Foundations of Computational Finance with MATLAB

CHAPTER 5The Time Value of Money

5.1 Introduction

The theory and applications of time value of money (TVM) concepts are foundational to finance. They are not just abstract concepts, however: They also make intuitive sense because we understand that the value of a financial sum today is not necessarily the same as the value of a sum to be received in the future.

Imagine that you were given a choice between receiving $1,000 today or $1,000 in one year. Assume there is no risk that you won't be paid in one year—payment is guaranteed on both dates. A natural response is, why would anyone wait a year to receive the same amount of money? If you took the money now, you could invest it in securities or earn interest in a savings account. If you had debts, you could use the money to reduce those debts' balances and save interest expense. Inflation is another factor to consider. Prices of most goods and services increase over time, so it's likely that the $1,000 would buy less in one year than it buys today. These are logical responses, and most rational persons would prefer not to wait one year for the same amount of money.

But what if the choice was between $1,000 today or $1,050 in one year? That is a 5 percent return on the money for waiting. How about $1,100 in one year, a 10 percent return? What if the offer is for $100 per month for the next 12 months, for a total of $1,200? At some point, you're likely to be indifferent to the cash flows because you'll value them equally.

TVM ...