BUS283 Lecture 2 Interest Rates

Module Overview

  • Course: BUS283 Financial Markets and Securities

  • Lecture: Lecture 2 - Interest Rates

  • Module Leader: Dr. Zhe Li

    • Position: Associate Professor (Senior Lecturer)

    • Co-programme director for BSc Accounting and Finance

    • Affiliation: School of Business and Management

Learning Objectives

  • Understand key concepts related to interest rates, including:

    • Time value of money

    • Measuring interest rates

    • Difference between real and nominal interest rates

    • Interest rates vs. returns

  • At the end of Lecture 2, students should be able to:

    • Calculate present and future values for debt securities.

    • Calculate real interest rates using nominal rates and expected inflation.

    • Differentiate between interest rates and returns, specifically current yield and capital gains.

Time Value of Money

  • Concept: People prefer to receive payments today rather than in the future.

    • Example: $1.00 received today is worth more than the same amount received in one year.

  • Rationale: The present value of money accounts for potential investment returns (e.g., earning interest).

  • Utility Variability: Individual satisfaction from consumption varies, influencing the time value perception.

Role of Interest Rates

  • Market Context: Interest rates reflect the demand for and supply of funding in the economy.

  • Variability: Many interest rates exist based on factors like borrowing period, borrower risk, and currency type.

  • Significance: Interest rates inform the future value of money and the current worth of assets.

Defining Interest Rates

  • Definition: According to Mishkin and Eakins (2018), interest rates are the cost of borrowing funds, typically expressed as an annual percentage.

  • Economic Indicator: Interest rates are critical indicators in economic analysis and influence financial markets and security valuations.

Practical Relevance of Interest Rates

  • Interest rates impact various stakeholders:

    • Business Owners: Decisions on borrowing money, affected by prevailing interest rates.

    • Investors: Considerations on whether to invest in stocks or bonds based on current rates.

    • Households: Decisions about refinancing mortgages based on interest rate trends.

Present Value Analysis

  • Key aspects of present value analysis include:

    • Evaluating cash flows based on their timing and amounts to deduce yield to maturity.

    • Understanding present value (PV) as the current worth of future cash flows.

Formulas for Present and Future Value

  • Present Value (PV):

    • Formula: PV = ( \frac{FV}{(1 + i)^n} )

    • Variables:

      • PV = Present Value

      • FV = Future Value

      • i = Interest Rate

      • n = Number of Years until Maturity

  • Future Value (FV):

    • Formula: FV = PV × (1 + i)^n

Types of Credit Instruments

  1. Simple Loan

    • Basics: One-time cash flow at maturity.

  2. Fixed Payment Loan

    • Basics: Set yearly cash flow payments.

  3. Coupon Bond

    • Basics: Fixed periodic coupon payments.

  4. Discount or Zero-Coupon Bond

    • Basics: One-time payment at maturity.

Yield to Maturity (YTM)

  • Concept: YTM is the interest rate that equates the price of a debt security with the present value of its future cash flows.

  • Relationship: There’s a negative correlation between bond price and interest rate; as rates go up, bond prices go down.

Current Yield (CY)

  • Definition: CY provides a simplified estimate of YTM and is calculated as:

    • Formula: CY = ( \frac{C}{P} )

    • Where C = Fixed coupon payment, P = Price of the bond.

Real vs. Nominal Interest Rates

  • Real Interest Rate: Adjusted for expected inflation.

    • Formula: ( r_i = i - e )

    • Variables:

      • ( r_i ) = Real Interest Rate

      • i = Nominal Interest Rate

      • e = Expected Inflation Rate

  • Implications: Lower real rates incentivize borrowing while higher rates deter lending.

Interest Rates vs. Returns

  • Breakdown of returns into:

    • Current yield

    • Capital gains

  • Formula for Rate of Return:

    • Rate of Return = ( \frac{C + P_{t+1} - P_t}{P_t} )

    • Where C = fixed coupon payment, Pt = Price of bond today, P(t+1) = Price of bond in one year.

Key Findings from Analysis

  • Price volatility of bonds is more pronounced for those with longer maturities due to interest rate risk.

  • Bonds with maturity equal to the holding period do not involve interest rate risk.

  • Long term bonds offer higher volatility in returns when interest rates change.

Conclusion of Lecture 2

  • Covered foundational concepts related to interest rates:

    • Present value analysis, yield to maturity, and interest rate risk.

    • Differences between real and nominal interest rates, and interest rates versus returns, illustrated through numerical examples.

Core Readings and Resources

  • Main Text: Chapter 3 (excluding Duration) in Mishkin, F.S. & Eakins, S.G. (2018). Financial Markets and Institutions (9th edition).

  • Online resources:

    • Financial Times Markets Data

    • Fred St. Louis Fed Data

    • Video on Time Value of Money