2 Key Concepts and Skills Know the important bond features and bond typesUnderstand bond values and why they fluctuateUnderstand bond ratings and what they meanUnderstand the impact of inflation on interest ratesUnderstand the term structure of interest rates and the determinants of bond yields
3 Chapter Outline Bonds and Bond Valuation More on Bond Features Bond RatingsSome Different Types of BondsBond MarketsInflation and Interest RatesDeterminants of Bond Yields
4 Issuer (Seller) of Bonds (Borrower) = “Bond Issuer” Bonds = Debt = Liability = Long-term debt1 Bond usually means the corporation borrows $1000 (face value)Corporations usually issue many BondsBond Issue:The total number of bonds that a corporation issues at the same time, in denominations of $1,000 or $5,000 eachLike any contractual debt:Bond issuer pays periodic interest to the bondholderBond issuer pays the face value back at the end of the bond term
5 Issuer (Seller) of Bonds (Borrower) = “Bond Issuer” When you issue a bond, you borrow the money, then use the money to buy assets that earn more cash than the cash you have to pay out to the bondholderLeverageExample:Borrow money at 8% interest and buy a machine that earns the corporation 13%The difference between 13% and 8%, or 5%, is left for the stockholders
6 Buyer of Bonds (Lender) = “Bondholder” Bonds = Asset1 Bond usually means the borrow lends money to the corporation or governmentLike any contractual debt:Bondholders are paid periodic interest for loaning money to the corporation and are paid back the face value at the end of the bond termWhen you buy a bond you are paying for a future steam of cash flow
7 Bond Vocabulary:Face value = par value = loan repayment at maturity = FVAnnual interest payments = “annual coupon”Coupon is from the days when you presented coupon to get paid interestAnnual interest rate (not discount rate) = coupon rate = annual interest rate for calculating interest payments = annual coupon/face valueNumber of interest payments per year = nPeriodic rate (not discount rate) = periodic coupon rate = (annual coupon rate)/nThe book is inconsistent with the use of “coupon” (sometimes annual, sometimes semi-annual)Periodic interest payment = periodic rate*face = PMTYears until maturity = term of bond = years until paying back face value and last periodic interest payment = xMaturity = specified date on which principal is repaid
8 Bond Vocabulary:Yield To Maturity (YTM) = discount rate used to value bond = i = YTMYTM = Bond Yield = Required Return = Market Rate = Rate required in the market on a bondYTMs are quoted like APRsYTM = (Period Discount Rate) * nExample: YTM = 10% and bond pays semiannual interest payments, then period discount rate = YTM/n = .10/2 =.05Effective Annual Yield on the Bond = (1+.10/2)2 = .1025
9 Bonds Bonds are interest only loans Corporations/Governments borrow money, pay interest each period, then pay back face amount at end of bond termCorporations/Governments plan to issue bonds and then set the coupon rate, but by the time they actually issue the bond the financial markets have already calculated a discount rate for the future values that is often different than the coupon rateCorporations/Governments issue bonds and get the “cash in” (Bonds sold in primary market)Many Bonds from Corporations/Governments can be traded in the financial markets (Bonds sold in the secondary market)
10 BondsEach bond has a price expressed as a percentage of the face value:For example, 103 means 1.03 times the face value of the bondWhen the corporation issues the $1,000 face-value bond, it receives $1,030At maturity, the corporation pays back only the face value of $1,000103 and 103% and 1.03 all convey the same meaning The bond is selling for 3% above the face value
11 Example 1On January 1, Cox Construction Corp. issues year bonds with a face of $1000 with a coupon rate of 9% at 103, with interest payable semiannually, on June 30 and December 31
12 This Bond with its 9% coupon, is priced to yield 8.74% at $1,030
13 But If The Loan Has A Face Value Of $750,000, Why Did The Bondholder Pay $772,500?
14 If a corporation offers a rate of interest that is higher than the market rate for similar securities, investors may be willing to pay a premium for the bondIf a corporation offers a rate of interest that is lower than the market rate for similar securities, investors will demand a discount on the bond
15 What Are Similar Securities? Similar securities are bonds or other investment vehicles issue by other corporations (different than the one being considered) that have similar business and financial risksThe similarities could be:Similar credit ratingsSimilar business activitiesSimilar capital structure
17 Definitions Premium Discount The excess of the price received over the face value of a bondYTM < Coupon Rate“Bond sold at a premium”DiscountThe amount by which the issue price is less than the face value of a bondYTM > Coupon Rate“Bond sold at a discount”
18 The Issuance of Bonds at a Discount: Example 2 On January 1, Muller, Inc., issues 700 6%, 20-year bonds with a face value of $1,000, at 96, with interest to be paid semiannually, on June 30 and December 31
19 This Bond with its 6% coupon, is priced to yield 6.25% at $960
20 Bond Price (Valuation) from Cash Flow Perspective
21 Excel Bond Valuation from Bondholder’s Point of View: =PV(rate,nper,pmt,fv,type)=PV(YTM/n,n*x,PMT,FV,0)Bond Valuation from Bond Issuer’s Point of View:=PV(YTM/n,n*x,-PMT,-FV,0)Finding YTM rate from Bondholder’s Point of View:=RATE(nper,pmt,pv,fv,type,guess)=RATE(n*x,PMT,-PV,FV,0)
24 CF Is From Point Of View Of Issuer Example 3CF Is From Point Of View Of Issuer
25 Bond Values And Why They Fluctuate Bond Valuation:As time passes, interest rates change in the market placeAs new information about the company, the industry, the economy comes out, interest rates changeAs time passes the amount of cash paid out to the bondholder does not changeBecause of this the value of the bond will fluctuateRates , Bond Value Rates , Bond Value
26 Graphical Relationship Between Price and YTM Bond characteristics: Coupon rate = 8% with annual coupons; Par value = $1000; Maturity = 10 years
27 Valuing a Discount Bond with Annual Coupons Payments (Example 4) Consider a bond with a coupon rate of 10% and coupons paid annually. The par value is $1000 and the bond has 5 years left until maturity. The yield to maturity is 11%. What is the value of the bond What is the price to you, buying in the secondary market?Using the formula:B = PV of annuity + PV of lump sumB = 100[1 – 1/(1.11)5] / / (1.11)5B = =Answer: “You would be willing to pay $ cash out (negative) for the future cash flows.” or said this way: “The bond with a 10% coupon is priced to yield 11% at $ ”Remember the sign convention on the calculator. The easy way to remember it with bonds is we pay the PV (-) so that we can receive the PMT (+) and the FV(+).Slide 6.8 discusses why this bond sells at less than par
28 Valuing a Premium Bond with Annual Coupons Payments (Example 5) Suppose you are looking at a bond that has a 10% annual coupon rate and a face value of $1000. There are 20 years to maturity and the yield to maturity is 8%. What is the value of the bond what is the price to you?Using the formula:B = PV of annuity + PV of lump sumB = 100[1 – 1/(1.08)20] / / (1.08)20B = =Answer: “You would be willing to pay $ cash out (negative) for the future cash flows.” or said this way: “The bond with a 10% coupon is priced to yield 8% at $ ”
29 Interest Rate RiskThe risk that arises for bond owners from fluctuating interest ratesHow much interest rate risk a bond has depends on:How sensitive its price is to interest rate changeThe sensitivity depends on two things:All things being equal, the longer the time to maturity, the greater the interest rate riskAll things being equal, the lower the coupon rate, the greater the interest rate risk
31 Interest Rate Risk To Loss Of Principal (current price) Longer time to maturitySmall changes in market rate have substantial affect on bond valueFace value is discounted over many periods and thus compounding magnifies small interest rate changesLower Coupon rateBond with lower coupon rate is proportionally more dependent on the face value(Bond with larger coupon rate has a larger cash flow early in life, so value less sensitive to discount rate)
32 Interest Rate Risk Increases At A Decreasing Rate
33 Computing YTMYield-to-maturity is the rate implied by the current bond priceFinding the YTM requires trial and error (iteration) if you do not have a financial calculator and is similar to the process for finding i with an annuityIf you have a financial calculator, enter N, PV, PMT and FV, remembering the sign convention (PMT and FV need to have the same sign, PV the opposite sign)
34 YTM with Annual Coupons (Example 6) Consider a bond with a 10% annual coupon rate, 15 years to maturity and a par value of $1000. The current price is $928.09Will the yield be more or less than 10%?The students should be able to recognize that the YTM is more than the coupon since the price is less than par.
35 YTM with Semiannual Coupons (Example 7) Suppose a bond with a 10% coupon rate and semiannual coupons, has a face value of $1000, 20 years to maturity and is selling for $Is the YTM more or less than 10%?What is the semiannual coupon payment?How many periods are there?
36 Use One Bond YTM To Find Price Of Another Bond: Example 8 BelowMarketrate =discountAbove = premium
37 Bonds and Stocks:Like stock, bonds bring capital (money) into the corporation so that it can invest in profitable projectsBondholders are creditorsThey have a fixed claim to cash flowStockholders are ownersThey have a residual claim to cash flow
38 Bonds and Stocks Debt is not an ownership interest in the firm Creditors do not have voting rightsInterest is tax deductibleDividends are not tax deductibleUnpaid debt is a liabilityLegal claim against assetsIf debt is not paid creditors have the legal claim to assets before shareholdersOne of the costs of issuing debt is the possibility that you will not be able to make interest payments creditors force firm into bankruptcy firm is terminatedThis does not arise when equity is issuedCorporations try to create hybrid financial instruments that are Debt/Equity in order to have:Tax benefits of debtBankruptcy benefits of equity
39 Differences Between Debt and Equity Not an ownership interestCreditors do not have voting rightsInterest is considered a cost of doing business and is tax deductibleCreditors have legal recourse if interest or principal payments are missedExcess debt can lead to financial distress and bankruptcyEquityOwnership interestCommon stockholders vote for the board of directors and other issuesDividends are not considered a cost of doing business and are not tax deductibleDividends are not a liability of the firm and stockholders have no legal recourse if dividends are not paidAn all equity firm can not go bankrupt
40 Bond Terms and Types Bonds = Long-term debt Finance jargon” Privately placedDirectly placed with the lenderPublic-issue bondsOffered to the publicFinance jargon”Long-term debt = funded debtShort-term debt = unfunded debtExample: “A firm planning to fund its debt requirements may be replacing short-term debt with long-tern debt”
41 Bond Terms and Types Trustee (Investment Bank, other…) Indenture Appointed by the corporation to represent bondholdersMust make sure terms are obeyedMust manage sinking fundMust represent bondholders in defaultIndenture“The written agreement between the corporation and the lender detailing the terms of the debt issue”
42 Bond Types Registered Form Bearer Form The form of bond issue in which the registrar of the company records ownership of each bondPayment is made directly to the owner of the bondBearer FormThe form of bond issue in which the bond is issued without record of the owner’s namePayment is made to whoever holds the bondUncommon in the USA
43 Bond TypesSecurity:Generic term that means Stocks or Bonds or other investment vehicles that are backed by an assetA document indicating ownership or creditorship; a stock certificate or bondDictionary definition of Security:Something deposited or given as assurance of the fulfillment of an obligation; a pledge; collateral
44 Bond TypesDebt securities are classified according to the collateral and mortgages used to protect the bondholderSecurities Backed By CollateralCollateral = any asset pledged on the debt (often means assets such as stocks or bonds – financial assets)If the borrower does not pay the interest and principal to the bondholder, the bondholder can take the collateralMortgage SecuritiesDebt secured by a mortgage on real assets (property, but not cash or inventory) of the borrowerCalled:Mortgage Trust Indenture, or Trust DeedMost utility and railroad bonds are secured by a pledge of assets
45 Bond Types Subordinate Debt Unsecured Debt These creditors have a claim on property not otherwise pledgedDebentureUnsecured debt (maturity >= 10 years)Most financial and industrial companies’ public bonds are debenturesNoteUnsecured debt (maturity < 10 years)Subordinate DebtMust give preference to superior debtDebt is not subordinate to equity
46 Bond Types Sinking Fund Protective Covenant An account managed by the trustee for the purposed of repaying the bonds, or early bond redemptionBond Issuer must put away some money each period to save up in order to pay off the bondProtective CovenantA part of the indenture limiting certain actions that might be taken in order to protect the lenderNegative (thou shalt not):Example: Limit the amount of dividends paidPositive (thou shalt):Example: CA/CL must be greater than 1.5
47 Bond Types Call Provision Call Premium (Pay for the Option) An agreement giving the corporation the option to repurchase the bond at a specific price prior to maturityCall Premium (Pay for the Option)The amount by which the call price > par valueExample: Bond face = $1,000, Call Price = $1,100Call Price goes down over timeDeferred Call ProvisionCan call only after a certain dateCall Protected BondCan’t be redeemed by issuerMake-Whole CallWhen bond called, bondholder gets PV of future cash flows at a reasonable rateDerivative security jargon:Call = BuyPut = Sell
48 Financial Markets Primary Markets Secondary Markets Original sale of equity or debtCorporation issues securitySecondary MarketsAfter original sale of equity or debtYou sell/buy securityDealer Markets (Over-the-counter markets (OTC))Dealers buy and sell for themselvesMost debt is sold this wayExample: NASDAQAuction Markets (Exchanges)Brokers and agents match buyers and sellersMost of the large firms’ equity is sold this wayExample: NYSE
49 Bond Characteristics and Required Returns The coupon rate depends on the risk characteristics of the bond when issuedWhich bonds will have the higher coupon, all else equal?Secured debt versus a debentureSubordinated debenture versus senior debtA bond with a sinking fund versus one withoutA callable bond versus a non-callable bondDebenture: secured debt is less risky because the income from the security is used to pay it off firstSubordinated debenture: will be paid after the senior debtBond without sinking fund: company has to come up with substantial cash at maturity to retire debt and this is riskier than systematic retirement of debt through timeCallable – bondholders bear the risk of the bond being called early, usually when rates are lower. They don’t receive all of the expected coupons and they have to reinvest at lower rates.
50 Bond Ratings And What They Mean Bond Rating firms:Moody’sStandard and Poor’s (S&P)They rate:The likelihood of defaultThe probability that creditors are protectedThey ask they question: What is the risk associated with the firm issuing the debt?They do not rate the probability of bond value change due to interest rate riskThe Debt Crisis of 2007 shows that Ratings can be less than accurate:How do they take risky loans and repackage them to get a AAA “Super Senior” rating? (That’s what they did!)
51 Bond Ratings – Investment Quality High GradeMoody’s Aaa and S&P AAA – capacity to pay is extremely strongMoody’s Aa and S&P AA – capacity to pay is very strongMedium GradeMoody’s A and S&P A – capacity to pay is strong, but more susceptible to changes in circumstancesMoody’s Baa and S&P BBB – capacity to pay is adequate, adverse conditions will have more impact on the firm’s ability to pay
52 Bond Ratings - Speculative Low GradeMoody’s Ba, B, Caa and CaS&P BB, B, CCC, CCConsidered speculative with respect to capacity to pay. The “B” ratings are the lowest degree of speculation.Very Low GradeMoody’s C and S&P C – income bonds with no interest being paidMoody’s D and S&P D – in default with principal and interest in arrearsIt is a good exercise to ask students which bonds will have the highest yield-to-maturity (lowest price) all else equal.
53 Some Different Types of Bonds Government BondsTreasury BillYears < 1Treasury Note1< years < 7Treasury BondsOtherNo default riskTreasury issues are exempt from state income tax (must pay Fed IT)
54 U.S. NATIONAL DEBT CLOCK The Outstanding Public Debt as of 13 Nov 2007 at 11:28:01 PM GMT is: The estimated population of the United States is 303,525,093 so each citizen's share of this debt is $30, The National Debt has continued to increase an average of $1.49 billion per day since September 29, 2006!
55 Some Different Types of Bonds Municipal Bonds “Munis”State and local government debtExample: Bond to build HighwayThese do have varying degrees of default riskAlmost always callableCoupons exempt from federal income taxes (must pay State IT)Attractive to high-income/high-tax bracket investorsBecause of this the yields are lowerWhich do you (with 25% Fed tax Bracket) prefer: corporate bond that yields 5%, or a muni (with comparable risk and maturity) that yields 3.90%?.039 > .05(1-.25) = .0375
56 Some Different Types of Bonds Zero Coupon BondsA bond that makes no coupon payments, and thus is initially priced at a deep discountIssuer must deduct interest every yearTax Benefit A deductions for taxes (fewer taxes paid like cash coming in) even though no cash going out (interest expense)Bondholder must accrue interest revenue every yearTaxes paid on revenue Cash going out (taxes paid) even though cash is not coming in (interest revenue)Regular amortization table is constructed to track interest accrual
57 Pure Discount Loans (Zero Coupon) Borrow an amount today, then pay back principal and all interest at the end of the loan periodExample: US Government Treasury Bills, or T-bills (government loans < 1year)PaybackAmountLoan amountreceived today
63 Floating-Rate Bonds Coupon Payments are adjustable Rated can be tied to an interest rate index such as the Treasury bill interest rate or 30-year Treasury bond rateRate and payments are adjusted periodicallyHolder may have the right to redeem the note at par on the coupon payment date after some specified amount of timeThis is called a “Put” ProvisionThe coupon rate has a floor and ceiling“Capped” or “Collared” means they have an upper and lower barrier
64 Other Bonds: Income Bonds: Convertible Bonds Put Bond Coupon payments are dependent on the company incomeConvertible BondsDebt that can be converted to a fixed amount of equity anytime before maturity at the holder’s optionHalf Debt half equity?How do you list it on the Balance Sheet?Put BondAllows holder to force the issuer to buy the bond back at a stated price (reverse of a call)CoCo and NoNo BondsThese have many features that require complex valuing techniques. Because the features can be valuable to the bondholder, the YTM could be negative!
65 Bond MarketsBecause the bond market is almost entirely OTC, it has little or no transparency (can’t see a great deal of Buy/Sells to gage market value of bonds)US Treasury market is the largest security market in the worldTerminology:Bid PriceThe price a dealer is willing to pay for a securityAsk PriceThe price a dealer is willing to take for a securityBid-ask spreadBid – Ask = Dealers Profit
66 The Impact Of Inflation On Interest Rates Increase in price over timeExample:Price of milk now = $3.39/gal.Price of milk in 1 year = $3.56/gal.
67 Inflation and Interest Rates Real RatesBase interest rate that does not take inflation into considerationThe percentage change in buying powerInterest rates or rates of return that have been adjusted downward from the nominal rate for inflationNominal RatesInterest rates or rates of return that have not been adjusted downward for inflation% change in the number of dollars you haveThe nominal rate of interest includes our desired real rate of return plus an adjustment for expected inflation
68 The Fisher Effect (Irving Fisher) The Fisher Effect defines the relationship between real rates, nominal rates and inflationR =r + h + r*hr = (R-h)/(1+h) = (1+R)/(1+h) - 1(1 + R) = (1 + r)(1 + h)R = nominal rater = real rateh = expected inflation rateApproximationR = r + h
70 Example 6.6If we require a 10% real return and we expect inflation to be 8%, what is the nominal rate?R = (1.1)(1.08) – 1 = .188 = 18.8%Approximation: R = 10% + 8% = 18%Because the real return and expected inflation are relatively high, there is significant difference between the actual Fisher Effect and the approximation.
71 The Fisher EffectReal rate is hard to observe directly, so we observe it indirectly:r = (R-h)/(1+h) = (1+R)/(1+h) - 1Real Rate is fairly constantTake into consideration taxes:r (R*(1-taxrate)-h)/(1+h)
72 The Term Structure Of Interest Rates And Determinants Of Bond Yields The risks associated with loaning money are added into a “base” interest rate known as the real rate
73 Bond Yields represent 6 effects: Some Components of Interest Rates:Real RateInflation PremiumInterest Rate Risk PremiumDefault Risk PremiumTaxability PremiumLiquidity Premium
74 Real RateCompensation investors demand for foregoing the use of their moneyBasic component underlying every interest rateWhen real rate high, all rates tend to be highDoesn’t really determine shape of term structure (overall effect)
75 Inflation PremiumThe portion of a nominal interest rate that represents compensation for expected future inflationVery strongly influences the shape of term structureInflation expected increase structure upwardInflation expected decrease structure downward
76 Interest Rate Risk Premium Compensation demanded for bearing interest rate risklonger-term bonds have a much greater risk of loss resulting from changes in interest rate than so short-term bondsThis premium increases at a decreasing rate
77 Term Structure Of Interest Rates (Based On Pure Discount Bonds) This shows the relationship between short and long-term interest ratesTells us what the nominal interest rates are on default-free (Treasury), pure discount securities of all maturitiesThis shows the relationship between nominal interest rates on default-free, pure discount securities and time to maturityThese rates are “pure” because they involve no risk of defaultThe term structure tells us the pure time value of money for different lengths of timeUpward sloping = long-term rates > short-term ratesDownward sloping = long-term rates < short-term rates
80 Term Structure Of Interest Rates Assumes:Real Rates remain constantInflation linearRates could be “Humped”Rates increase at first, but then decline as we look at longer-termed notes
81 Treasury Yield CurveA plot of the yields on Treasury Notes and Bonds relative to MaturityTreasury Yield Curve and the Term Structure Of Interest Rates re almost the same thingThe difference is:Treasury Yield CurveBased On Coupon Bond YieldsTerm Structure Of Interest RatesBased On Pure Discount Bonds
82 Treasury Yield Curve (Coupon Bond Yields) www: Click on the web surfer to go to Bloomberg to get the current Treasury yield curve
83 Default Risk PremiumBonds other than Treasury: Credit risk/default riskThe portion of a nominal interest rate or bond yield that represents compensation for the possibility of defaultLower rated bonds have higher yields
84 Taxability PremiumThe portion of a nominal interest rate or bond yield that represents compensation for unfavorable tax statusRemember municipal versus taxableBonds that are taxed at both the state and Federal level are less favorable than a bond that is only taxed at the Fed. level
85 Liquidity PremiumThe portion of a nominal interest rate or bond yield that represents compensation for a lack of liquidityLiquidity:How quickly an asset can be converted to cashExample:Maybe the bond is hard to sell quickly and therefore would require a premium for that lack of liquidityLess liquid bonds have higher yields than more liquid bonds
86 Three Principles in Bond Finance Rates are inversely related to priceMarket rate , Bond Price Par, Discount, PremiumMarket rate = Coupon RateBond sells at Par or Face ValueMarket rate > Coupon RateBond sells at a DiscountMarket rate < Coupon RateBond sells at a PremiumThe more years there are to maturity, the higher the interest rate risk becomes“Interest rate risk to loss of principal”
87 Bond Vocabulary: Current Yield = Annual Interest Payment/Closing Price Not equal to YTM (unless bond sells for par); it does not include the capital gain from discounted face value (principal)Premium BondCY >YTMDiscount BondCY <YTMIn all cases (Current Yield) + (Expected one-period capital gain/loss yield of the bond) must be equal to the YTM
88 SecuritizationSecuritization = “The process of Securitization involves the collection or pooling of loans and the sale of securities backed by those loans (Cash flows in loan)Whereas, Banks once made loans and kept them on their books, now they can initiate loans and then sell the loans to someone else.Securitization = packaging a set of cash flows and then selling claims (bonds or other) against themClaims = asset backed securitiesThis means that the cash is the asset that backs it
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