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Bond Valuation

Bond Valuation. Economics 71a: Spring 2007 Mayo Chapter 13 Lecture notes 4.4. Goals. Easy valuation Present values Yield Yield to maturity Difficult issues Interest rates Defaults Call options. Present Values and Bonds. Bond example: Par = 1000 Coupon = 5% = $50 (per year)

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Bond Valuation

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  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 ExamplePresent 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 InterestPays 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 Interest Rate Annual % 5% 1 2 5 10 20 Years into future Time of maturity

  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 ExamplePresent 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

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