CHAPTER 8 Bonds and Their ValuationKey Features of a BondSlide 3How does adding a “call provision” affect a bond?What’s a sinking fund?Slide 6Financial Asset ValuesSlide 8What’s the value of a 10-year, 10% coupon bond if kd = 10%?Slide 10Slide 11What would happen if inflation fell, and kd declined to 7%?The bond was issued 20 years ago and now has 10 years to maturity. What would happen to its value over time if the required rate of return remained at 10%, or at 13%, or at 7%?Slide 14Slide 15What’s “yield to maturity”?What’s the YTM on a 10-year, 9% annual coupon, $1,000 par value bond that sells for $887?Slide 18Slide 19Find YTM if price were $1,134.20.DefinitionsFind current yield and capital gains yield for a 9%, 10-year bond when the bond sells for $887 and YTM = 10.91%.Slide 23What’s interest rate (or price) risk? Does a 1-year or 10-year 10% bond have more risk?Slide 25What is reinvestment rate risk?Slide 27Slide 28Do all bonds of the same maturity have the same price and reinvestment rate risk?Slide 30Semiannual BondsSlide 32You could buy, for $1,000, either a 10%, 10-year, annual payment bond or an equally risky 10%, 10-year semiannual bond. Which would you prefer?If $1,000 is the proper price for the semiannual bond, what is the proper price for the annual payment bond?Slide 35Slide 36Slide 37If you bought bonds, would you be more likely to earn YTM or YTC?Slide 39Slide 40Bond Ratings Provide One Measure of Default RiskWhat factors affect default risk and bond ratings?Slide 43Slide 44Top Ten Largest U.S. Corporate Bond Financings, as of July 1999BankruptcySlide 47Slide 48Slide 49Slide 508 - 1Copyright © 2001 by Harcourt, Inc. All rights reserved.CHAPTER 8Bonds and Their ValuationKey features of bondsBond valuationMeasuring yieldAssessing risk8 - 2Copyright © 2001 by Harcourt, Inc. All rights reserved.Key Features of a Bond1. Par value: Face amount; paid at maturity. Assume $1,000.2. Coupon interest rate: Stated interest rate. Multiply by par to get $ of interest. Generally fixed.8 - 3Copyright © 2001 by Harcourt, Inc. All rights reserved.3. Maturity: Years until bondmust be repaid. Declines.4. Issue date: Date when bondwas issued.8 - 4Copyright © 2001 by Harcourt, Inc. All rights reserved.How does adding a “call provision” affect a bond?Issuer can refund if rates decline. That helps the issuer but hurts the investor.Therefore, borrowers are willing to pay more, and lenders require more, on callable bonds.Most bonds have a deferred call and a declining call premium.8 - 5Copyright © 2001 by Harcourt, Inc. All rights reserved.What’s a sinking fund?Provision to pay off a loan over its life rather than all at maturity.Similar to amortization on a term loan.Reduces risk to investor, shortens average maturity.But not good for investors if rates decline after issuance.8 - 6Copyright © 2001 by Harcourt, Inc. All rights reserved.1. Call x% at par per year for sinking fund purposes.2. Buy bonds on open market.Company would call if kd is below the coupon rate and bond sells at a premium. Use open market purchase if kd is above coupon rate and bond sells at a discount.Sinking funds are generally handled in 2 ways8 - 7Copyright © 2001 by Harcourt, Inc. All rights reserved.Financial Asset Values     PV =CF1+ k... +CF1+k1 n1221CFkn.0 1 2 nkCF1CFnCF2Value...+ ++8 - 8Copyright © 2001 by Harcourt, Inc. All rights reserved.The discount rate (ki) is the opportunity cost of capital, i.e., the rate that could be earned on alternative investments of equal risk.ki = k* + IP + LP + MRP + DRP.8 - 9Copyright © 2001 by Harcourt, Inc. All rights reserved.What’s the value of a 10-year, 10% coupon bond if kd = 10%?     Vk kBd d$100 $1,100011 10 10 . . . +$1001+kd100 1000 1 2 1010%100 + 1,000V = ?...= $90.91 + . . . + $38.55 + $385.54= $1,000.++++8 - 10Copyright © 2001 by Harcourt, Inc. All rights reserved.10 10 100 1000N I/YR PV PMT FV -1,000The bond consists of a 10-year, 10% annuity of $100/year plus a $1,000 lump sum at t = 10: $ 614.46 385.54 $1,000.00PV annuity PV maturity value PV annuity ===INPUTSOUTPUT8 - 11Copyright © 2001 by Harcourt, Inc. All rights reserved. 10 13 100 1000N I/YR PV PMT FV -837.21When kd rises, above the coupon rate, the bond’s value falls below par, so it sells at a discount.What would happen if expected inflation rose by 3%, causing k = 13%?INPUTSOUTPUT8 - 12Copyright © 2001 by Harcourt, Inc. All rights reserved.What would happen if inflation fell, and kd declined to 7%? 10 7 100 1000N I/YR PV PMT FV -1,210.71Price rises above par, and bond sells at a premium, if coupon > kd.INPUTSOUTPUT8 - 13Copyright © 2001 by Harcourt, Inc. All rights reserved.The bond was issued 20 years ago and now has 10 years to maturity. What would happen to its value over time if the required rate of return remained at 10%, or at 13%, or at 7%?8 - 14Copyright © 2001 by Harcourt, Inc. All rights reserved.MBond Value ($)Years remaining to Maturity1,3721,2111,00083777530 25 20 15 10 5 0kd = 7%.kd = 13%.kd = 10%.8 - 15Copyright © 2001 by Harcourt, Inc. All rights reserved.At maturity, the value of any bond must equal its par value.The value of a premium bond would decrease to $1,000.The value of a discount bond would increase to $1,000.A par bond stays at $1,000 if kd remains constant.8 - 16Copyright © 2001 by Harcourt, Inc. All rights reserved.What’s “yield to maturity”?YTM is the rate of return earned on a bond held to maturity. Also called “promised yield.”8 - 17Copyright © 2001 by Harcourt, Inc. All rights reserved.What’s the YTM on a 10-year, 9% annual coupon, $1,000 par value bond that sells for $887? 90 90 900 1 9 10kd=?1,000PV1 . . .PV10PVM887Find kd that “works”!...8 - 18Copyright © 2001 by Harcourt, Inc. All rights reserved. 10 -887 90 1000N I/YR PV PMT FV 10.91     VINTkMkBdNdN1 11 ... +INT1+kd     887901100011 10 10k kd d +901+ kd,Find kd + + + +++++INPUTSOUTPUT ...8 - 19Copyright © 2001 by Harcourt, Inc. All rights reserved.If coupon rate < kd, discount.If coupon rate = kd, par bond.If coupon rate > kd, premium.If kd rises, price falls.Price = par