Time value of money

Learning Unit 3: Understanding Interest Rate Theories and Time Value of Money

Introduction

Learning Unit 3 focuses on important concepts concerning interest rates and the time value of money. The time value of money is a foundational principle in finance indicating that a certain amount of money today has different purchasing power compared to the same amount in the future due to its potential earning capacity.

Objectives of Unit 3

After completing this unit, you should be able to:

  • Define the time value of money and its implications.

  • Establish the relationship between present value (PV) and future value (FV).

  • Understand how interest is calculated.

  • Use the concept of interest rates to adjust cash flows to a specific point in time.

  • Calculate both FV and PV for various scenarios:

    • A present amount invested today.

    • A series of equal cash flows (an annuity).

    • A series of mixed cash flows.

  • Differentiate between an ordinary annuity and an annuity due.

  • Utilize interest factor tables for efficient calculation of present and future values, and determine unknown interest or growth rates based on known variables.

  • Create an amortization schedule for installment loans.

Key Concepts

Time Value of Money (TVM)

TVM is the principle that a certain sum of money has greater value today than it will in the future due to its potential earning capacity. This concept is crucial for making informed financial decisions regarding investments and loans.

Interest Rates

  • Simple Interest: Calculated only on the principal amount, it does not take into account the interest that accrues on the interest.

  • Compound Interest: Calculated on the principal and also on the accumulated interest of previous periods, which can significantly boost the total amount over time.

Interest Rate Structures

Risk Structure of Interest Rates

  • Default Risk: Occurs when the issuer of a bond cannot make scheduled interest payments or pay back the principal. U.S. T-bonds are generally considered free from default risk.

  • Risk Premium: The additional interest charged above the risk-free rate to compensate investors for taking on risk.

  • Liquidity: Refers to how easily an asset can be converted into cash.

The Term Structure of Interest Rates

The term structure refers to the relationship between interest rates of bonds with different maturities. It outlines how interest rates can vary and have implications based on economic conditions, investor expectations, and liquidity preferences.

  • Yield Curve: A graphical representation plotting the interest rates of bonds of the same credit quality but differing maturities.

    • Upward Sloping: Indicates that long-term interest rates are higher than short-term rates, usually a sign of economic growth.

    • Flat: Reflects similar rates for short and long maturities, suggesting uncertainty in future economic activity.

    • Inverted: Long-term rates fall below short-term rates, often preceding economic downturns.

Interest Rate Theories

  1. Expectations Theory: Suggests that long-term interest rates are an average of current and expected future short-term rates.

  2. Segmented Markets Theory: Argues that bonds of different maturities are not perfect substitutes, and the interest rate for each maturity level is influenced by the specific supply and demand characteristics.

  3. Liquidity Premium Theory: Combines the previous two by asserting that longer-term bonds will carry a liquidity premium due to time and risk considerations.

Types of Annuities

  • Ordinary Annuity: Payments occur at the end of each period.

  • Annuity Due: Payments occur at the beginning of each period.

Calculating Present and Future Values

  1. Present Value: The current value of a future sum of money given a specified rate of return. The formula used is: [ PV = \frac{FV}{(1+i)^n} ]

  2. Future Value: The expected value of a current amount of money at a specific date in the future, calculated using: [ FV = PV(1+i)^n ]

Amortization Schedules

An amortization schedule details each payment on an amortizing loan, outlining areas such as principal repayment and interest paid over the life of the loan.

Conclusion

Unit 3 provides comprehensive coverage of the time value of money, interest rate theories, and their applications in finance. Grasping these concepts is vital for making informed financial decisions whether for personal investments or managing loans effectively.