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Chapter 4 Principles PrinciplesofCorporateFinance Ninth Edition Valuing Bonds Slides by Matthew Will Copyright © 2008 by The McGraw-Hill Companies, Inc.

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Presentation on theme: "Chapter 4 Principles PrinciplesofCorporateFinance Ninth Edition Valuing Bonds Slides by Matthew Will Copyright © 2008 by The McGraw-Hill Companies, Inc."— Presentation transcript:

1 Chapter 4 Principles PrinciplesofCorporateFinance Ninth Edition Valuing Bonds Slides by Matthew Will Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved McGraw Hill/Irwin

2 Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved 4- 2 McGraw Hill/Irwin Topics Covered  Using The Present Value Formula to Value Bonds  How Bond Prices Vary With Interest Rates  The Term Structure and YTM  Explaining the Term Structure  Real and Nominal Rates of Interest

3 Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved 4- 3 McGraw Hill/Irwin Valuing a Bond

4 Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved 4- 4 McGraw Hill/Irwin Valuing a Bond Example  If 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 Flows Sept 0809101112 1151151151151115

5 Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved 4- 5 McGraw Hill/Irwin Valuing a Bond Example continued  If 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%)

6 Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved 4- 6 McGraw Hill/Irwin Valuing a Bond Example - Germany  In 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?

7 Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved 4- 7 McGraw Hill/Irwin Valuing a Bond Another Example - Japan  In 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?

8 Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved 4- 8 McGraw Hill/Irwin Valuing a Bond Example - USA  In 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?

9 Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved 4- 9 McGraw Hill/Irwin Valuing a Bond Example continued - USA  Take 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?

10 Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved 4- 10 McGraw Hill/Irwin Bond Prices and Yields Interest Rates, % Bond Price, %

11 Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved 4- 11 McGraw Hill/Irwin Duration Calculation

12 Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved 4- 12 McGraw Hill/Irwin Duration YearCFPV@YTM% of Total PV% x Year 168.7565.54.0600.060 268.75 62.48.0580.115 368.75 59.56.0550.165 468.75 56.78.0520.209 5 68.75841.39.7753.875 1085.741.00 Duration 4.424 Example (Bond 1) Calculate the duration of our 6 7/8 % bond @ 4.9 % YTM

13 Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved 4- 13 McGraw Hill/Irwin Duration YearCFPV@YTM% of Total PV% x Year 1 9082.95.0810.081 2 9076.45.0750.150 3 9070.46.0690.207 4 9064.94.0640.256 5 1090724.90.7113.555 1019.701.00 Duration= 4.249 Example (Bond 2) Given a 5 year, 9.0%, $1000 bond, with a 8.5% YTM, what is this bond’s duration?

14 Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved 4- 14 McGraw Hill/Irwin Duration & Bond Prices Interest rate, percent Bond Price, percent

15 Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved 4- 15 McGraw Hill/Irwin Maturity and Prices Interest Rates, % Bond Price, %

16 Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved 4- 16 McGraw Hill/Irwin 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 future Yield To Maturity (YTM) - The IRR on an interest bearing instrument YTM (r) Year 1981 1987 & Normal 1976 1 5 10 20 30

17 Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved 4- 17 McGraw Hill/Irwin Yield To Maturity  All interest bearing instruments are priced to fit the term structure  This is accomplished by modifying the asset price  The modified price creates a New Yield, which fits the Term Structure  The new yield is called the Yield To Maturity (YTM)

18 Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved 4- 18 McGraw Hill/Irwin Yield Curve Maturity U.S. Treasury Strip Spot Rates as of June 2006

19 Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved 4- 19 McGraw Hill/Irwin Yield to Maturity Example  A $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?

20 Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved 4- 20 McGraw Hill/Irwin Yield to Maturity Example  A $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 -1078.801051051051051105 Calculate IRR = 8.5%

21 Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved 4- 21 McGraw Hill/Irwin Term Structure What Determines the Shape of the TS? 1 - Unbiased Expectations Theory 2 - Liquidity Premium Theory 3 - Market Segmentation Hypothesis Term Structure & Capital Budgeting  CF should be discounted using Term Structure info  Since 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.

22 Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved 4- 22 McGraw Hill/Irwin example 1000=1000 (1+R 3 ) 3 (1+f 1 )(1+f 2 )(1+f 3 ) Spot/Forward rates

23 Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved 4- 23 McGraw Hill/Irwin Forward Rate Computations (1+ r n ) n = (1+ r 1 )(1+f 2 )(1+f 3 )....(1+f n ) Spot/Forward rates

24 Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved 4- 24 McGraw Hill/Irwin Example What is the 3rd year forward rate? 2 year zero treasury YTM = 8.995 3 year zero treasury YTM = 9.660 Spot/Forward rates

25 Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved 4- 25 McGraw Hill/Irwin Example What is the 3rd year forward rate? 2 year zero treasury YTM = 8.995 3 year zero treasury YTM = 9.660 Answer FV of principal @ YTM 2 yr1000 x (1.08995) 2 = 1187.99 3 yr1000 x (1.09660) 3 = 1318.70 IRR of (FV1318.70 & PV=1187.99) = 11% Spot/Forward rates

26 Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved 4- 26 McGraw Hill/Irwin Example Two 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

27 Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved 4- 27 McGraw Hill/Irwin coupons paying bonds to derive rates Spot/Forward rates Bond Value = C 1 + C 2 (1+r)(1+r) 2 Bond Value = C 1 + C 2 (1+R 1 )(1+f 1 )(1+f 2 ) d1 = C 1 d2 = C 2 (1+R 1 )(1+f 1 )(1+f 2 )

28 Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved 4- 28 McGraw Hill/Irwin example 8% 2 yr bond YTM = 9.43% 10% 2 yr bond YTM = 9.43% What is the forward rate? Step 1 value bonds 8% = 975 10%= 1010 Step 2 975 = 80d1 + 1080 d2 -------> solve for d1 1010 =100d1 + 1100d2 -------> insert d1 & solve for d2 Spot/Forward rates

29 Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved 4- 29 McGraw Hill/Irwin example continued Step 3 solve algebraic equations d1 = [975-(1080)d2] / 80 insert d1 & solve = d2 =.8350 insert d2 and solve for d1 = d1 =.9150 Step 4 Insert d1 & d2 and Solve for f 1 & f 2..9150 = 1/(1+f 1 ).8350 = 1 / (1.0929)(1+f 2 ) f 1 = 9.29% f 2 = 9.58% PROOF Spot/Forward rates

30 Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved 4- 30 McGraw Hill/Irwin Debt & Interest Rates Classical Theory of Interest Rates (Economics)  developed by Irving Fisher Nominal Interest Rate = The rate you actually pay when you borrow money

31 Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved 4- 31 McGraw Hill/Irwin Debt & Interest Rates Classical Theory of Interest Rates (Economics)  developed by Irving Fisher Nominal Interest Rate = The rate you actually pay when you borrow money Real Interest Rate = The theoretical rate you pay when you borrow money, as determined by supply and demand Supply Demand $ Qty r Real r

32 Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved 4- 32 McGraw Hill/Irwin Debt & Interest Rates Nominal r = Real r + expected inflation (approximation) Real r is theoretically somewhat stable Inflation is a large variable Q: Why do we care? A: This theory allows us to understand the Term Structure of Interest Rates. Q: So What? A: The Term Structure tells us the cost of debt.

33 Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved 4- 33 McGraw Hill/Irwin Debt & Interest Rates Actual formula

34 Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved 4- 34 McGraw Hill/Irwin Inflation Annual Inflation, % Annual U.S. Inflation Rates from 1900 - 2006

35 Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved 4- 35 McGraw Hill/Irwin Global Inflation Rates Averages from 1900-2006

36 Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved 4- 36 McGraw Hill/Irwin UK Bond Yields 10 year nominal interest rate 10 year real interest rate

37 Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved 4- 37 McGraw Hill/Irwin T-Bills vs. Inflation (’53-’06) % United States

38 Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved 4- 38 McGraw Hill/Irwin T-Bills vs. Inflation (’53-’06) % Japan

39 Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved 4- 39 McGraw Hill/Irwin T-Bills vs. Inflation (’53-’06) % Germany

40 Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved 4- 40 McGraw Hill/Irwin Web Resources www.finpipe.com www.investinginbonds.com www.investorguide.com http://finance.yahoo.com http://money.cnn.com/markets/bondcenter www.federalreserve.gov www.stls.frb.org www.ustreas.gov Click to access web sites Internet connection required

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