Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Chapter 4 Bond Valuation © 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 1 Key Features of a Bond Par 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. Maturity: 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. © 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 2 Call Provision Issuer can refund if rates decline. That helps the issuer but hurts the investor. Therefore, borrowers are willing to pay more, and lenders require higher returns, on callable bonds. © 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 3 Value of a 10-year, 10% coupon bond if rd = 10% 0 1 2 10% V=? VB = 10 ... 100 $100 100 $100 100 + 1,000 $1,000 . . . + + + 1 N (1 + rd) (1 + rd) (1 + rd)N = $90.91 + = $1,000. . . . + $38.55 + $385.54 © 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 4 The bond consists of a 10-year, 10% annuity of $100/year plus a $1,000 lump sum at t = 10: PV annuity PV maturity value Value of bond INPUTS OUTPUT 10 N 10 I/YR = $ 614.46 = 385.54 = $1,000.00 PV -1,000 100 PMT 1000 FV © 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 5 What would happen if expected inflation rose by 3%, causing r = 13%? INPUTS OUTPUT 10 N 13 I/YR PV -837.21 100 PMT 1000 FV When rd rises, above the coupon rate, the bond’s value falls below par, so it sells at a discount. © 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 6 What would happen if inflation fell, and rd declined to 7%? INPUTS OUTPUT 10 N 7 I/YR PV -1,210.71 100 PMT 1000 FV If coupon rate > rd, price rises above par, and bond sells at a premium. © 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 7 Bond Value ($) vs. Years remaining to Maturity Suppose 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%? See next slide. © 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 8 Bond Value ($) vs. Years remaining to Maturity 1,372 1,211 rd = 7%. rd = 10%. 1,000 M 837 rd = 13%. 775 30 25 20 15 10 5 © 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 0 9 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. © 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 10 What’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. © 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 11 YTM on a 10-year, 9% annual coupon, $1,000 par value bond selling for $887 0 rd=? 1 10 ... 90 PV1 . . . PV10 PVM 9 90 90 1,000 887 © 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 12 Find rd VB = INT INT M ... + + + N 1 (1 + rd) (1 + rd) (1 + rd)N 1,000 90 90 ... 887 = + + + 1 N (1 + rd) (1 + rd) (1 + rd)N INPUTS OUTPUT 10 N I/YR 10.91 -887 PV 90 PMT 1000 FV © 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 13 Coupon Rate vs. Yield to Maturity 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. © 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 14 Find YTM if price were $1,134.20. INPUTS 10 N OUTPUT I/YR 7.08 -1134.2 90 PV PMT 1000 FV Sells at a premium. Because coupon = 9% > rd = 7.08% bond’s value > par. © 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 15 Definitions Current yield = Annual coupon pmt Current price Capital gains yield = Exp total return Change in price Beginning price Exp Exp cap = YTM = + Curr yld gains yld © 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 16 9% coupon, 10-year bond, P = $887, and YTM = 10.91% Current yield $90 = $887 = 0.1015 = 10.15%. © 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 17 YTM = Current yield + Capital gains yield. Cap gains yield = YTM - Current yield = 10.91% - 10.15% = 0.76%. Could also find values (prices) in Years 1 and 2, get difference, and divide by value in Year 1. Same answer. © 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 18 Semiannual 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. INPUTS 2N N rd/2 I/YR OK PV INT/2 PMT OK FV OUTPUT © 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 19 Value of 10-year, 10% coupon, semiannual bond if rd = 13%. 2(10) INPUTS 20 N OUTPUT 13/2 6.5 I/YR PV -834.72 100/2 50 PMT 1000 FV © 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 20 Callable Bonds and Yield to Call A 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. © 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 21 Nominal Yield to Call (YTC)=? INPUTS 10 N OUTPUT -1135.9 50 I/YR PV PMT 3.765 x 2 = 7.53% 1050 FV © 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 22 If 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%. © 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 23 rd = r* + IP + DRP + LP + MRP. Here: rd r* IP DRP LP MRP = Required rate of return on a debt security. = = = = = Real risk-free rate. Inflation premium. Default risk premium. Liquidity premium. Maturity risk premium. © 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 24 Estimating IP Treasury 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. © 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 25 Bond 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%. © 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 26 Bond Ratings S&P and Fitch Moody’s % defaulting within: 1 yr. 5 yrs. Investment grade bonds: AAA Aaa 0.00 0.00 AA Aa 0.03 0.19 A A 0.08 0.76 BBB Baa 0.20 2.45 BB Ba 1.05 6.91 B B 2.02 10.52 CCC Caa 24.88 36.84 Junk bonds: © 2016Fitch Cengage Ratings Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as Source: permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 27 Bond Ratings and Bond Spreads (December 2013) Long-term Bonds 10-Year T-bond AAA AA A BBB BB B CCC Yield (%) 2.87 3.65 3.65 3.87 4.81 5.87 6.26 7.40 Spread (%) 0.78 0.78 1.00 1.94 3.00 3.39 4.53 © 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 28 Interest rate (or price) risk for 1-year and 10-year 10% bonds Interest rate risk: Rising rd causes bond prices to fall 1-Year rd Price Change 5.0% $1,048 4.8% 10.0% $1,000 4.5% 15.0% $957 10-Year Price Change $1,386 38.6% $1,000 33.5% $749 © 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 29 What 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%. © 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 30 What is reinvestment rate risk? Year 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. © 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 31 The 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. © 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 32 Term 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. © 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 33 Hypothetical Treasury Yield Curve 14% Interest Rate 12% 10% MRP IP r* 8% 6% 4% 2% 19 17 15 13 11 9 7 5 3 1 0% Years to Maturity © 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 34 Bankruptcy Two main chapters of Federal Bankruptcy Act: Chapter 11, Reorganization Chapter 7, Liquidation Typically, company (stock holders) wants Chapter 11, creditors may prefer Chapter 7. © 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 35 Bankruptcy 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. © 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 36 Assignment Review slides of chapter 7 from FINC3131 Chapter 4 problems: 1,2,3,4,5,6,7,8,9,10,11,12,13,16 © 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 37