Time Lines
by MaestriOne of the most important tools in time value analysis is the time line, which is used by analysts to help visualize what is happening in a particular problem and then to help set up the problem for solution. To illustrate the time line concept, consider the following diagram:
Time 0 is today; Time 1 is one period from today, or the end of Period 1; Time 2 is two periods from today, or the end of Period 2; and so on. Thus, the numbers above the tick marks represent end-of-period values. Often the periods are years, but other time intervals such as semiannual periods, quarters, months, or even days can be used. If each period on the time line represents a year, the interval from the tick mark corresponding to 0 to the tick mark corresponding to 1 would be Year 1, the interval from 1 to 2 would be Year 2, and so on. Note that each tick mark corresponds to the end of one period as well as the beginning of the next period. In other words, the tick mark at Time 1 represents the end of Year 1, and it also represents the beginning of Year 2 because Year 1 has just passed.
Cash ?ows are placed directly below the tick marks, and interest rates are shown directly above the time line. Unknown cash ?ows, which you are trying to ?nd in the analysis, are indicated by question marks. Now consider the following time line:
Here the interest rate for each of the three periods is 5 percent; a single amount (or lump sum) cash out?ow is made at Time 0; and the Time 3 value is an unknown in?ow. Since the initial $100 is an out?ow (an investment), it has a minus sign. Since the Period 3 amount is an in?ow, it does not have a minus sign, which implies a plus sign. Note that no cash ?ows occur at Times 1 and 2. Note also that we generally do not show dollar signs on time lines to reduce clutter.
Now consider a different situation, where a $100 cash out?ow is made today, and we will receive an unknown amount at the end of Time 2:
Here the interest rate is 5 percent during the first period, but it rises to 10 percent during the second period. If the interest rate is constant in all periods, we show it only in the first period, but if it changes, we show all the relevant rates on the time line.
Time lines are essential when you are ?rst learning time value concepts, but even experts use time lines to analyze complex problems. We will be using time lines throughout the book, and you should get into the habit of using them when you work problems.
Draw a three-year time line to illustrate the following situation: (1) An out?ow of $10,000 occurs at Time 0. (2) In?ows of $5,000 then occur at the end of Years 1, 2, and 3. (3) The interest rate during all three years is 10 percent.
Taken From : Five-Minute MBA – Corporate Finance
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