YR PV PMT FV 7.08 OUTPUT Find YTM if price were $1,134.20. Sells at a premium. Because coupon = 9% > mrkt i% = 7.08%, bond’s value > par.

  50. Definitions Current yield = “Interest Yield” Capital gains yield =Change in value = YTM = + Exp total return Exp cap gains yld Exp Curr yld

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