4Key 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…)
5Key Features of a BondMaturity: Years until bond must be repaid. Declines over time.Issue date: Date when bond was issued.Default risk: Risk that issuer will not make interest or principal payments.
6Three Main TypesConsolsZero-coupon bondsFixed-coupon bonds
7The value of financial assets 12Nr%CF1CFNCF2Value...
8FI 3300 - Corporate Finance Leng Ling ConsolsPays a fixed coupon every period forever.Has no maturity.Price =
9Zero-coupon bond (ZCB) 1 FI Corporate Finance Leng LingZero-coupon bond (ZCB) 1Zero coupon rate, no coupon paid during bond’s life.Bond holder receives one payment at maturity, the face value (say, $1000).F = face value of the bondN = number of years to maturitycost of ZCB debt capital (in decimals)
10Zero-coupon bond (ZCB) 2 As long as interest rates are positive, the price of a ZCB must be less than its face value.Why? With positive interest rates, the present value of the face value (i.e., the price) has to be less than the face value.
11FI 3300 - Corporate Finance Leng Ling ZCB Problems1) Find the price of a ZCB with 20 years to maturity, par value of $1000 and a required rate of return of 15% p.a.N=20, I/Y=15, FV=1000, PMT=0. Price = $61.102) XYZ Corp.’s ZCB has a market price of $ 354. The bond has 16 years to maturity and its face value is $1000. What is the cost of debt for the ZCB (i.e., the required rate of return).PV=-354, FV=1000, N=16, PMT=0.Required rate of return/ Cost of debt =6.71%
12Fixed-coupon bond (FCB) 1 Firm pays a fixed amount (‘coupon’) to the investor every period until bond matures.At maturity, firm pays face value of the bond to investor.Face value is also called par value. Unless otherwise stated, always assume face value to be $1000.Period: can be year, half-year (6 months), quarter (3 months).
13Fixed-coupon bond (FCB) 2 FCB gives you a stream of fixed payments plus a single payment (face value) at maturity.This cash flow stream is just an annuity plus a single cash flow at maturity.Therefore, we calculate the price of a FCB by finding the PV of the annuity and the single payment.
14Fixed-coupon bond (FCB) 3 Price of the FCB, PFCBFixed periodic couponNumber of periods to maturityFace valueCost of debt capital
15Value 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.
16The 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
17What would happen if r = 13%? N I/YR PV PMT FVINPUTSOUTPUTIf coupon rate < rd, then price < par, sells at a discount.
18What would happen if r = 7%? N I/YR PV PMT FV-1,210.71INPUTSOUTPUTIf coupon rate > rd, then price > par, sells at a premium.
19Coupon rate vs. rd, and price If coupon rate < rd, bond sells at a discount.If coupon rate = rd, bond sells at its par value.If coupon rate > rd, bond sells at a premium.If rd rises, price falls.Price = par at maturity.
20FI 3300 - Corporate Finance Leng Ling Example 1A 10-year annual coupon bond was issued four years ago at par. Since then the bond’s yield to maturity (YTM) has decreased from 9% to 7%. Which of the following statements is true about the current market price of the bond?The bond is selling at a discountThe bond is selling at parThe bond is selling at a premiumThe bond is selling at book valueInsufficient information
21FI 3300 - Corporate Finance Leng Ling Example 2One year ago Pell Inc. sold 20-year, $1,000 par value, annual coupon bonds at a price of $ per bond. At that time the market rate (i.e., yield to maturity) was 9 percent. Today the market rate is 9.5 percent; therefore the bonds are currently selling:at a discount.at a premium.at par.above the market price.not enough information.
22Bond Values over Time (1) Suppose a 10% fixed coupon 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%?See next slide.
23Bond Value over Time (2) rd = 7%. rd = 10%. M rd = 13%. 1,372 1,211 1,000837rd = 13%.775
24Bond Value over Time (3)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 rd remains constant.
25What’s “yield to maturity”? YTM is the rate of return earned on a bond held to maturity. It assumes the bond will not default.
26Definitions Annual coupon pmt Current price Current yield = Capital gains yield == YTM =Change in priceBeginning priceExp totalreturnExpCurr yldExp capgains yld
279% coupon, 10-year bond, P = $887, and YTM = 10.9117% Current yield == = %.$90$887
28YTM = Current yield + Capital gains yield. Cap gains yield = YTM - Current yield= % %= %.Could also find p1, and then (p1-p0)/p0, same answer. How to find p1?
29Semiannual 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
30Value of 10-year, 10% coupon, semiannual bond if rd = 13%. 2(10) 13/ /2N I/YR PV PMT FVINPUTSOUTPUT
31FI 3300 - Corporate Finance Leng Ling Find YTM, Coupon rate1)A $1,000 par value bond sells for $ It matures in 20 years, has a 10 percent coupon rate, and pays interest semi-annually. What is the bond’s yield to maturity on a per annum basis (to 2 decimal places)?Verify that YTM = 11.80%2) ABC Inc. just issued a twenty-year semi-annual coupon bond at a price of $ The face value of the bond is $1,000, and the market interest rate is 9%. What is the annual coupon rate (in percent, to 2 decimal places)?Verify that annual coupon rate = 6.69%
32FI 3300 - Corporate Finance Leng Ling Long FCB questionHMV Inc. needs to raise funds for an expansion project. The company can choose to issue either zero-coupon bonds or semi-annual coupon bonds. In either case the bonds would have the SAME nominal required rate of return, a 20-year maturity and a par value of $1,000. If the company issues the zero-coupon bonds, they would sell for $ If it issues the semi-annual coupon bonds, they would sell for $ What annual coupon rate is HMV Inc. planning to offer on the coupon bonds? State your answer in percentage terms, rounded to 2 decimal places.Verify that annual coupon rate = 7.01%
33Callable 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. How much is the yield to call?
34Nominal Yield to Call (YTC) N I/YR PV PMT FV3.765 x 2 = 7.53%INPUTSOUTPUT
35Interest rate (or price) risk for 1-year and 10-year 10% bonds Interest rate risk: Rising rd causes bond’s price to fall.rd10-year1-yearChangeChange5%$1,048$1,38638.6%4.8%10%1,0001,00025.1%4.4%15%956749
36Interest rate risk and time to maturity The 10-year bond is more sensitive to interest rate changes because of longer time to maturity, and hence has higher interest rate risk.
37Term 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.
38Yield Curve Interest Rate (%) BB-Rated Maturity 15 10 5 Years to 1 5 15101520
39IP, DRP, LP, Bond Spreads Inflation Premium (IP) Default Risk Premium (DRP)Liquidity Premium (LP)Bond’s of large companies often have very small LPs. Bond’s of small companies often have LPs as high as 2%.Bond Spread: the difference between a corporate bond’s yield and a Treasury security’s yield of the same maturity.
41Bond Ratings and Bond Spreads (YahooFinance, March 2009) Long-term BondsYield (%)Spread (%)10-Year T-bond2.68AAA5.502.82AA5.622.94A5.793.11BBB7.534.85BB11.628.94B13.7011.02CCC26.3023.62
42Bankruptcy 1 Two main chapters of Federal Bankruptcy Act: Chapter 11, ReorganizationChapter 7, LiquidationTypically, the management wants Chapter 11, creditors may prefer Chapter 7.
43Bankruptcy 2If a 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.
44Bankruptcy 3Company must demonstrate in its reorganization plan that it is “worth more alive than dead.”Otherwise, judge will order liquidation under Chapter 7.
45If 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