Section outline

  • Module Homepage

  • 1. Introduction

    Welcome to "Time Value of Money"! This module takes us on a time travel with money and thereby covers one of the basic pillars of finance.


    The main learning goals of this module are:
      • Know how to make cash flows comparable over time.
      • Get familiar with the basics of Compounding and Discounting (time traveling with money).
      • Understand Present Values and Future Values.
      • Be able to compute the present and future value of any cash flow or cash flow stream.
      • Know how to handle perpetuities and annuities.
    Activities: 2
  • 2. Future Values

    This section explains how to determine the future value of simple investments proposals, where we invest money today and let it grow at a certain rate of return over the investment horizon.

    Activities: 3
  • This section expands the computation of future values to investment proposals that make multiple interest payments per investment period, such as semi-annual, quarterly, or monthly payments. In the process, we get to know how to compute the effective annual interest rate (EAR) that allows us to compare investment proposals with different interest payment schemes. We also learn how to handle investment proposals that make continuous interest payments.

    Activities: 3
  • This section shows how to compute the future value of investment proposals with multiple cash flows that occur at different points in times. It thereby generalizes the computation of future values for virtually any investment decision, including savings accounts, retirement plans, etc.

    Activities: 3
  • 5. Present Values

    The preceding sections have shown how to compute the future value of different cash flow strings. In this section, we start time travelling in the opposite direction. We want to know the present value of cash flows that we expect to collect in the future.

    Activities: 7
  • 6. Perpetuities

    By now, we are well familiar with the concept of present value and future value. We have also seen, however, that the computations can become quite cumbersome for investment projects with long-term cash flow streams. In this section, we take the duration of the cash flow stream to the extreme and discuss the valuation of investment projects that are expected generate a constant (or a constantly growing) cash flow and run forever. These are so-called perpetuities. As we will see in later modules, the concept of a perpetuity is extremely popular in the context of firm valuation.

    Activities: 3
  • 7. Annuities

    The last step of the module is to value investment proposals with recurring cash flow streams that last for a specific period of time. An example of such a project could be a pension plan that makes an annual payment over, say, 25 years after retirement. The section develops very useful shortcuts to value such annuities and it provides a broad set of examples to practice this valuation approach in real-life situations.

    Activities: 10