Presentation on theme: "Bonds, Bond Valuation, and Interest Rates"— Presentation transcript:
1Bonds, Bond Valuation, and Interest Rates Chapter 5Bonds, Bond Valuation, and Interest Rates
2Topics in Chapter Key features of bonds Bond valuation Measuring yield Assessing risk
3Determinants of Intrinsic Value: The Cost of Debt Net operatingprofit after taxesRequired investmentsin operating capital−Free cash flow(FCF)=FCF1FCF2FCF∞...Value =(1 + WACC)1(1 + WACC)2(1 + WACC)∞For value box in Ch 4 time value FM13.Weighted averagecost of capital(WACC)Market interest ratesFirm’s debt/equity mixCost of debtCost of equityMarket risk aversionFirm’s business risk
4Interest Rates & Interest-Bearing Securities Based on supply & demand for moneyDriven by risk factorsRole of Federal ReserveBasis Point.01% or
5Risk & Term Structure of Interest Rates rd = r* + IP + DRP + LP + MRPrd = 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.
6Risk & 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 rate typically 1-4% depending on monetary policy assumes expected inflation = zeroIP = Inflation premium Ave. inflation over life of bondDRP = Default risk premium Compensation for possible default Function of bond ratings
7Risk & Term Structure r = r* + IP + DRP + LP + MRP LP = Liquidity Premium Compensation for possible difficulty selling bond quickly at fair market valueMRP = Maturity Risk Premium Compensation for possible loss in value due to increase in interest rates over maturity of bond. Affects longer maturities more than shorter.
8Premiums Added to r* (real risk-free rate) for Different Types of Debt ST Treasury:only IP for ST inflationLT Treasury:IP for LT inflation, MRPST corporate:ST IP, DRP, LPLT corporate:IP, DRP, MRP, LP
10Relationship b/w Nominal & Real Interest Rates, & Inflation Nom = Real + InflationBut, inflation not additive, it grows or compounds, so multiplyNom = (Real) x (Infl)And (1+Nom) = (1 + real) x (1 + infl)Is better determinant; known as Fisher effect
11Estimating 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.
12Bond 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%.
13Term 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.
15What factors can explain shape of this yield curve? Upward slope due to:Increasing expected inflationIncreasing maturity risk premiumWhat about liquidity & default risk?
16Treasury 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
17Computing YieldsEstimate 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.
18Assume 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 = [ (8)]/10 = 7.5%.IP20 = [ (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).
19Step 2: Find MRP based on this equation: Assume the MRP is zero for Year 1 and increases by 0.1% each year.Step 2: Find MRP based on this equation: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%.
21Upward vs. Downward sloping yield curves due to? Real risk-free rate = 3%Expected inflation forYear 1 =7%, Yr 2 = 5%; Yr 3 = 3%What are interest rates for 1, 2, & 3 yr borrowings?
22Interest 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?
23Interest 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?
24Coupon Bonds Bond = Debt = Borrowing Fixed Maturity (Maturity Date) = NPar Value=Face Value=Maturity Value=$1000=FVCoupon Rate=Stated Rate (locked in in bond contract)Coupon payment= Coupon rate x face value=PMTMarket 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!!!
25Bond Perspectives Debt Asset Needs $ Borrower Issuer or seller DebtholderCost of borrowingInterest Paid (Expense) – generates tax benefit (Svgs)Cost of Debt= Rd or Kd;After-tax cost = Rd (1-t)Has $LenderBuyer or InvestorBondholderCreditorRequires return to invest $ in bonds based on riskInterest Received (earned) (Revenue) - pay tax on itCapital Appreciation
26Key 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…)
27Key Features of a BondMaturity: 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.
28Value 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 factorsDiscount (interest rate) depends on:Riskiness of CFs reflected by DRP, MRP, LPGeneral level of interest rates, which reflects inflation, supply & demand for $, production opportunities, time preferences for consumption
29Value of a 10-year, 10% coupon bond if rd = 10% 121010%...V = ?100100,000$100$100$1,000V=+...++B(1 + rd)1(1 + rd)N(1 + rd)N= $ $ $385.54= $1,000.
30The bond consists of a 10-year, 10% annuity of $100/year plus a $1,000 lump sum at t = 10: N I/YR PV PMT FV-1,000$385.54$1,000.00PV annuityPV maturity valueValue of bond=INPUTSOUTPUT
31What would happen if expected inflation rose by 3%, causing r = 13%? N I/YR PV PMT FVINPUTSOUTPUTWhen market interest rate (rd)rises above coupon rate, bond’s value (PV or price) falls below par, so discount.
32What happens if one year passes but the market i stays at 13%? N I/YR PV PMT FVINPUTSOUTPUT
33What happens if a second year passes but the market i stays at 13%? N I/YR PV PMT FVINPUTSOUTPUT
34What happens if 9 years pass but the market i stays at 13%? N I/YR PV PMT FVINPUTSOUTPUTAs a bond approaches maturity, it’s price approaches the face or maturity value of $1000
36What would happen if inflation fell, and rd declined to 7%? N I/YR PV PMT FV-1,210.71INPUTSOUTPUTIf coupon rate > mrkt i% (rd), price rises above par, and bond sells at a premium.
37Bond Pricing in Excel PV = ? $1210.71 Years to Mat: 10 Coupon rate: 10%Annual Pmt:$100Par value = FV:$1,000Going rate, rd:7%
38Summary of Bond price and interest rate relationships If market rate of interest increases above the stated (coupon) rate, then bond’s price falls and sells at discountIf market rate of interest drops below the stated (coupon) rate, then bond’s price increases and sells at a premium**INVERSE RELATIONSHIP b/w Market i% and Bond’s PRICE!***
39Bond prices & changing interest rates Suppose the bond was issued 20 years ago and now has 10 years to maturity. What would happen to its value over time if required rate of return remained at 10%, or at 13%, or at 7%?
40Bond Value ($) vs Years remaining to Maturity 1,372rd = 7%.1,211rd = 10%.M1,000837rd = 13%.775
41Bond 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.
42What’s market value of 10 year 10% coupon bond when market = 7%? N I/YR PV PMT FV?INPUTSOUTPUTBond sells at a premium::Price today = $1,
43If you buy a 10%, 10 year bond today for $1,210 If you buy a 10%, 10 year bond today for $1,210.71, and hold it to maturity, what’s your rate of return?( )N I/YR PV PMT FV?INPUTSOUTPUTSolve for i% = 7% = Yield to maturity (YTM)
44What’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 lifeInterest 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
45Find i % (rd) that “works”! ... YTM on a 10-year, 9% annual coupon, $1,000 par value bond selling for $887901910rd=?1,000PV1.PV10PVM887Find i % (rd) that “works”!...
46Find YTM (i % or rd) ... ... INT INT M V = + + B(1 + rd)1(1 + rd)N(1 + rd)N901,000...90887=+++(1 + rd)1(1 + rd)N(1 + rd)NINPUTSN I/YR PV PMT FV10.91OUTPUT
47YTM in Excel Years to Mat: 10 Coupon rate: 9% Annual Pmt: $90.00 Current price:$887.00Par value = FV:$1,000.00
48Bond Prices & Int. RatesIf 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.
49Find YTM if price were $1,N I/YR PV PMT FV7.08INPUTSOUTPUTSells at a premium. Because coupon = 9% > mrkt i% = 7.08%, bond’s value > par.
50Definitions Current yield = “Interest Yield” Capital gains yield =Change in value= YTM =Exp totalreturnExp capgains yldExpCurr yld
51Definitions Annual coupon pmt Current price Current yield = Capital gains yield == YTM =Change in priceBeginning priceExp totalreturnExpCurr yldExp capgains yld
529% coupon, 10-year bond, P = $887, and YTM = 10.91% Current yield == = 10.15%.$90$887
53YTM = Current yield + Capital gains yield. Cap gains yield = YTM - Current yield= 10.91% %= 0.76%.Could also find values in Years 1 and 2,get difference, and divide by value inYear 1. Same answer.
54Semiannual Bonds 1. 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/ OK INT/2 OKN I/YR PV PMT FVINPUTSOUTPUT
55Value of 10-year, 10% coupon, semiannual bond if rd = 13%. 2(10) 13/ /2N I/YR PV PMT FVINPUTSOUTPUT
56Spreadsheet Functions for Bond Valuation PRICEYIELD
57Call 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 premiumYield to call: yearly rate of return earned on a bond until it’s called
58Callable Bonds and Yield to Call A 10-year, 10% semiannual coupon, $1,000 par value bond is selling for $1, with an 8% yield to maturity. It can be called after 5 years at $1,050.
59Nominal Yield to Call (YTC) N I/YR PV PMT FV3.765 x 2 = 7.53%INPUTSOUTPUT
60If 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 = 7.53%, not YTM = 8%.
61Investor returns on callable bonds In general, if a bond sells at a premium, then coupon > market rate, so a call is likely.So, investors expect to earn:YTC on premium bonds.YTM on par & discount bonds.
62What’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.
63Sinking funds are generally handled in 2 ways Call 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.
72What is reinvestment rate risk? The risk that CFs will have to be reinvested at future lower rates, reducing income.Illustration: Suppose you just won $500,000 playing the lottery. You’ll invest the money and live off interest. You buy a 1-year bond with a YTM of 10%.
73Year 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.
74The Maturity Risk Premium Long-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.
75Other types of Bonds Zero coupon: Convertible: Income: Pays no coupon & disct below parConvertible:To bondholder’s optionIncome:Pays interest only if interest earned by issuer; won’t bankrupt co.
76Other types of Bonds Revenue: Floating rate: Interest paid from revenue generated by project being financed by bondsFloating rate:Adjusts coupon rate periodically based on market interest rates
77Bankruptcy Two main chapters of Federal Bankruptcy Act: Chapter 11, ReorganizationChapter 7, LiquidationTypically, company wants Chapter 11, creditors may prefer Chapter 7.
78Company has 120 days to file a reorganization plan. If 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.
79Company must demonstrate in its reorganization plan that it is “worth more alive than dead.” Otherwise, judge will order liquidation under Chapter 7.
80If 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 stock
81In a liquidation, unsecured creditors generally get zero In 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.