The Economics addin can be used
to evaluate a single project using timevalue 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 addin.
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 addin 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
nonzero 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 nonnumeric entry like *** should
be used as the End. 


The Results 

The yellow cells in column S are computed by formulas inserted
by the addin. 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 addin 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 addin 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 addin 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 addin.


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 addin use userdefined 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 userdefined 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 userdefined
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. 

