Computation Section
 - Time Dimension

It may be desirable to construct a cash flow for the project that indicates the expenditure of money over time. For an example we use the WBS with only two levels of detail. This makes the graphics and data simpler, but similar results can be obtained with any level of detail. To add the time dimension, click the Include Time box as shown below. Also enter the number of periods of the analysis. For the example we assume the project will take six months.



In addition to the WBS, two columns are provided to specify the start and end time of each activity.



To the right of the schedule there is a time/cost display showing the six month period with an additional column for time 0. Column J, for time 0, holds investment amounts that occur at the beginning the six month period. There are none for the example. Columns K through P show how the work package costs are spread over the six periods. The range is colored yellow to indicate that it contains formulas. The models assume that the costs are spread evenly over the intervals defined by the start and finish columns. These formulas can be manually changed or replaced by numbers for other distributions of cash flow.

The row at the bottom of the display, row 25, holds the cash flows for the six periods. An entry, say K25, is obtained by multiplying the costs in column E by the proportions in column K. The cash flows are interesting to the planner concerned with financing the project. They will also be used for equivalency calculations in other lessons.

  The numbers in row 13 are the present worth factors, identified by P/F. We will have much to say about these factors later, but it is sufficient to say at this point that when a cash flow occurs at some time t, multiplying it by the P/F factor computes an equivalent value for the cash flow at time 0 called the net present worth, NPW. When we multiply a row in our time/cost matrix by the vector of P/F factors, we obtain the equivalent value of the entire row of cash flows. We see in column Q the NPW value for each work package. For positive interest rates, NPW values are less than the total cash flow. For example, the cost of 14,000 in row E15 results in a NPW of 13,591.




Clicking the Summarize button at the top of the page summarizes the total NPW values for the second level activities and an estimate of the NPW of the entire project. These depend on the interest entered in cell K11. With an interest rate of 0, the NPW values are the simple sums of the cash flows over time.

  All the results cells that are colored yellow hold formulas that recalculate automatically if any data item is changed. Thus the display is dynamic.



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tree roots

Operations Management / Industrial Engineering
by Paul A. Jensen
Copyright 2004 - All rights reserved