Computation Section
Investment Economics


The add-in can also be used to analyze economic alternatives when taxes are considered. We repeat the example used earlier, but add tax considerations.

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. The cash flow for this situation without consideration of taxes is shown in the figure below.

To include taxes, we observe that the tax rate for ordinary income is 25%, and the tax rate for capital gains is 15%. The initial cost of the asset is to be depreciated over a 5 year tax life using the MACRS method. The tax salvage is zero. If the businessman's after-tax minimal acceptable rate of return is 10%, should he invest in this project?

The project is defined by choosing the Add_Project item from the Economics menu. Clicking the tax box on the dialog, enables the depreciation buttons at the lower left. We have chosen MACRS from the five depreciation types available.

Project Definition
On clicking OK, the project definition appears on the worksheet. Several new columns are necessary with taxes in the analysis. Most of these are in the investment data part of the worksheet.

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Investment Data

The columns associated with the investment data are each described below.

The index identifies the investment. There may be several investments that comprise a project and each has a row in the display.

A short description of the cash flow component.

Depr. Type

Assets are depreciated with one of the common methods. Several are provided. Refer to standard texts for a complete description.

  • None: The asset is not depreciated.
  • MACRS: The Modified Asset Cost Recovery System is a US government approved depreciation method. It provides depreciation percentages for each year of the tax life. The tax life must be 3, 5, 7, 10, 15, 20 27 or 39. Any other values will produce a calculation error.
  • Straight Line: The depreciation is the same in every year of the tax life.
  • SYD: The sum-of-years digits-method is provides accelerated depreciation.
  • DRDB: The Double Rate Declining Balance method depreciates the remaining book value at twice the straight line rate.
  • 1.5DB: Although this type is not listed on the dialog, it is allowed by the functions that computed depreciation values.
  • DRDB with a switch point. This is entered by placing DRDBsw in the type cell. The depreciation is determined with a switch point at the optimum time.
  • 1.5DB with a switch point. This is entered by placing 1.5DBsw in the type cell. The depreciation is determined with a switch point at the optimum time.
This is the expenditure for the investment. It should be a negative number. The value is the basis for the depreciation and the cash flow at the start time.
Tax Life

This is the life used for computing depreciation. It may be different than the actual life of the asset.

This is the time at which the asset investment is expended and the beginning of the depreciation period. The first depreciation amount occurs one year after the start time.
This is the time when the asset is retired. At this time the salvage value is received and any tax effects for disposal are received or expended.
This the amount received by selling the asset at the end of its life. It is usually a positive number, but it could be negative if there is a cost of disposal. The salvage value is entered as a percentage of the first cost. If it is entered as a positive percentage, the salvage will be an income. If it is a negative percentage the salvage value is an expenditure.
Tax Salvage

This is the salvage value used to compute depreciation. It is entered as a percentage. The depreciation of all types is computed using the

Initial Cost - Tax Salvage

This is true even for the depreciation methods that usually assume 0 tax salvage. Thus a depreciable asset that includes some non-depreciable proportion can be easily entered. Use 0 tax salvage if the depreciation method normally assumes this value.

Fin. NPW
This is the Final net present worth associated with the asset over its life, considering depreciation effects, disposal at sale and taxes.

Cash Flow Data

This data is similar to the data for projects not considering taxes. The only change is an additional column holding the tax rate. For most cash flows this column will hold the ordinary tax rate, however, the rates may be changed for individual cash flows.

Cash Flows


Selecting Show Cash Flows from the Economics menu builds the cash flow described by the project. When the project has tax parameters defined, the cash flow has two new columns, one for the depreciation in each year and one for the taxes. The results for all investments and cash flows are combined in these columns. For the example, we see the depreciation amounts prescribed by the MACRS method. The column at the far right is the after-tax cash flow. It is used to compute the NPW and IRR values at the top of the display.

The graphical display shows the after-tax cash flow.


Comparing Projects
When two or more projects have been defined, they can be compared in the same manner as projects without taxes. All projects involved in a comparison must have the same tax treatment. To illustrate a comparison, we introduce project Tax2 below with more investment than Tax and greater annual return. Tax2 uses straight line depreciation.

Click the image to expand
The cash flow for Tax2 illustrates the effect of the straight-line depreciation over the five year tax life.Since the useful life is ten years, there is no depreciation after year 5.
The comparison of Tax with Tax2 is shown below. We have chosen Tax2 as the challenger because it has the greatest initial investment. The extra investment of Tax2 over Tax is justified because it has a 13.39% rate of return, greater than the minimum acceptable rate of return. From the two investments we would choose Tax2.



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

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