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

4- 2 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

4- 3 Valuing a Bond

4- 4 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

4- 5 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%)

4- 6 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?

4- 7 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?

4- 8 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?

4- 9 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?

4- 10 Bond Prices and Yields Interest Rates, % Bond Price, %

4- 11 Duration Calculation

4- 12 Duration of Total PV% x Year Duration Example (Bond 1) Calculate the duration of our 6 7/8 % 4.9 % YTM

4- 13 Duration of Total PV% x Year Duration= Example (Bond 2) Given a 5 year, 9.0%, $1000 bond, with a 8.5% YTM, what is this bond’s duration?

4- 14 Duration & Bond Prices Interest rate, percent Bond Price, percent

4- 15 Maturity and Prices Interest Rates, % Bond Price, %

4- 16 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 & Normal

4- 17 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)

4- 18 Yield Curve Maturity U.S. Treasury Strip Spot Rates as of June 2006

4- 19 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 , what is the YTM?

4- 20 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 , what is the YTM? C0C1C2C3C4C Calculate IRR = 8.5%

4- 21 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.

4- 22 example 1000=1000 (1+R 3 ) 3 (1+f 1 )(1+f 2 )(1+f 3 ) Spot/Forward rates

4- 23 Forward Rate Computations (1+ r n ) n = (1+ r 1 )(1+f 2 )(1+f 3 )....(1+f n ) Spot/Forward rates

4- 24 Example What is the 3rd year forward rate? 2 year zero treasury YTM = year zero treasury YTM = Spot/Forward rates

4- 25 Example What is the 3rd year forward rate? 2 year zero treasury YTM = year zero treasury YTM = Answer FV of YTM 2 yr1000 x ( ) 2 = yr1000 x ( ) 3 = IRR of (FV & PV= ) = 11% Spot/Forward rates

4- 26 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

4- 27 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 )

4- 28 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% = %= 1010 Step = 80d d > solve for d =100d d > insert d1 & solve for d2 Spot/Forward rates

4- 29 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 = 1/(1+f 1 ).8350 = 1 / (1.0929)(1+f 2 ) f 1 = 9.29% f 2 = 9.58% PROOF Spot/Forward rates

4- 30 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

4- 31 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

4- 32 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.

4- 33 Debt & Interest Rates Actual formula

4- 34 Inflation Annual Inflation, % Annual U.S. Inflation Rates from

4- 35 Global Inflation Rates Averages from

4- 36 UK Bond Yields 10 year nominal interest rate 10 year real interest rate

4- 37 T-Bills vs. Inflation (’53-’06) % United States

4- 38 T-Bills vs. Inflation (’53-’06) % Japan

4- 39 T-Bills vs. Inflation (’53-’06) % Germany

4- 40 Web Resources Click to access web sites Internet connection required