Chapter 06: Interest Rates and Bond Valuation Study Notes

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Chapter 06: Interest Rates and Bond Valuation

Key Concepts and Skills

After studying this chapter, students should be able to:
- Identify important bond features and types of bonds.
- Describe bond values and why they fluctuate.
- Discuss bond ratings and what they mean.
- Evaluate the impact of inflation on interest rates.
- Explain the term structure of interest rates and the determinants of bond yields.

Chapter Outline

Bonds and Bond Valuation
More on Bond Features
Bond Ratings
Some Different Types of Bonds
Bond Markets
Inflation and Interest Rates
Determinants of Bond Yields

Bond Definitions

Bond: A debt contract classified as an interest-only loan.
- Par Value (Face Value): Typically around $1,000.
- Coupon Rate: The interest rate paid by the bond issuer.
- Coupon Payment: The dollar amount of interest paid annually.
- Maturity Date: The date when the bond’s principal is repaid.
- Yield to Maturity (YTM): The total return anticipated on a bond if it is held until it matures.

Key Features of a Bond

Par Value:
- Face amount that is repaid at maturity (typically $1,000 for corporate bonds).
Coupon Interest Rate:
- The stated interest rate, usually equal to YTM at issuance; the coupon payment can be calculated by multiplying the coupon rate by the par value.
Maturity:
- The remaining years until the bond must be repaid.
Yield to Maturity (YTM):
- The required rate of return for bonds of similar risk and maturity.
- Functioning as the discount rate to determine present value, it signifies the total return expected if the bond is held until maturation and typically equals the coupon rate at the time of issue. It is quoted as an Annual Percentage Rate (APR).

Bond Value

Bond Value Formula: $\text{Bond Value} = PV(\text{coupons}) + PV(\text{par})$
- This can be expressed as:
  $\text{Bond Value} = PV(\text{annuity}) + PV(\text{lump sum})$

Important Reminders:

As interest rates (r) increase, present values decrease:
$r \uparrow \Rightarrow PV \downarrow$
Conversely, when interest rates decrease, bond prices increase.

Bond-Pricing Equation

Components:
- PV (Annuity): Value of future cash flows (coupons).
- PV (Lump Sum): Value of par value at maturity.
- Coupon Payment (C): Represents regular interest payments.
- Face Value (F): Amount received at maturity.

Texas Instruments Financial Calculators and Excel Formulas

Key variables used in calculations:
- N = Number of periods to maturity.
- I/Y = Interest rate per period = YTM.
- PV = Present value = Bond value.
- PMT = Coupon payment.
- FV = Future value = Face value = Par value.

Spreadsheet Formulas:

=FV(Rate, Nper, Pmt, PV, 0/1)
=PV(Rate, Nper, Pmt, FV, 0/1)
=RATE(Nper, Pmt, PV, FV, 0/1)
=NPER(Rate, Pmt, PV, FV, 0/1)
=PMT(Rate, Nper, PV, FV, 0/1)

Valuing Bonds: Examples

Discount Bond

Assumptions:
- Coupon Rate: 10%
- Par: $1,000
- Maturity: 5 years
- YTM: 11%
- Calculator Results: Bond value $ -963.04
- Using Formula:
- $B = PV(\text{annuity}) + PV(\text{lump sum})$
- $B = 369.59 + 593.45 = 963.04$

Notes:

When YTM > Coupon rate, the price is below par, designating it as a “Discount Bond.”

Premium Bond

Assumptions:
- Coupon Rate: 10%
- Par: $1,000
- Maturity: 20 years
- YTM: 8%
- Calculator Results: Bond value $ -1196.36
- Using Formula:
- $B = PV(\text{annuity}) + PV(\text{lump sum})$
- $B = 981.81 + 214.55 = 1196.36$

Notes:

When YTM < Coupon rate, the price is above par, designating it as a “Premium Bond.”

Price and Yield Relationships

Graphical Relationship Between Price and YTM:
- As the yield to maturity increases, bond prices decrease, reflecting an inverted relationship.
Effects of Coupon Rate:
- When the coupon rate equals the YTM, price = par.
- When the coupon rate is less than YTM, price < par (Discount).
- When the coupon rate is more than YTM, price > par (Premium).

Interest Rate Risks

Price Risk

Definition:
- The change in bond price due to fluctuations in interest rates. Long-term bonds exhibit more price risk than short-term bonds, while bonds with low coupon rates experience more risk than those with high coupon rates.

Reinvestment Rate Risk

Definition:
- The uncertainty regarding the rates at which cash flows can be reinvested. Short-term bonds have a greater reinvestment rate risk than long-term bonds, and high coupon bonds are more susceptible to this risk than low coupon bonds.

Yield-to-Maturity (YTM) Calculations

YTM with Annual Coupons

Example of a bond with a 10% annual coupon rate, 15 years to maturity, current price $928.09.
Analyzing the relationship shows the expectations on yields relative to coupon rates.

YTM with Semi-Annual Coupons

Analysis of bonds with semi-annual coupons demonstrates adjustments for yield-to-maturity calculations.
- Formula Adjustments:
  $N = 2t$
  $r = \frac{annual yield}{2}$

Bond Valuation Principles

Summary of Bond Valuation Formulates

Finding the Value of a Bond:

Bond value is calculated by the present value of future cash flows.
The relationship is reiterated with the inclusion of coupon payments and time to maturity to ensure proper valuation.

Yield on a Bond

For established yields, bonds are evaluated by determining their present value against future cash flows.

Current Yield and Capital Gains Yield

Current Yield (CY):
$\text{CY} = \frac{\text{Annual Coupon Payment}}{\text{Current Price}}$
Capital Gains Yield (CGY):
$\text{CGY} = \frac{\text{Change in Price}}{\text{Beginning Price}}$
Expected Total Return = YTM = Expected CY + Expected CGY.

Debt vs. Equity Differences

Debt Characteristics

No ownership interest nor voting rights.
Interest is tax-deductible.
Creditors can take legal action if interest or principal payments are missed.
Excessive debt can lead to financial distress.

Equity Characteristics

Ownership interest conferred to stockholders.
Dividends are not tax-deductible and are not mandatory until declared.
An all-equity firm cannot be subjected to bankruptcy.

Bond Indenture

Definition: A legal contract between the bond issuer and the bondholder, detailing terms such as:
- Total bonds issued.
- Secured versus unsecured bonds.
- Sinking fund and call provisions.

Yield to Call vs Yield to Maturity

Scenarios illustrated to help understand comparative measures.
Yield to Call (YTC) typically examined alongside YTM to understand profitability potential upon the bond’s early redemption.

Bond Classifications

Registered vs. Bearer Bonds: Differentiated by ownership and issuance.
Secured: Backed by collateral or mortgage.
Debentures: Unsecured bonds generally having lower ratings.

Bond Ratings

High Grade: Moody's Aaa/AAA denote very strong repayment ability.
Medium Grade: Indicates strong capacity to pay but with susceptibility to changes.
Speculative / Low Grade: Bonds rated Ba and below subject to increased risk of default.

Government Bonds Characteristics

Municipal Securities

Bonds issued by state and local governments, often tax-exempt at the federal level.

Treasury Securities

Bonds issued by the federal government, categorized into Bills, Notes, and Bonds based on maturity lengths.

Inflation and Interest Rates

Real Rate of Interest: Change in purchasing power.
Nominal Rate of Interest: Quoted rate, including expected inflation adjustments.

The Fisher Effect

Equation:
$R = r + h$
Where:
- R: Nominal interest rate.
- r: Real interest rate.
- h: Expected inflation rate.

Risk-Free Rate and Premiums

Spelled out differences between treasury yields and corporate bonds, illustrating required return formations based on risk premiums.

Factors Affecting Required Return

Default risk, taxability, liquidity, and maturity premiums all contribute to determining the necessary returns required by bondholders.

Conclusion

Quick Quiz Recap

Through interactive Q&A, students can revise key concepts:
- Determination of bond value.
- Features of bond indentures.
- Understanding bond ratings and their relevance.
- Inflation's impacts on interest rates.
- Structure of interest rates and factors governing required returns.