Engineering Finance
Computation
Economics Add-in

The Economics add-in can be used to evaluate a single project using time-value of money principles. The evaluation assumes that all investments, revenues and expenses associated with the project over its entire life are known with certainty. The purpose of the evaluation is to show whether the project meets a specified criterion for acceptability. The usual criterion for acceptance is the minimum acceptable rate of return for the investor. This page shows a summary of the steps of the evaluation.

The Problem

A businessman is considering the purchase of an asset that has an initial cost of $2000. The asset promises an annual return of $600. It's operating cost is $100 the first year, $150 the second, and increases by $50 in each subsequent year. The salvage value for the asset in 10 years is $400, or 20% of its initial cost. The cash flow for this situation showing the individual components explicitly is in the figure below. If the businessman's minimal acceptable rate of return is 10%, should he invest in this project?

The Project

Install the Economics add-in. Choose Add Project from the menu.

Provide a name for the project. Select the name carefully because it cannot be changed later. Use a name with no spaces or punctuation. It must start with a letter.

Fill in the number of investments (1 for the 2000 investment at time 0). Fill in the dialog with the number of cash flows (3, one for the revenue, one for the uniform part of the operating cost, and one for the gradient part of the operating cost). The bottom half of the dialog is used when taxes and/or inflation and/or uncertainty is to be modeled.

The Change Project command allows the number of cash flows to be increased or decreased.

The add-in creates a form to hold the project data. The example shows some items already filled in. Specify the investment in row 9 as a negative number. The Salvage is the percentage of the investment that is returned at the end of the life of the asset (20% = 400/2000). The Start value indicates when the asset is put into service and the End value indicates the end of its life.

The return is entered in row 13 as a uniform series with value 600. The first payment time (at the end of year 1) is entered in the Start cell and the last payment time (at the end of year 10) is entered in the End cell. The uniform part of the operating cost is entered in row 14 as a negative number (-100). The operating cost is increasing by an amount $50 per year. This is entered as a negative gradient (-50) in row 15. The Start cell indicates when the first non-zero payment occurs (2) and the End cell indicates when the last payment occurs. The Parameter for the gradient is the periodicity of the payments (1 means that it occurs annually). All the words and numbers in the white cells can be changed.

Not shown in the example is the Single cash flow type. This represents a single amount at a specified time. The time is to be placed in the Start column. The End column is not used for this type and a non-numeric entry like *** should be used as the End.

The Results

The yellow cells in column S are computed by formulas inserted by the add-in. These are the results of the analysis. Cell S9 is the present worth of the investment considering both the amount of the investment and the salvage. Cells S13 through S15 hold the present worth values of the annual cash flow components.

Cell S2 holds the sum of the investment and cash flow present worth values. The is the net present worth of the project over its life. Since the value (81.93) is positive, the investment returns more than 10%, the MARR. This implies that the investment should be acceptable to the decision maker. A negative value implies that the project does not return the MARR. Cell S3 holds the equivalent net annual worth of the project. It is also positive because it is proportional to the net present worth. Cell S4 holds the present worth over the study period. Since the study period (10) is the same as the life, this is the same as the present value over the life.

The Internal Rate of Return (IRR)

The internal rate of return is the interest rate that makes the net present worth of the project equal to zero. It is a measure of the profitability of the project. It is discovered by a binary search procedure. Selecting Compute Rates presents the dialog below. The project E6_2 is selected from the Name field.

For some projects there may be more than one solution that yields a zero net present worth. Different solutions may be found by specifying the initial guess and range of the search process. The example is called a simple investment since a single investment is followed by net revenues in the following years. This kind of investment has only one solution for the IRR.

The add-in successively changes the MARR in cell O1 until the IRR is determined. The rate is placed in cell Q5 on the project definition. It is colored green to indicate that the number is computed by an algorithm. If some of the parameters of the project are changed, the yellow cells will automatically compute new values. The IRR cell will not change, however, unless the algorithm is run again.

The IRR is 11.13% for the example. The fact that it is greater than 10%, the MARR means that the project is acceptable. The IRR will always be greater than the MARR when the project net present worth is positive.

The Cash Flow

For a complicated project with several cash flow components, it is often difficult to determine the flow of cash values in the several years of the project life. For a tabular presentation choose Show Cash Flow from the menu. In the resulting dialog, choose the project in the name field. The buttons on the right select the results to be displayed.

We have chosen to display the cash flow in each period and the cumulative values. At the top of the display is a series of measures that are computed with the Excel economic functions. Row 2 indicates that this is a simple investment, implying that the cumulative cash flow has only one zero crossing. In this event the IRR is unique. The Payback is the number of periods before the initial investment is recovered. The MARR is an input value. Row 5 holds the minimum period index, necessary for some of the computations. The NPW(0) is the net present worth at time zero. The IRR guess is an input that will effect the computed value of the IRR if that value is not unique. Row 8 shows the computed value of the IRR computed with the IRR function of Excel.
Graph of the Cash Flow

It is often instructive to view a graph of the cash flow. Select Graph Cash Flow from the menu and select the project name in the dialog. The terms Actual and Real refer to different evaluations of the dollar amounts when inflation is considered. With no inflation, we use Actual to refer to the cash amounts at each period. The Cash Scale and Time Scale control the size of the display.

A cash flow table must have already been constructed for a project to appear on the name list.

The cash flow for the example is graphed below. Cash amounts at the same time are accumulated to a single value. For example the 450 appearing at time 10 is the sum of the salvage value of 400 and the net income of 50.

We have illustrated the evaluation of a single project when inflation and taxes are neglected. The form holding the project data may be much more complex than the simple example presented here. A project may have several investments occurring at different times and many annual receipts and disbursements. There is no limit to the complexity the add-in can handle except the size of the worksheet and the limitations of the user's computer.

The evaluation of projects with taxes and inflation is more complex requiring additional data and more difficult computations. The add-in handles these variations using commands and dialog boxes similar to those illustrated on this page.

More detail is available on the pages describing the Economics add-in.

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Economics Add-in
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Links

The Links command is very important when an economic model is constructed in one computer and opened in another computer. The forms created by the add-in use user-defined functions. These are linked to the computer where they are created. When opened in a second computer the links are no longer valid and an error message will appear.

 

When a workbook containing economic analyses is to be moved to a different computer choose the Links command from the menu. The selection opens the dialog below.

When the OK button is selected with the Freeze Solutions option chosen, all the user-defined functions are replaced with their numeric values. The workbook then opens in another computer with no errors.

After opening the workbook in the second computer, choose the Links command and choose the Make Links option.

When the OK button is clicked, all the user-defined functions are replaced in their original positions, thus making the forms in the workbook exactly the same as in the original. The command also can be used to correct the links, even when they were not originally frozen with the Freeze Solutions option.

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Engineering Finance
by Paul A. Jensen
Copyright 2005 - All rights reserved

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