Kế toán, kiểm toán - Chapter 4: Bond valuation

Chapter 4Bond Valuation1Topics in ChapterKey features of bondsBond valuationMeasuring yieldAssessing risk2Key Features of a BondPar 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)3Maturity: 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.4Call ProvisionIssuer 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.5What’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.6Sinking funds are generally handled in 2 waysCall x% at par per year for sinking fund purposes.Call if rd is below the coupon rate and bond sells at a premium.Buy bonds on open market.Use open market purchase if rd is above coupon rate and bond sells at a discount.7PV=CF ... +CF1N2(1 + r)2CF.012NrCF1CFNCF2Value...++Financial Asset Valuation(1 + r)1(1 + r)N8Value of a 10-year, 10% coupon bond if rd = 10%VB=$100$1,000 . . . +$1001001000121010%100 + 1,000V = ?...= $90.91 + . . . + $38.55 + $385.54= $1,000.++(1 + rd)1(1 + rd)N(1 + rd)N9 10 10 100 1000 N I/YR PV PMT FV -1,000 $ 614.46 385.54 $1,000.00PV annuity PV maturity value Value of bond ===INPUTSOUTPUTThe bond consists of a 10-year, 10% annuity of $100/year plus a $1,000 lump sum at t = 10:10When rd rises, above the coupon rate, the bond’s value falls below par, so it sells at a discount. 10 13 100 1000 N I/YR PV PMT FV -837.21INPUTSOUTPUTWhat would happen if expected inflation rose by 3%, causing r = 13%?11What would happen if inflation fell, and rd declined to 7%?If coupon rate > rd, price rises above par, and bond sells at a premium. 10 7 100 1000 N I/YR PV PMT FV -1,210.71INPUTSOUTPUT12Suppose the bond was issued 20 years ago and now has 10 years to maturity. What would happen to its value over time if the required rate of return remained at 10%, or at 13%, or at 7%?13M1,3721,2111,00083777530 25 20 15 10 5 0rd = 7%.rd = 13%.rd = 10%.Bond Value ($) vs Years remaining to Maturity14At 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 rd remains constant.15What’s “yield to maturity”?YTM is the rate of return earned on a bond held to maturity. Also called “promised yield.”It assumes the bond will not default.16YTM on a 10-year, 9% annual coupon, $1,000 par value bond selling for $887 9090 9001910rd=?1,000PV1 . . .PV10PVM887Find rd that “works”!...17 10 -887 90 1000 N I/YR PV PMT FV 10.91VINTMB=(1 + rd)1(1 + rd)N ... +INT88790(1 + rd)11,000(1 + rd)N= +90(1 + rd)N + + + +INPUTSOUTPUT ...Find rd(1 + rd)N18If coupon rate rd, bond sells at a premium.If rd rises, price falls.Price = par at maturity. 19Find YTM if price were $1,134.20.Sells at a premium. Because coupon = 9% > rd = 7.08%, bond’s value > par. 10 -1134.2 90 1000 N I/YR PV PMT FV 7.08INPUTSOUTPUT20DefinitionsCurrent yield =Capital gains yield = = YTM = +Annual coupon pmtCurrent priceChange in priceBeginning priceExp totalreturnExp Curr yldExp capgains yld219% coupon, 10-year bond, P = $887, and YTM = 10.91%Current yield = = 0.1015 = 10.15%. $90 $88722Cap gains yield = YTM - Current yield = 10.91% - 10.15% = 0.76%.Could also find values in Years 1 and 2,get difference, and divide by value inYear 1. Same answer.YTM = Current yield + Capital gains yield.23Semiannual Bonds1. Multiply years by 2 to get periods = 2N.2. Divide nominal rate by 2 to get periodic rate = rd/2.3. Divide annual INT by 2 to get PMT = INT/2. 2N rd/2 OK INT/2 OK N I/YR PV PMT FV INPUTSOUTPUT24 2(10) 13/2 100/2 20 6.5 50 1000 N I/YR PV PMT FV -834.72INPUTSOUTPUTValue of 10-year, 10% coupon, semiannual bond if rd = 13%.25Spreadsheet Functions for Bond Valuation See IFM10 Ch04 Mini Case.xls for details.PRICEYIELD26Callable Bonds and Yield to CallA 10-year, 10% semiannual coupon,$1,000 par value bond is selling for$1,135.90 with an 8% yield to maturity.It can be called after 5 years at $1,050.27 10 -1135.9 50 1050 N I/YR PV PMT FV 3.765 x 2 = 7.53% INPUTSOUTPUTNominal Yield to Call (YTC)28If you bought bonds, would you be more likely to earn YTM or YTC?Coupon rate = 10% vs. YTC = rd = 7.53%. Could raise money by selling new bonds which pay 7.53%.Could thus replace bonds which pay $100/year with bonds that pay only $75.30/year.Investors should expect a call, hence YTC = 7.5%, not YTM = 8%.29In general, if a bond sells at a premium, then coupon > rd, so a call is likely.So, expect to earn:YTC on premium bonds.YTM on par & discount bonds.30rd = r* + IP + DRP + LP + MRP.Here: 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.31What is the nominal risk-free rate?rRF = (1+r*)(1+IP)-1 = r*+ IP + (r*xIP) ≈ r*+ IP. (Because r*xIP is small)rRF = Rate on Treasury securities.32Estimating IPTreasury Inflation-Protected Securities (TIPS) are indexed to inflation.The 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.33Bond Spreads, the DRP, and the LPA “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%.34Bond Ratings Provide One Measure of Default RiskInvestment GradeJunk BondsMoody’sAaaAaABaaBaBCaaCS&PAAAAAABBBBBBCCCD35Bond Ratings and Bond Spreads (YahooFinance, March 2008)Long-term BondsYieldSpread U.S. Treasury4.40% AAA6.40%2.00% AA 6.24%1.84% A 6.27%1.87% BBB6.15%1.75% BB 7.00%2.60% B 8.00%3.60% CCC7.45%3.05%36What factors affect default risk and bond ratings? Financial performanceDebt ratioCoverage ratios, such as interest coverage ratio or EBITDA coverage ratioCurrent ratios(More)37Provisions in the bond contractSecured versus unsecured debtSenior versus subordinated debtGuarantee provisionsSinking fund provisionsDebt maturity(More)38Other factorsEarnings stabilityRegulatory environmentPotential product liabilityAccounting policies39Interest rate (or price) risk for 1-year and 10-year 10% bondsrd1-yearChange10-yearChange5%$1,048$1,38610%1,0004.8%1,00038.6%15%9564.4%74925.1%Interest rate risk: Rising rd causes bond’s price to fall.40Interest rate (or price) risk for 1-year and 10-year 10% bondsrd1-yearChange10-yearChange5%$1,048$1,38610%1,0004.8%1,00038.6%15%9564.4%74925.1%Interest rate risk: Rising rd causes bond’s price to fall.4105001,0001,5000%5%10%15%1-year10-yearrdValue42What is reinvestment rate risk?The risk that CFs will have to be reinvested in the future at lower rates, reducing income.Illustration: Suppose you just won $500,000 playing the lottery. You’ll invest the money and live off the interest. You buy a 1-year bond with a YTM of 10%.43Year 1 income = $50,000. At year-end get back $500,000 to reinvest.If rates fall to 3%, income will drop from $50,000 to $15,000. Had you bought 30-year bonds, income would have remained constant.44The Maturity Risk PremiumLong-term bonds: High interest rate risk, low reinvestment rate risk.Short-term bonds: Low interest rate risk, high reinvestment rate risk.Nothing is riskless!Yields on longer term bonds usually are greater than on shorter term bonds, so the MRP is more affected by interest rate risk than by reinvestment rate risk.45Term Structure Yield CurveTerm structure of interest rates: the relationship between interest rates (or yields) and maturities.A graph of the term structure is called the yield curve.46Hypothetical Treasury Yield Curve47Relationship Between Treasury Yields and Corporate YieldsCorporate yield curves are higher than that of the Treasury bond. However, corporate yield curves are not neces-sarily parallel to the Treasury curve.The spread between a corporate yield curve and the Treasury curve widens as the corporate bond rating decreases.48Hypothetical Treasury and Corporate Yield Curves49BankruptcyTwo main chapters of Federal Bankruptcy Act:Chapter 11, ReorganizationChapter 7, LiquidationTypically, company wants Chapter 11, creditors may prefer Chapter 7.50If company can’t meet its obligations, it files under Chapter 11. That stops creditors from foreclosing, taking assets, and shutting down the business.Company has 120 days to file a reorganization plan.Court appoints a “trustee” to supervise reorganization. Management usually stays in control.51Company must demonstrate in its reorganization plan that it is “worth more alive than dead.” Otherwise, judge will order liquidation under Chapter 7.52If the company is liquidated, here’s the payment priority:Past due property taxesSecured creditors from sales of secured assets.Trustee’s costsExpenses incurred after bankruptcy filingWages and unpaid benefit contributions, subject to limitsUnsecured customer deposits, subject to limitsTaxesUnfunded pension liabilitiesUnsecured creditorsPreferred stockCommon stock53In a liquidation, unsecured creditors generally get zero. This makes them more willing to participate in reorganization even though their claims are greatly scaled back.Various groups of creditors vote on the reorganization plan. If both the majority of the creditors and the judge approve, company “emerges” from bankruptcy with lower debts, reduced interest charges, and a chance for success.54