CHAPTER 3 3-1 VALUING BONDS Brealey, Myers, and Allen Principles of Corporate Finance 12th Edition Slides by Matthew Will Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Valuing a Bond 3-2 The price of a bond is the present value of all cash flows generated by the bond (i.e. coupons and face value) discounted at the required rate of return cpn cpn (cpn par ) PV .... 1 2 (1 r ) (1 r ) (1 r ) t Note: “cpn” is commonly used as an abbreviation for “coupon” Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Valuing a Bond 3-3 Example - France In October 2014 you purchase 100 euros of bonds in France which pay a 4.25% coupon every year. If the bond matures in 2018 and the YTM is 0.15%, what is the value of the bond? 4.25 4.25 4.25 104.25 PV 2 3 1.0015 1.0015 1.0015 1.00154 116.34 euros Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Valuing a Bond as an Annuity 3-4 PV(bond) = PV(annuity of coupons) + PV(principal) PV (bond) (cpn PVAF) (final payment discount factor) 1 1 100 4.25 4 4 . 0015 . 0015 1 . 0015 1 . 0015 116.34 Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Valuing a Bond 3-5 Example (continued) What is the price of a 7.25 % annual coupon bond, with a $1,000 face value, which matures in 3 years? Assume a required return of 0.35%. Bond prices are quoted as a percentage of par. Par value × price % = $ price $1,000 × price % = $1,205.56 price % = 120.56 % Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Valuing a Bond 3-6 Example - USA In November 2014 you purchase a 3 year US Government bond. The bond has an annual coupon rate of 4.25%, paid semi-annually. If investors demand a 0.965% semiannual return, what is the price of the bond? PV 21.25 21.25 21.25 21.25 21.25 1021.25 1.004825 1.0048252 1.0048253 1.0048254 1.0048255 1.0048256 $1,096.90 Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Treasury Yields 3-7 The interest rate on 10-year U.S. Treasury bonds 1900-2012 16 14 12 Yield (%) 10 8 6 4 2012 2 1900 1903 1906 1909 1912 1915 1918 1921 1924 1927 1930 1933 1936 1939 1942 1945 1948 1951 1954 1957 1960 1963 1966 1969 1972 1975 1978 1981 1984 1987 1990 1993 1996 1999 2002 2005 2008 2011 0 Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Maturity and Prices 3-8 Different maturity bonds have different interest rate risk 2 500 30-year bond When the interest rate equals the 4.25% coupon, both bonds sell for the same value Bond price ($) 2 000 1 500 1 000 3-year bond 500 Interest rate (%) = YTM Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 10 9.5 9 8.5 8 7.5 7 6.5 6 5.5 5 4.5 4 3.5 3 2.5 2 1.5 1 0.5 0 0 Bond Rates of Return 3-9 Example A bond increases in price from $963.80 to $1,380.50 and pays a coupon of $21.875 during the same period. What is the rate of return? 21.875 (1380.50 963.80) Rate of return .455 963.80 ROR = 45.5% Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Duration Formula 3-10 1 PV (C1 ) 2 PV (C2 ) 3 PV (C3 ) T PV (CT ) Duration ... PV PV PV PV duration Modified duration volatility (%) 1 yield Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Duration Calculation 3-11 Year Ct PV(C t ) at 5.0% Proportion of Total Value [PV(C t )/V ] Proportion of Total Value Time 1 2 3 100 100 1100 95.24 90.7 950.22 0.084 0.08 0.836 0.084 0.16 2.509 V = 1136.16 1 Duration= 2.753 years Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Duration & Bond Prices Bond price, percent 3-12 Interest rate, percent Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Interest Rates 3-13 • Short- and long-term interest rates do not always move in parallel. Between September 1992 and April 2000, U.S. short-term rates rose sharply while long term rates declined. Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Term Structure of Interest Rates 3-14 YTM (r) 1981 1987 & Normal 1976 1 5 10 20 30 Year 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 Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Yield Curve 3-15 U.S. Treasury Strip Spot Rates as of November 2014 Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Yield to Maturity 3-16 Example $1,000 Treasury bond expires in 5 years. Pays coupon rate of 10.5%. What is YTM if market price is 107.88? C0 −1078.80 C1 C2 C3 C4 C5 105 105 105 105 1105 Calculate IRR = 8.5% Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Explaining the Term Structure 3-17 Expectations Theory o Term structure and capital budgeting CF should be discounted using term structure info When rate incorporates all forward rates, use spot rate that equals project term Take advantage of arbitrage Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Debt & Interest Rates 3-18 • Classical Theory of Interest Rates (Economics) o 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 r Supply Real r Demand $ Qty Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Annual U.S. Inflation Rates, 1900-2014 3-19 Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Global Inflation Rates, 1900-2014 3-20 Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Interest Rates & Inflation 3-21 • In the presence of inflation, an investor’s real interest rate is always less than the nominal interest rate 1 + nominal rate 1 + real rate = 1 + inflation rate Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Interest Rates & Inflation 3-22 Example If you invest in a security that pays 10% interest annually and inflation is 6%, what is your real interest rate? 1.10 1 + real rate = 1.06 Real interest rate = .03774 or 3.774% Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Govt. Bills vs. Inflation, 1953-2014 3-23 Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Default Risk 3-24 • Default or Credit Risk - The risk that a bond issuer may default on its bonds • Default premium - The additional yield on a bond that investors require for bearing credit risk • Investment grade - Bonds rated Baa or above by Moody’s or BBB or above by Standard & Poor’s • Junk bonds - Bond with a rating below Baa or BBB Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Default Risk 3-25 Moody' s Standard & Poor's Aaa AAA Aa AA A A Baa BBB Ba B BB B Caa Ca C CCC CC C Safety The strongest rating; ability to repay interest and principal is very strong. Very strong likelihood that interest and principal will be repaid Strong ability to repay, but some vulnerability to changes in circumstances Adequate capacity to repay; more vulnerability to changes in economic circumstances Considerable uncertainty about ability to repay. Likelihood of interest and principal payments over sustained periods is questionable. Bonds in the Caa/CCC and Ca/CC classes may already be in default or in danger of imminent default C-rated bonds offer little prospect for interest or principal on the debt ever to be repaid. Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Prices and Yields of Corporate Bonds 3-26 Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Yield Spread 3-27 Yield Spreads between Corporate and 10-year Treasury Bonds Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Sovereign Bonds and Default Risk 3-28 • Sovereign Bonds and Default Risk oForeign currency debt Default occurs when foreign government borrows dollars If crisis occurs, governments may run out of taxing capacity and default Affects bond prices, yield to maturity oOwn currency debt Less risky than foreign currency debt Governments can print money to repay bonds Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
