WFU Law School
Law & Valuation

Chapter 1 - Time Value of Money

This chapter introduces you to "time value of money" concepts.  For some of you, this will be a referesher of familiar ideas -- and may even be simplistic.  For others, these concepts will be an empowering revelation. 

In either case, you should be aware that time-value concepts frame the valuation techniques we will be using throughout this course.  You should become comfortable with these foundation stones -- we'll be building on them.

We invest in the future in many ways. Sometimes we invest money in the expectation of financial returns: bank accounts, mutual funds, stocks, machinery, whole businesses. We also invest our present selves in the hope of a better future: education, exercise, friends, dietary supplements. Whatever form our investment takes, there is a common element. We believe present sacrifices are justified by the future gains we anticipate.

In short, we make many present decisions based on how we perceive and value the future. For example, is taking this course (and studying this chapter) worth the potential future returns -- as measured in intellectual satisfaction, GPA, job opportunities, worldly success and eternal glory?  These are complex questions.  The future is always unknowable.  But any decision, and ultimately any valuation of future possibilities, turns on how we value in the present returns in the future.  Is it worth reading on?


Chapter Subsections

This chapter has a modest aim.  We will focus narrowly on money decisions -- as though they are all that mattered -- and study the time value of money.

We will consider:

  • the difference between present value and future value
  • the future value of
    • a single amount, compounded annually and more frequently
    • a stream of amounts (called annuities)
  • the present value of
    • a single amount
    • cash flow streams (mixed flows, annuities, perpetuities)
  • the stream of payments needed to pay off an increasing sum (loan amortization)

In the process, you should learn some basic computational tools for making these value comparisons. You can apply these tools to solve the problems at the end of the chapter. Notice that for now we consider valuation in a world of certainty -- where interest rates, future payments, and next year are all certain to happen.

In chapter 2, we will consider the real world of uncertainty - a world of risk.

Live as if you are to die tomorrow, study as if you are to live forever.

Thomas More


©2003 Professor Alan R. Palmiter

This page was last updated on: March 16, 2005