Ch06 Bond valuation

Chapter Overview

• Chapter 6 focuses on Interest Rates and Bond Valuation.

• Key concepts include interest rate fundamentals, bond financing, corporate bonds, valuation models, and yield to maturity (YTM).

Learning Goals

• LG1: Describe interest rate fundamentals and risk premiums.

• LG2: Review legal aspects of bond financing and costs.

• LG3: Discuss features and types of corporate bonds.

• LG4: Understand key inputs and models in bond valuation.

• LG5: Apply basic valuation to bonds, exploring required return and time to maturity impacts.

• LG6: Explain yield to maturity (YTM) and semiannual bond valuation procedures.

Interest Rates & Required Returns

Definition

• Interest Rate: Represents the cost of borrowing money; applies mainly to debt instruments (e.g., loans, bonds).

• Required Return: The cost of funds acquired through equity ownership.

Influencing Factors

• Inflation: Affects the general price level, influencing interest rates.

• Risk: Higher perceived risks lead to higher expected returns from investors.

• Liquidity Preference: Preference for short-term securities affects interest rates.

Real Rate of Interest

• Represents equilibrium between supply of savings and demand for investments in a frictionless market.

• Changes with economic conditions and preferences.

• Conditioned by lack of inflation, liquidity preference, and risk.

Nominal or Actual Rate of Interest

Definition

• Nominal Rate: Actual interest charged and paid; differs from the real rate due to inflation and risk premiums.

Composition

• Expressed as:

  • r1 = RF + RP1

  • Risk-Free Rate (RF): Reflects the real rate plus an inflation premium (IP).

  • Higher expectations of inflation lead to a larger IP and higher nominal rates.

Valuation Fundamentals

• Valuation links risk and return to determine an asset's worth.

• Three key inputs in valuation:

  • Cash Flows: Expected returns.

  • Timing: When cash flows occur.

  • Risk: Determines required returns to match risk levels.

Corporate Bonds

Definition

• Long-term debt instruments paying periodic interest to bondholders.

Key Features

• Coupon Rate: Percentage of par value paid annually, often semiannually.

• Principal/Face Value: Amount borrowed and to be repaid on maturity.

• Maturity Date: Date the bond principal must be repaid.

Bond Valuation Process

Basic Formula

• Valuation:P = C + i(1+i)^-t

  • P = price of bond

  • C = yearly coupon payment

  • F = face value

  • i = interest rate

  • t = time to maturity

Example Calculation

• A bond with a £1,000 face value and 8% coupon rate over 30 years when YTM = 10%.

• Coupon payment = £80.

• Value calculation gives a total of £811.46.

Risk Premiums

Types of Risks

• Default Risk Premium: Risk of issuer not fulfilling payment obligations.

• Interest Rate Risk: Changing interest rates that impact bond value.

• Longer maturity bonds are more sensitive to interest rate changes compared to shorter maturity bonds.

Semiannual Compounding

Adjustment Methods

1. Divide YTM by 2.

2. Multiply time by 2.

3. Divide coupon payment by 2.

Bond Valuation Behavior

• Bond market values are often not equal to par value.

• Changes in required returns due to economic conditions or firm risk impact bond values.