LECTUREPEDIA - Ajarn Paul Tanongpol, J.D.; M.B.A.;B.A.; CBEST
QUIZ every 2 weeks - Grading Standard: ATTENDANCE 10% + QUIZ 10% + MID-TERM 30% + FINAL 50% . . .

VI.

VALUE ADDITIVITY PRINCIPLE

In project selection, if the value of the project exceeds the cost, the project should be accepted. The definition of cost generally does not include the tax treatment. The basic assumption of value additivity principle (VAP) assumes a perfect market, i.e. no transaction cost and no taxes. In this section of our discussion, we will begin with the fundamental theorem of VAP without taxes and end with VAP with taxes. Under VAP, the project will be accepted if the following condition holds:

                                                                                             [6.1]

and

                                                                                                   [6.2]

where …

      = current value of total cash flow of firm at time 1;

     = value of cash flow that results if no investment is made;

     = value of incremental cash flow from total budget; and

      = value of cash return from project 1.

            The purpose of this introductory note to VAP is to see the non-tax situation. From this non-tax, we will use VAP to show its relationship in debt financing by the firm. Debt financing is firm’s financing by bond. A bond is a private debt instrument issued by the firm. It is a promissory note with the face value of an amount certain and it is sold at a discount. The discount is equal to the rate of returns guaranteed by the bond.

Value Additivity and Debt Financing without Taxes

When the firm undertakes a project, it expects to receive a stream of income from that project. The VAP states that the value of the sum of streams received by the firm equals the sum of the individual stream. It is assumed that the stream is more than one payment.

 and                                                                              [6.3]

        = individual streams of income; and

        = market value of all streams.

            If the debt financing is financed by bond issuance, there will be two types of bondholders. There are those who are existing bondholders, and those who are new bondholders. The new bondholders are represented by ; the existing bondholders are represented by . Therefore, the total cash flow is written as:

                                                                                      [6.4]

The cash flow comes from old bondholders and new bondholders. Thus far, we have considered one source of financing by the firm: bond. The firm also raised its capital through issuing share. If there is an increase in bondholders, the firm will have less money to pay shareholders, i.e. less dividends. Investors look to the valuation of the firm before they invest in the firm’s security. The value of the firm is determined by ; the firm’s value is the sum of stocks and bonds. The value of the firm is fixed as V; if the firm issues more bonds, the stock (S) will fall. According to this assumption, the choice of financing does not affect the value of the firm. However, in reality, this assumption might not hold true. If the firm is burden with debt, it would have less to pay shareholders. It is clear that this assumption is not adequate to fully appreciate the VAP without considering the effect of corporate taxes on the firm’s choice of financing.

Value Additivity and Debt Financing with Taxes

In order to fully appreciate VAP, corporate tax and the effect of corporate tax must be added into the valuation of the firm. The cash flow that we spoke of in section 6.1 must be an after-tax cash flow. For that reason, we must adopt the following definitions for our discussion:

        = firm’s cash flow;

        = firm’s after-tax cash flow;

         = firm tax rate;

       = cash income before deduction of interest and depreciation;

     = depreciation for tax purposes;

        = interest payment by the firm; and

        = cash outlay by the firm on investment.

The cash flow of the firm s written as:

                                                                           [6.5]

The cash flow of the firm depends on the depreciation adjusted for the firm’s corporate tax rate. The more the firm spent on acquiring assets, the more it can depreciate and use it to offset against its taxable income. We see from  that tax law is biased in favor of the firm’s expenditure on acquiring assets. The third quantity is investment. Investment has a negative on the firm’s cash flow. The more the firm invests the small the cash flow will become.

            Investment is considered as a cash outlay; thus, it is minus from the cash stream of the firm’s cash flow. However, the amount of money is used in the investment, it will be accounted for in the depreciation and interest payment. If the investment is used to buy assets for the firm, the money spent is an investment. That investment is minus from the firm’s cash flow. However, at the same time, the value of the asset, for which the investment was used, will be added back into the firm’s cash flow. The add-back of the depreciation will not be the full amount, but equal to the amount allowed by the depreciation schedule. If the asset is depreciated over a period of five years on a straight line, the amount added back to the cash flow is 1/5 of the total value.

            The interest payment is similarly treated by multiplying the entire amount of the interest payment by the corporate tax rate. The value of  used for depreciation is the same for interest payment. Since the value of is the same for interest payment and depreciation, it is said that tax law is indifferent towards either type of finance. However, in practice, the firm would be in favor of debt financing because the entire amount of the interest payment is allowed as a deduction; whereas the depreciation amount is a partial amount taken to offset against the income over a period of the useful life of the asset.

            By introducing tax into the equation, the cash flow is represented as:

                                                                                        [6.6]

where …

       = pretax earnings (inflow) of the firm;

        = investment outlay (outflow) of the firm; and

    = tax payment.

The above statement [6.6] assumes that cash on-hand is considered as an investment. The corporate tax is the same as we have defined in prior discussion as:

                                                                             [6.7]

The interest payment to bondholders in equation [6.6] is represented by . The depreciation remains the same. By substitution, the firm’s cash flow is rewritten as:

                                                                  [6.8]

Statement [6.8] can be expressed in a vector format as:

                                                                    [6.9]

Where the variable in [6.9] is a vector with elements for .

            From the above expression, it is noted that the higher the interest payment to debt, the higher the cash flow amount. It is clear that for cash flow purposes, the firm would be biased in favor of debt. High debt leads to larger the cash flow stream. Cash flow does not tell us anything about the firm’s performance. It measures all the inflow and outflow of cash in the firm.

            The tax component of the cash flow streams in equation [6.9] is nothing special. It follows conventional definition and application of tax:  and it is applied in a straight forward manner. The lesson learned from this discussion of VAP with tax implication of the firm’s debt financing is that tax law favors debt financing. Not that if the firm issues more shares to shareholders, it has to pay dividends to shareholders. Dividend payment is not a deductible expense. However, the interest payments on bond are deductible.

Last modified: 11/11/08