LECTUREPEDIA - Ajarn Paul Tanongpol, J.D.; M.B.A.;B.A.; CBEST
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III.

THE INVESTMENT CRITERIONS WITH FIRM’S TAX

Most basic analysis in finance does not take into consideration the tax implication of the firm’s financial circumstances. Firm’s decision on project selection is based on cash flow alone; however, increasingly, the assumption of a tax free world becomes increasingly impractical. Many firms decide to accept or reject a project solely on the basis of tax consequences. In a project Z, it is said that the project is accepted by the firm if the project’s cash flow is great than zero:  > 0. The simplicity of a tax-free world is expressed thus:

                                    [3.a]

The project is accepted as feasible if . Under this assumption, there is indifference, if . However, this evaluation process may not be as accurate because the value of  left out two components, namely depreciation and interest payment.

            Another method of project valuation is the use of the discount model. The discount model assumes that the income streams from the project are discounted in the market by rates determined by the investor’s risk preference. The market value of the cash flow under the discounted model can generally be stated as:

                                                                                           [3.b]

The value of  would be adequate as a tool for feasibility determination if it is an after-tax valuation. However, so long as it is assumed that  is a tax free project, it is not adequate to answer the question of whether the project is feasible.

            This section of our discussion takes corporate income tax into account in the firm’s investment decision whether to accept or reject a project. In short, this section covers the quantitative decision analysis for feasibility studies in a nutshell.

3.1       Cash Flow and Valuation

In any project selection, the firm evaluates the proposed project’s cash flow to determine its feasibility. In order to determine the project’s feasibility, the firm must consider the effect of corporate tax. In order to fully appreciate the effect of corporate tax on the proposed project, tax deductible interest, depreciation, and the capital budget of the firm must be considered. For project’s cash flow and valuation, the following definitions are used:

       = project cash flow at time t;

       = pretax cash earning from firm;

        = capital budget of firm;

    = tax payment

         = corporate tax rate

       = tax deductible interest to time t bondholders; and

     = depreciations deduction

                                                                                         [3.1]

The project’s cash flow is equal to the net income less investment and tax payment. The tax payment is defined as:

                                                                                [3.2]

The firm’s tax liability is the corporate tax rate:  minus depreciation and interest payment to bondholders. The tax payment defined by equation [3.2] uses net income as the taxable-base. Net income is income less deductible expenses and two additional deductions, namely depreciation and interest payment to bondholders. We can substitute equation [3.2] into [3.1], thus:

t

                                                                   [3.3]

            The statement can be written as a general statement of cash flow in a vector format:

                                                                        [3.4]

Each variable is a vector with elements for t = 1, …, ∞. As a vector statement, we can express the each element of the equation as:

 and so on.

So long as the project is in operation during the time set for the production, the income will be accumulated since the income is considered as an income stream. A project will most likely produce an income stream, not a lump sum. For the increment in income from the initial investment, the incremental is defined as:

                                                                                                   [3.5]

The notation  refers to the changes in the income stream from initial investment to the time t+n. This notation can re-express the general statement of equation [3.3] as follows:

                                                          [3.6]

The above statement can be rewritten in a vector format as:

                                                              [3.7]

As before, .

            Thus far, we have set criteria for project selection by stating that the value of the project includes all income streams from the project. The value of the income stream (V) is the value of the income stream of the project: . Therefore, the value of the project in an incremental change in income stream from the project is expressed as:

                                                                                                  [3.8]

The after-tax value of the project income stream is defined as . The change in the value of the project is equal to the incremental of all income stream combined; thus, . The project is feasible when the value of the income stream in an incremental term is maximized.

                                                                                                            [3.9]

            From our analysis of the project feasibility, we note that the greater the value of debt financed or , the greater the value of the incremental ; therefore, the firm is preferential to debt financed in all projects because the benefits from debt financing are depreciation (DP) and interest payment on loan () used to financed the project. The implication of corporate tax in project valuation is determinative because project valuation is not complete without tax consideration. It is said that in a perfect situation, that is an operational situation without tax consideration, there are only two types of valuation methods: net present value and discount model. When corporate tax is introduced into the calculation, it is said that the valuation is under an imperfect condition. It is considered imperfect because tax is firm indicative according to the firm’s corporate tax bracket and, therefore, the firm’s definition of tax utility must be evaluated as part of the project valuation process.

3.2       Project Selection Criterion with Taxes

In section 3.1, we consider project valuation by looking at the net present value of the project through a discount model in the firm’s perspective. Section 3.1 shows us how to select a project; this section shows us the criteria used in project selection. In so doing, we are considering the interest of shareholder and bondholder. The valuation of the project still follows the same path of analysis. The termis the payment of interest or bond yield to the bondholder, .

        = project Z;

        = after-tax cash flow of project Z;

       = cash income;

        = investment outlays;

     = depreciation; and

      = bond interest of the firm beginning at time 1.

                                                                      [3.10]

            From the condition stated in equation [3.10], it is clear that the best financing mode for a project is by means of debt. The higher the value of  the higher the net present value of the stream of cash flow from the project will become. The two determining factors in equation [3.10] that help generate cash flow for the project is depreciation expense and bond interest payment. The implication is clear: tax law is bias in favor to financing projects by debt, i.e. someone else’ money. The more the firm spent on asset acquisition and the more the firm digs itself in debt, the better the after-tax cash flow of the firm will become.

            The project will be accepted if the value of the after-tax cash flow from the project () exceeds the initial investment (). The best alternative project must satisfy the following condition:

                                                                                                  [3.11]

            At the beginning of this section, it was asserted that the in adequacy of the general approach of project valuation is that it assumes that there is no corporate tax. In equation [3.11], we are following the same type of project valuation, but the stream of income under consideration is the after-tax income flow. The standard for the selection remains the same; so long as the after-tax income stream of the project is greater than zero, the project will be accepted.

3.3       The Discount Model with Taxes

The discount model is a traditional and conventional means to evaluate the feasibility of a project. The future income is discounted by the cost of capital in order to obtain the net present value of the income stream. A normal discounted model is stated as:

                                                                                           [3.12]

            The term  is the project income stream in a tax-free situation. The net present value of equation [3.12] is commonly found in project valuation in normal courses in finance. However, the assumption of  is oversimplified because would only be practical in a tax-free countries, such as Monaco, and the Bahamas.

                                                                                           [3.12]

            In order to engage a proper project valuation, the net present value of the income stream used in the assessment must be the after-tax income stream. The after-tax stream is designated as:

                                                             [3.13]

The assumption of equation [3.13] requires that (i) all debt used to finance the project at time 0 yields a perpetual interest stream; and (ii) there will not be additional debt issued to support the project for the length of the project. Condition one is rational because the interest stream must be counted from the commencement of the project. As for condition two, in order for the valuation to hold true, no additional debt must be issued. If there will be additional debt issued to finance the project that is already deployed, it is difficult to determine the returns for the project. The valuation of the project must have a fixed cost of initial investment. This calculation will not be possible if there is no definite capital injection into the project.

            The income after-tax income stream of the project  is the sum of all stream of the project. To express the statement in terms of the interest payment to all , all deductible interest payment during the life of the project financed by debt can be stated as:

                                                                                                  [3.14]

where

            For a project financed by bond, the value of the project is the sum of all income streams from the project plus the tax benefits from bond amount. This general statement is expressed as:

                                                                                                [3.15]

In the statement above,  is the bond used to finance the project. Although the entire amount of the bond is considered a liability, for after-tax income stream valuation purposes, the amount of the bond issued multiplied by the corporate tax rate yields the tax benefit from the bond. Firm equation [3.15, it can be determined which project is the best alternative by the following condition:

                                                                                         [3.16]

            The project will be selected when all the after-tax income stream plus the tax benefit from bond financing minus the initial investment is equal to or greater than zero. The condition of equal to or greater than zero needs to be explained. The project will be acceptable even if the value of the after-tax stream of income is equal to zero because the company comes out ahead after-tax treatment. If the income stream of the project without tax is equal to zero, the project is indeed not feasible. The after-tax valuation of the project equal to zero is indeed a beneficial project by the mere fact of tax deduction from the bond debt.

            The valuation of the bond payment can also be expressed under the discount model to determine the actual financing amount that the firm will have to bear. This discounting of the bond is expressed as;

                                                                                         [3.17]

The discounted value of the bond is the amount that the bondholder will pay or the amount of money that the firm will receive. This is not the same as the full value of the bond. The full value of the bond is the bond value not discounted; this amount will always be greater than the discounted amount:

                                                                                         [3.18]

Under equation [3.17], the value of the bond is discounted, similarly the value of the after-tax income stream financed by the bond can also be expressed under the discounted model, thus:

                                                                                         [3.19]

By substitution, we can write the sum of the after-tax income stream from a project financed by bond as:

                                                                         [3.20]

            The tax implication of this discussion leads us to conclude that in order to fairly and fully assess the viability of the proposed project, all tax benefits must be taken into consideration. Tax benefits are the deductions that the firm received through all operating expenses; these are expenses that are used to adjust the sales income to derive the net income: . Additional tax benefits come from depreciation expense and interest payment paid on bonds or maintenance costs paid on assets used.

Last modified: 11/11/08