Computing Factors

Throughout the course we ask for numerical results regarding equivalent cash flows. Then it is important to be able to evaluate the equivalence factors quickly and correctly. In this lesson we consider several ways to do this.

 There are many ways to evaluate equivalence factors. For this course use tables, our factor calculator or the Economics add-in for Microsoft Excel.

 Tables

The traditional way to evaluate equivalence factors is through tables. A single table holds the factors for a specified interest rate for a collection of time intervals. The figure below shows an example of the 10% table. To look up a factor value for a given number of periods n, choose the row for that value of n and the column for the desired factor. The factor value is at the intersection of the row and column. For example, the value of (P/F, 0.1, 10) is read as 0.3855.

Click on the tool icon to open a table of interest rates. Clicking on a rate will open a PDF document with table for that interest rate.

 Factor Tables

We also provide an Excel worksheet that constructs a table for any interest rate. Clicking the Excel icon will download an Excel data file. Depending on how your browser is set you may have to open Excel separately.

 General Table

 Factor Calculator

We have prepared a calculator that evaluates factors for arbitrary parameters. This calculator is very handy for simple problems. Enter the interest rate and the time interval in the data fields and click on a factor button to perform the computation. The multiplier data field is available for simple problems requiring multiplication of the factor by a constant. The calculator is programmed with Flash and is interactive.

Click on the tool icon to open factor calculator.

 Factor Calculator

The computational tool of choice for this course is Microsoft Excel. This program is widely used and is available for Windows and Mac OS. The factor formulas can be computed directly in Excel and the program includes a number of built in financial functions. We illustrate these later on this page, but in this paragraph we describe our recommended tool, the Economics add-in. This add-in is fully described on the ORMM site. Click the icon to go to that site.

The figure below shows equivalence factors for 10% interest and 10 years as computed by the add-in. They are evaluated with formulas placed in column U. The formulas entered in column U are shown in the yellow field to the right. Each function has two arguments, the interest rate in cell U3, and the time interval in cell U4. The last two letters of the the function name identifies its purpose. For example FP computes the F/P function. Note that the arguments of the functions are references to cells U3 and U4. It is much better to reference the data cells that to place numerical values of the arguments directly in the function statement.

The functions are User Defined functions. The User Defined list is accessed through the Insert/Function menu item or the insert function icon on the Standard Toolbar. The functions associated with the Economics add-in are prefaced by "E_".

Clicking the icon opens a page that gives instructions and examples for the functions.

It may seem inconvenient to use the add-in at this point because other methods can be used to compute the factors. Other features of the add-in will be used extensively in other parts of this course, and a little effort spent now will bear fruit later.

 Excel Formulas

Since the factors are all defined as formulas that depend on i, the interest rate and N , the time interval, they can be computed directly in Excel with formulas entered into Excel. The example below show the factors computed in column G. The formulas in these cells are shown in the yellow field on the right. All the formulas refer to cells G3 that holds the interest rate and G4 that holds the time interval. It always good to reference data cells in a formulas rather than enter the data directly in the formula. Then when the data is changed, and formulas automatically compute the results.

It is not usually convenient to enter the formulas directly because it is easy to make mistakes.

 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. We use in this paragraph the PV, FV and PMT functions. Some of the others are used in later sections.

Some of the factors are computed with Excel functions below. The factors involving the gradient are not available. The first two arguments of all the functions are the interest, in cell O3, and the time interval in cell O4. The third and fourth arguments in the example yield the desired factors. The negative signs are necessary to obtain positive values for the factors.

The Built-in functions are useful for more complex situations, but are not really very helpful for computing factors.

Engineering Finance
by Paul A. Jensen