**4**

# TIME VALUES

Most securities involve cash flows at different points in time. To compare different securities, the cash flows on each security can be transformed into an equivalent value at the present time (i.e., present value) or at some future point in time (i.e., future value). Then, these present (or future) values can be compared and the best security chosen.

This chapter presents future value and present value computations assuming the same interest rate or discount rate for all periods. This assumption is usually called a flat term (or maturity) structure of interest rates. Later chapters extend the analysis to the case where the interest rates differ by maturity.

## A Time Line

Since cash flows for securities occur at different points in time, it is important for the reader to have a clear understanding of the time line in Figure 4.1. Points in time are shown above the line, and periods in time are shown below the line. Point in time 0 is the present (or now). Point in time 1 is one period from now. Period 1 begins at time 0 and extends until time 1. The length of a period is arbitrary and depends on the particular situation under consideration. The length of a period may be a day, a month, a half-year, or a year.

We will always assume that cash flows occur at the end of a period. Cash flows occurring at time 0 are denoted with a subscript of 0, cash flows at time 1 have a subscript of 1, etc.

**Figure 4.1** Example of a time line

## Future Value

Suppose we have a dollar at time ...