Chapter 7: Interest Rates and Bond Valuation

Bond Features and Valuation

• Debt Securities: Corporations or governments issue bonds to borrow money from the public on a long-term basis, generally as interest-only loans.

  • Example: Beck Corporation borrows $1,000 for 30 years at an interest rate of 12%.
  • Coupon Payment: $120 annually ($1,000 * 0.12).
  • Maturity: The specified date when the principal amount ($1,000) is repaid.

• Term Definitions:

  • Coupon: The interest payment made on a bond.
  • Face Value (Par Value): The principal amount of the bond that is repaid at the end of the term.
  • Coupon Rate: Annual coupon divided by face value (i.e. $120/$1,000 = 12%).

Bond Values and Yields

• Bond Valuation: The value of a bond fluctuates with market interest rates.

  • When rates rise, bond values fall; when rates fall, bond values rise.

• Bond Valuation Calculation: To determine a bond's value, you need:

  • Time until maturity
  • Face value
  • Coupon payments
  • Yield to maturity (YTM)

• Example of Bond Valuation:

  • Xanth Co. issues a bond with:
  • 10 years to maturity
  • An annual coupon of $80
  • Market YTM of 8%
  • Cash flows:
  • Annual coupon: $80 for 10 years, plus $1,000 at maturity.
  • Present value calculations:
  • Present Value of $1,000: PV = \frac{1000}{(1 + 0.08)^{10}} = \frac{1000}{2.1589} = 463.19
  • Present Value of annuity:
  • PV_{annuity} = C \times \left(\frac{1 - (1 + r)^{-t}}{r}\right) = 80 \times 6.7101 = 536.81
  • Total bond value = $463.19 + $536.81 = $1,000 (par value bond).

Interest Rate Risk

• Interest Rate Risk: Refers to risks related to fluctuating interest rates, and depends on:

  • Time to maturity
  • Coupon rate
  • Longer time = higher risk
  • Lower coupon = higher risk

• Example: The effect of interest rate changes on bond value demonstrates substantial sensitivity in longer-term bonds compared to shorter-term ones.

Finding Yield to Maturity

• Yield Calculations: Current yield differs from yield to maturity
  • Current yield = Annual coupon / Price
  • Example: For a bond price of $955.14 and $80 coupon, current yield = \frac{80}{955.14} = 0.0838 \text{ or } 8.38\%

Bond Ratings and Types of Bonds

• Bond Ratings: Offered by agencies like Moody’s and S&P to assess creditworthiness.
  • Scale from AAA (highest quality, lowest risk) to below investment grade for junk bonds.
• Types of Bonds:
  • Municipal bonds: Tax-exempt, used by state/local governments.
  • Zero coupon bonds: No periodic coupon payments, sold at deep discounts, providing only face value at maturity.

Conclusion

• Understanding Bonds: Essential concepts include bond valuation, yield calculations, interest rate sensitivity, types of bonds, and their respective risks. Each plays a critical role in investment decision-making.

• Cash Flows: Cash flows, indentures, protective covenants, junk bonds' characteristics, bid-ask prices, nominal versus real returns, and the term structure of interest rates are foundational to comprehending bond investments.

Key Terms

• Nominal vs. Real Rates:
  • Nominal not adjusted for inflation; Real adjusted for inflation
• Term Structure: Relationship between interest rates and time to maturity
• Yield Curve: Graph of yields on Treasury securities relative to their maturities
• Accrued Interest: Interest accumulated on a bond since the last coupon payment, affecting the clean vs. dirty price.