1. Bond Valuation Economics 71a: Spring 2007 Mayo Chapter 13 Lecture notes 4.4

2. Goals  Easy valuation Present values Yield Yield to maturity  Difficult issues Interest rates Defaults Call options

3. Present Values and Bonds  Bond example: Par = 1000 Coupon = 5% = $50 (per year) Required return, k = 7% Maturity = 3 years

4. Bond Example Present Value

5. Bond Pricing  Bonds trade at a given price  May be above or below your valuation  Strategy Buy if price < present value Sell if price > present value

6. Yield  Interest/Price  Example Par = 1000 Coupon = 5% Current price = 900 Yield = 50/900 = 5.56%

7. Yield to Maturity  Required return to get get PV = Price  Similar to internal rate of return  Requires computer

8. Yield to Maturity

9. Semiannual Interest Pays every 6 months  Par = 1000  Coupon = 5%, pays (1/2)50 = 25 every 6 months  Maturity = 3 years  k = 8% (k per 6 months = 4%)

10. Semi-annual Bond

11. Goals  Easy valuation Present values Yield Yield to maturity  Difficult issues Interest rates Defaults Call

12. Interest Rates  k = RF + RP  RF = risk free rate  RF rises Bond price falls  RF falls Bond price rises  Sensitivity to interest changes = “Duration”

13. Bond Prices and Duration  Two bonds: 1 and 5 year zero coupon  RP = 0 (government bond)  Interest rate change 3% to 5%  1 year bond Price = 970.87 -> 952.38  5 year bond Price = 862.61 -> 783.53  Longer maturity leads to more interest sensitivity

14. The Term Structure  Different rates for different horizons 6 month 1 year 2 years 5 years 10 years 30 years

15. Yield Curve 1 2 5 10 20 Years into future Time of maturity Interest Rate Annual % 5%

16. The Yield Curve  The yield curve changes over time  See “The living yield curve” website  Inverted yield curves  The yield curve and GDP

17. Bond Example Present Value

18. Defaults  When bond defaults, investors get firm assets (likely zero)  Probability related to bond rating  Risk premium increases with probability of default  k = RF + RP Higher default probability Higher RP Lower price

19. Call Option  Definition Option that lets firm buy back bond Get paid par + some percentage Shuts down bond investment  Similar to refinancing  Depends on interest movements  Impacts price, but difficult to value

20. Final Thoughts on Bonds  Stable income streams  Easier to evaluate than stocks More structure Fewer hunches  Easier for sophisticated professionals to have an edge  Stocks are more guesswork