CHAPTER 7 Interest Rates

Bond Features and Prices

  • Bonds are debt securities issued by corporations or governments for long-term borrowing.

  • Key Components of Bonds:

    • Coupon: Stated interest payment made on the bond (e.g., $120 annually for 30 years).

    • Face Value (Par Value): Principal amount repaid at the end (e.g., $1,000).

    • Coupon Rate: Annual coupon divided by face value ($120 ÷ $1,000 = 12%).

    • Maturity: Date principal is repaid (e.g., 30 years).

Bond Values and Yields

  • Bond value fluctuates due to changes in market interest rates.

    • Interest Rate Relationships:

    • When rates rise, bond value decreases (the present value of cash flows declines).

    • When rates fall, bond value increases (the present value of cash flows rises).

  • Information to Value a Bond:

    • Number of periods until maturity, face value, annual coupon, yield to maturity (YTM).

Example: Bond Values and Yields

  • If Xanth Co. issues a bond with a 10-year maturity and a coupon of $80, the following calculations apply:

    1. Calculate present value of cash flows from the bond.

    2. Cash flows include coupon payments and face value at maturity.

  • Present Value Calculation:
    PV = \frac{1,000}{(1+0.08)^{10}} = \frac{1,000}{2.1589} \approx 463.19

  • Total Value = Present Value of Coupons + Present Value of Face Value.

Cash Flows for Bonds

  • Bonds have two types of cash flows: coupon payments (annuity) and face value (lump sum).

Discount Bonds

  • If interest rates increase, the value of a bond with a lower coupon becomes a discount bond.

    • Bond value example with increased rates at 10%:
      Total\,Value = PV{coupons} + PV{face}\ = 460.70 + 424.10 = 884.80

Premium Bonds

  • If interest rates drop, bonds may sell for more than face value (premium bonds):

    • Example:
      PV = \frac{1,000}{(1+0.06)^{10}} = \frac{1,000}{1.4859} \approx 671.38

  • Premium Example:

    • Total\,Value = 591.90 + 544.14 = 1,136.03

General Expression for Bond Value

  • For a bond with face value $F, coupon $C, maturity $t, and yield $r:
    Bond\,Value = \sum_{i=1}^{t} \frac{C}{(1+r)^i} + \frac{F}{(1+r)^t}

Current Yield and Yield to Maturity

  • Current Yield: Ratio of annual coupon to current price.

    • Example calculation:

    • Current Yield = \frac{Annual\,Coupon}{Current\,Price}

  • Yield to Maturity: Total expected return if the bond is held until maturity.

Interest Rate Risk

  • Defined as potential change in a bond's value due to fluctuations in interest rates.

  • **Key factors:

    • Time to maturity: longer maturities increase risk.

    • Coupon rate: lower coupon rates increase risk.**

Finding the Yield to Maturity

  • Calculation involves trial and error until bond's calculated value matches the market price.

Bond Ratings

  • Firms may have their debt rated to reflect creditworthiness, high ratings indicate low default risk.

    • Ratings range from AAA/Aaa (highest) to D (in default).

Bonds Types

  • Different Bonds:

    • Corporate Bonds: Safe, secured or unsecured debt notes.

    • Municipal Bonds: Tax-exempt bonds issued by local governments.

    • Treasury Bonds: Government bonds with no default risk.

Zero Coupon Bonds

  • Bonds sold at discount, no interim cash flows, only face value at maturity.

Sukuk and Islamic Bonds

  • Islamic finance compliant bonds structured to avoid interest payments.

Summary: Bond Valuation and Yields

  1. Finding the value requires coupon, yield, time to maturity, and face value.

  2. Yield determined via trial and error, increasing discount rates will decrease bond value.

Conclusion

  • Bond yields reflect real rates and various premiums for factors like inflation, interest rate risk, default risk, and liquidity.