1. Valuing Debt FINA 7330 Corporate Finance Lecture 13

2. Topics Covered Real and Nominal Rates of Interest Term Structure and Yield to Maturity The Term Structure and Bond Pricing Theories of the Term Structure

3. Irving Fisher and the Theory of Interest Rates The Real Interest Rate is determined by the real economic activity and demographics of the Economy (The Demand and Supply for Capital) The Nominal Interest Rate is the real rate adjusted for inflation 1 + R = (1 + r) * (1 + E[inf.])

4. U.K. Rates

5. Inflation and Interest Rates Note the Real Rate tends to be rather stable but the Nominal Rate is more volatile. What makes it more volatile? The Expected inflation rate! Does the theory fit the facts? We can’t measure Expected inflation, but assume actual inflation follows expected inflation closely then:

6. The Return on US Treasury Bills and the Inflation rate (1953-2003)

7. Normal Yield Curve

8. Current Yield Curve

9. Treasury Yields Maturity Yield 12/13/2006 5.17 12/13/2007 5.03 12/12/2008 4.76 12/12/2009 4.66 12/12/2011 4.60 12/11/2013 4.60 12/10/2016 4.61 12/8/2026 4.80 12/5/2036 4.71

10. How to Determine Yield Curve WSJ U.S. Treasury Strips Maturity Type Yield Nov 06 ci 4.51 Nov 06 np 4.72 Feb 07 bp 4.96 May 07 np 4.95 Aug 07 np 4.92 ……………………………………. May 16 bp 4.66 Aug 16 bp 4.61 Nov 16 bp 4.69

11. The Term Structure and Bond Prices Consider Two Year Treasury (3.125s October 08) Price is 97:03 = 97.09 4/07 10/07 4/08 10/08 1.5625 1.5625 1.5625 101.5625 YTM:

12. The Term Structure and Bond Prices Consider Two Year Treasury (3.125s October 08) Price is 97:03 4/07 10/07 4/08 10/08 1.5625 1.5625 1.5625 101.5625 YTM: 4.66

13. But consider the term structure Two Year Treasury (3.125s October 08) Price is 97:03 4/07 10/07 4/08 10/08 1.5625 1.5625 1.5625 101.5625 Strip Yields 4.94 4.87 4.50 4.64 PV 1.5248 1.4899 1.4616 92.7551 Value = 97.23

14. Bond Prices and Yields Yield Price

15. Duration Calculation

16. Risk and Duration The relationship between Risk and Duration Volatility = Duration/(1 + YTM) So in example, D = 3.714, YTM = 2.75% Volatility = 3.615% % Change Value at 3.25% 1083.14 -1.78 Value at 2.25% 1123.04 1.83 Volatiltiy 3.61%

17. 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 1068.75841.39.7753.875 1085.741.00 Duration 4.424 Example (Bond 1) Calculate the duration of our 6 7/8 % bond @ 4.9 % YTM

18. Example r n is the “Spot Rate” = the annualized yield on a discount bond making 1 payment n years in the future f n is the “Forward Rate” = the implied yield on a one year discount bond issued n-1 years in the future. Spot/Forward rates

19. Spot and Forward Rates In general: (1+ r n ) = (1 + r 1 )(1 + f 2 )(1 + f 3 )…)(1 + f n )

20. Example What is the 3rd year forward rate? 2 year zero treasury YTM = 4.63 3 year zero treasury YTM = 4.57 Spot/Forward rates

21. Example What is the 3rd year forward rate? 2 year zero treasury YTM = 4.63 3 year zero treasury YTM = 4.57 Answer (1+r 3 ) 3 = (1+r 2 ) 2 (1+f 3 ) (1+r 3 ) 3 /(1+r 2 ) 2 = (1 + f 3 ) 1.1435/1.0947 = 1.0445 f 3 = 4.45% Spot/Forward rates

22. Matrix Pricing