bma9e04 valuing bonds principles of corporate finance 9th edition 公司金融教学课件

,Chapter 4,PrinciplesofCorporateFinanceNinth Edition,Valuing Bonds,Slides byMatthew Will,Copyright 2008 by The McGraw-Hill Companies, Inc. All rights reserved,McGraw Hill/Irwin,Topics Covered,Using The Present Value Formula to Value BondsHow Bond Prices Vary With Interest RatesThe Term Structure and YTMExplaining the Term StructureReal and Nominal Rates of Interest,Valuing a Bond,Valuing a Bond,ExampleIf today is October 1, 2007, what is the value of the following bond? An IBM Bond pays $115 every September 30 for 5 years. In September 2012 it pays an additional $1000 and retires the bond. The bond is rated AAA (WSJ AAA YTM is 7.5%)Cash FlowsSept 08091011121151151151151115,Valuing a Bond,Example continuedIf today is October 1, 2007, what is the value of the following bond? An IBM Bond pays $115 every September 30 for 5 years. In September 2012 it pays an additional $1000 and retires the bond. The bond is rated AAA (WSJ AAA YTM is 7.5%),Valuing a Bond,Example - GermanyIn July 2006 you purchase 100 Euros of bonds in Germany which pay a 5% coupon every year. If the bond matures in 2012 and the YTM is 3.8%, what is the value of the bond?,Valuing a Bond,Another Example - JapanIn July 2006 you purchase 200 Yen of bonds in Japan which pay a 8% coupon every year. If the bond matures in 2011 and the YTM is 4.5%, what is the value of the bond?,Valuing a Bond,Example - USAIn July 2006 you purchase a 3 year US Government bond. The bond has an annual coupon rate of 4%, paid semi-annually. If investors demand a 2.48% return on 6 month investments, what is the price of the bond?,Valuing a Bond,Example continued - USATake the same 3 year US Government bond. The bond has an annual coupon rate of 4%, paid semi-annually. If investors demand a 1.50% return on 6 month investments, what is the new price of the bond?,Bond Prices and Yields,Interest Rates, %,Bond Price, %,Duration Calculation,Duration,YearCFPVYTM% of Total PV% x Year168.7565.54.0600.060268.75 62.48.0580.115368.75 59.56.0550.165468.75 56.78.0520.2095 68.75841.39.7753.8751085.741.00 Duration 4.424,Example (Bond 1)Calculate the duration of our 6 7/8 % bond 4.9 % YTM,Duration,YearCFPVYTM% of Total PV% x Year1 9082.95.0810.0812 9076.45.0750.1503 9070.46.0690.2074 9064.94.0640.2565 1090724.90.7113.5551019.701.00 Duration= 4.249,Example (Bond 2)Given a 5 year, 9.0%, $1000 bond, with a 8.5% YTM, what is this bonds duration?,Duration & Bond Prices,Interest rate, percent,Bond Price, percent,Maturity and Prices,Interest Rates, %,Bond Price, %,Term Structure,Spot Rate - The actual interest rate today (t=0)Forward Rate - The interest rate, fixed today, on a loan made in the future at a fixed time.Future Rate - The spot rate that is expected in the futureYield To Maturity (YTM) - The IRR on an interest bearing instrument,YTM (r),Year,1981,1987 & Normal,1976,1 5 10 20 30,Yield To Maturity,All interest bearing instruments are priced to fit the term structureThis is accomplished by modifying the asset priceThe modified price creates a New Yield, which fits the Term StructureThe new yield is called the Yield To Maturity (YTM),Yield Curve,Maturity,U.S. Treasury Strip Spot Rates as of June 2006,Yield to Maturity,ExampleA $1000 treasury bond expires in 5 years. It pays a coupon rate of 10.5%. If the market price of this bond is 107.88, what is the YTM?,Yield to Maturity,ExampleA $1000 treasury bond expires in 5 years. It pays a coupon rate of 10.5%. If the market price of this bond is 107.88, what is the YTM?,C0C1C2C3C4C5 -1078.801051051051051105Calculate IRR = 8.5%,Term Structure,What Determines the Shape of the TS?1 - Unbiased Expectations Theory2 - Liquidity Premium Theory3 - Market Segmentation HypothesisTerm Structure & Capital BudgetingCF should be discounted using Term Structure infoSince the spot rate incorporates all forward rates, then you should use the spot rate that equals the term of your project.If you believe in other theories take advantage of the arbitrage.,example 1000=1000 (1+R3)3(1+f1)(1+f2)(1+f3),Spot/Forward rates,Forward Rate Computations(1+ rn)n = (1+ r1)(1+f2)(1+f3).(1+fn),Spot/Forward rates,ExampleWhat is the 3rd year forward rate?2 year zero treasury YTM = 8.9953 year zero treasury YTM = 9.660,Spot/Forward rates,ExampleWhat is the 3rd year forward rate?2 year zero treasury YTM = 8.9953 year zero treasury YTM = 9.660Answer FV of principal YTM2 yr1000 x (1.08995)2 = 1187.993 yr1000 x (1.09660)3 = 1318.70IRR of (FV1318.70 & PV=1187.99) = 11%,Spot/Forward rates,ExampleTwo years from now, you intend to begin a project that will last for 5 years. What discount rate should be used when evaluating the project?2 year spot rate = 5%7 year spot rate = 7.05%,Spot/Forward rates,coupons paying bonds to derive rates,Spot/Forward rates,Bond Value = C1 + C2 (1+r)(1+r)2,Bond Value = C1 + C2 (1+R1)(1+f1)(1+f2),d1 = C1 d2 = C2 (1+R1)(1+f1)(1+f2),example 8% 2 yr bond YTM = 9.43%10% 2 yr bond YTM = 9.43%What is the forward rate?Step 1value bonds 8% = 975 10%= 1010Step 2 975 = 80d1 + 1080 d2 - solve for d11010 =100d1 + 1100d2 - insert d1 & solve for d2,Spot/Forward rates,example continuedStep 3 solve algebraic equationsd1 = 975-(1080)d2 / 80insert d1 & solve = d2 = .8350insert d2 and solve for d1 = d1 = .9150Step 4Insert d1 & d2 and Solve for f1 & f2. .9150 = 1/(1+f1) .8350 = 1 / (1.0929)(1+f2) f1 = 9.29% f2 = 9.58%PROOF,Spot/Forward rates,Debt & Interest Rates,Classical Theory of Interest Rates (Economics)developed by Irving FisherNominal Interest Rate = The rate you actually pay when you borrow money,Debt & Interest Rates,Classical Theory of Interest Rates (Economics)developed by Irving FisherNominal Interest Rate = The rate you actually pay when you borrow moneyReal Interest Rate = The theoretical rate you pay when you borrow money, as determined by supply and demand,Supply,Demand,$ Qty,r,Real r,Debt & Interest Rates,Nominal r = Real r + expected inflation (approximation)Real r is theoretically somewhat stableInflation is a large variableQ: Why do we care?A: This theory allows us to understand the Term Structure of Interest Rates.