Chapter 6: Bonds and Interest Rates

Debt vs. Equity

Debt (Bonds)

• Characteristics:

  • No ownership interest (no voting rights)

  • Interest is tax-deductible

  • Legal recourse for creditors in case of missed payments

  • Excess debt can lead to financial distress or bankruptcy

  • Can be held to maturity, liquidity often fragmented

  • Price discovery is less transparent

Equity (Stocks)

• Characteristics:

  • Ownership interest with voting rights

  • Dividends are not tax-deductible and become liabilities only when declared

  • No risk of bankruptcy if an all-equity firm

  • Liquidity - found on centralized exchanges

  • Transparent price discovery

Bond Features and Jargon

Definitions and Terms

• Bond: A security that allows corporations or governments to borrow funds from the public.

  • Example: AT&T issues 30-year bonds at 8% interest to finance 5G technology, with annual coupon payments and par value of $1,000.

• Par Value (Face Value): The principal amount paid at maturity, typically $1,000 for corporate bonds.

• Coupon Rate: The stated interest rate of the bond, reflecting its risk characteristics, constant at issuance, typically equal to yield to maturity initially.

• Coupon Payment: Annual or semi-annual payments to bondholders (e.g., $80 in the AT&T example).

• Maturity: The time until the bond's principal is repaid, varying from several months to decades.

• Yield to Maturity (YTM): The market required rate of return for a bond, can differ from the coupon rate.

Bond Valuation

• Cash Flows: Bond value is calculated based on the present value (PV) of future cash flows: coupon payments and par value at maturity.

• Bond Value Formula:
  $\text{Bond Value} = PV( \text{annuity payments} ) + PV( \text{lump sum} )$

• The value of a bond decreases with rising interest rates since present values drop.

Bond Pricing Equation

${Bond Value}=\frac{C}{(1+YTM)}+\frac{C}{(1+YTM)^2}+\ldots+\frac{F}{(1+YTM)^t}$

• Variables:

  • C = Coupon payment

  • F = Face value

  • YTM = Yield to maturity (rate)

  • t = Number of periods to maturity

Risk Factors in Bonds

Interest Rate Risk

• Price Risk: Correlation between bond price and interest rates; longer-term bonds face more price risk.

• Reinvestment Rate Risk: Uncertainty surrounding reinvestment rates of cash flows; higher for short-term bonds and high coupon-rate bonds.

Yield-to-Maturity (YTM) Calculation

• YTM represents the market's required rate of return based on current bond price.

• Example Calculation:

  • Given a bond with annual 10% coupon, 15-year maturity, and price of $928.09, the yield would be greater than 10% if current price < par value.

Bond Market Characteristics

• Bond Markets: Various markets characterized by issuer type, liquidity, price discovery through over-the-counter transactions.

• Government Bonds: Including treasury securities and municipal securities, offer unique benefits such as tax exemptions.

Bond Ratings

• Rating Scale:

  • High Grade (e.g., Moody’s Aaa) indicates strong capacity to pay.

  • Medium Grade indicates adequate capacity but susceptibility to adverse conditions.

  • Low Grade (e.g., Moody’s C) is speculative concerning payments.

  • D indicates bonds in default.

Factors Affecting Required Returns

• Premiums:

  • Default Risk Premium: Compensation for potential default by the issuer.

  • Taxability Premium: Adjustment due to the tax treatment of the bond.

  • Liquidity Premium: Compensation for bonds that are harder to sell.

  • Maturity Premium: Extra yield for longer-term securities due to uncertainty.
    These premiums affect the required returns on bonds by compensating investors for various risks.

Summary Calculation Techniques

• Bond Value Formula:
  $\text{Bond Value}=C\times\left[\frac{1-\frac{1}{(1+r)^{t}}^{}}{r}\right]+\frac{F}{(1+r)^t}$
  where C = coupon paid, r = rate per period, t = number of periods, and F = face value.

• Finding YTM:

  • Iterative process adjusting the discount rate until the calculated bond value equals market value.