Net Worth

Most economic analyses require the evaluation of an equivalent value for a complex cash flow. Again there are several ways to do this.

 For applications we compute the present worth and uniform worth of a complex cash flow.

As an example we use the cash flow at the left.

 Present Worth P = -30 + 10(P/A, i, 10) + 5(P/G, i, 7)(P/F, i, 3) Uniform series over 10 periods: A = P(A/P, i, 10) Future Worth at time 10: F = P(F/P, i, 10) = A(F/A, i, 10)

For our illustration we use i = 10%.

 Tables

The traditional way to evaluate equivalent values of cash flows is through tables. We repeat part of the 10% factor table below.

We compute the equivalent of the cash flow by substituting the factor values from the table. In the calculations below have used accurate factor values, but we rounded the results to two decimal places.

 Present Worth P = -30 + 10(P/A, i, 10) + 5(P/G, i, 7)(P/F, i, 3) P = -30 + 10(6.14457) + 5(12.7631)(0.7513) P = - 30 + 61.45 + 47.94 P = 79.39 Uniform series over 10 periods: A = P(A/P, i, 10) A = 79.34(0.1627) A = 12.92 Future Worth at time 10: F = P(F/P, i, 10) F = 79.34(2.59374) F = 205.91

 Factor Calculator

Rather than use the tables, we could have used the factor calculator to provide the factor values in the computations above. To compute the net worth, the results of the several component calculations must be added.

Click on the tool icon to open the factor calculator.

 Factor Calculator

 Cash Flow Calculator

We provide a convenient calculator for simple net value problems. The figure below shows the calculator with data entered for the example problem. Enter the individual amounts in the fields below the graph. Enter interest rate, periods for the uniform worth and periods for the future worth at the lower left. When the enter button is clicked the cash flow appears and the associated present, uniform and future worth are computed.

Problems are restriced to ten of fewer periods and individual cash flow amounts must be between -99 and +99. Click on the tool icon to open a live version of the cash flow calculator.

 Cash Flow Calculator

The example is easily evaluated with our recommended tool, the Economics add-in. This add-in is fully described on the ORMM site. The add-in can solve problems of arbitrary complexity and will be used throughout the remainder of this course.

This add-in is fully described on the ORMM site. Click the icon to go to that site.

 Built-In Excel Functions

Excel has several financial functions that are always available when Excel is loaded. The figure below shows part of the Financial Functions list. The list is accessed through the Insert/Function menu item or the insert function icon on the Standard Toolbar. The PV, NPV, FV and PMT functions are useful for computing equivalent values. The Excel financial functions are shown in the dialog from Excel. The funtion call, PV(rate, nper, pmt, fv, type), appears below the function list and the purpose of the funciton appears below that. The help file defines the arguments.

The Built-in functions are useful for computing equivalent values of some cash flows. Cash flow components are limited to three types.

1. a single pv at time 0
2. a periodic pmt payment than occurs for nper periods.
3. a single payment fv at time nper.

The equivalent value is computed at interest rate specified by the rate parameter. For periodic payments, the type parameter indicates whether the payments at the end of each period, true, or at the beginning of each period false. If the parameter is left out, the end-of-period payments are assumed.

There are no Built-in functions that include the gradient component so our example cannot be evaluated.

Engineering Finance
by Paul A. Jensen