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Valuing Bonds

3. Valuing Bonds. 3-1 Using the present value formula to value bonds. 3-1 Using the present value formula to value bonds. Example

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Valuing Bonds

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  1. 3 Valuing Bonds

  2. 3-1 Using the present value formula to value bonds

  3. 3-1 Using the present value formula to value bonds • Example • Today is October 1, 2010; what is the value of the following bond? An IBM bond pays $115 every September 30 for five years. In September 2015 it pays an additional $1,000 and retires the bond. The bond is rated AAA (WSJ AAA YTM is 7.5%).

  4. 3-1 Using the present value formula to value bonds • Example: France • In October 2011 you purchase 100 euros of bonds in France which pay a 5% coupon every year. If the bond matures in 2016 and the YTM is 3.0%, what is the value of the bond?

  5. 3-1 Using the present value formula to value bonds • Another Example: Japan • In July 2010 you purchase 200 yen of bonds in Japan which pay an 8% coupon every year. If the bond matures in 2015 and the YTM is 4.5%, what is the value of the bond?

  6. 3-1 Using the present value formula to value bonds • Example: USA • In February 2012 you purchase a three-year U.S. government bond. The bond has an annual coupon rate of 11.25%, paid semiannually. If investors demand a 0.085% semiannual return, what is the price of the bond?

  7. 3-2 how bond prices vary with interest rates • Example, Continued: USA • Take the same three-year U.S. government bond. If investors demand a 4.0% semiannual return, what is the new price of the bond?

  8. Figure 3.1 Interest rate on 10-year treasuries Yield, % Year

  9. 3-2 how bond prices vary with interest rates Bond price Interest rate, %

  10. Figure 3.2 Maturity and Prices Bond price When interest rate = 11.25% coupon, both bonds sell for face value Interest rate, %

  11. 3-2 how bond prices vary with interest rates

  12. 3-2 Duration calculation

  13. 3-3term structure of Interest Rates • Short- and long-term rates are not always parallel • September 1992–April 2000: U.S. short-term rates rose sharply while long-term rates declined

  14. 3-3Term structure of interest rates YTM (r) • Spot Rate: Actual interest rate today (t = 0) • Yield To Maturity (YTM): IRR on interest-bearing instrument 1981 1987 & Normal 1976 1 5 10 20 30 Year

  15. Figure 3.4 spot rates on u.s. treasury strips, 02/2012

  16. 3-3 Law of One Price • All interest-bearing instruments priced to fit term structure • Accomplished by modifying asset price • Modified price creates new yield, which fits term structure • New yield called yield to maturity (YTM)

  17. 3-3 Yield to Maturity • Example • $1,000 Treasury bond expires in 5 years. Pays coupon rate of 10.5%. What is YTM if market price is 107.88? Calculate IRR = 8.5%

  18. 3-4 Term Structure • Expectations Theory • 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

  19. 3-5 Debt and Interest Rates • Classical Theory of Interest Rates (Economics) • Developed by Irving Fisher: • Nominal Interest Rate = Actual rate paid when borrowing money • Real Interest Rate = Theoretical rate paid when borrowing money; determined by supply and demand r Supply Real r Demand $ Qty

  20. Figure 3.5 annual u.s. Inflation Rates, 1900-2011

  21. Figure 3.6 Global Inflation Rates, 1900-2011

  22. 3-5 Debt and Interest Rates • Nominal r = Real r + expected inflation (approximation) • Real r theoretically somewhat stable • Inflation is a large variable • Term structure of interest rates shows cost of debt

  23. 3-5 Debt and Interest Rates • Debt and Interest Formula:

  24. Figure 3.7 UK Bond Yields 10-year nominal interest rate Interest rate, % 10-year real interest rate

  25. Figure 3.8 Govt. Bills vs. Inflation, 1953-2011

  26. Figure 3.8 Govt. Bills vs. Inflation, 1953-2011

  27. Figure 3.8 Govt. Bills vs. Inflation, 1953-2011

  28. 3-6 The risk of default • Corporate Bonds and Default Risk • Payments promised to bondholders represent best-case scenario • Most bonds’ safety judged by bond ratings

  29. Table 3.6 Prices and yields of corporate bonds, 01/2011

  30. Table 3.7 Bond ratings

  31. 3-6 the risk of default • Sovereign Bonds and Default Risk • Sovereign debt is generally less risky than corporate debt • Inflationary policies can reduce real value of debts

  32. 3-6 The risk of default • Sovereign Bonds and Default Risk • Foreign 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

  33. 3-6 The risk of default • Sovereign Bonds and Default Risk • Own Currency Debt • Less risky than foreign currency debt • Governments can print money to repay bonds

  34. 3-6 The risk of default • Sovereign Bonds and Default Risk • Eurozone Debt • Can’t print money to service domestic debts • Money supply controlled by European Central Bank

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