Notice that to this point, we have examined the Capital budgeting decision as if the means of financing was irrelevant. Indeed, implicit in the results so far is that it is best to evaluate the project as if there are no financing implications whatsoever.

However, we know that the existence of taxes (and other frictions) could make the firm’s financing decision important in the decision itself.

One of the Critical Considerations with respect to financing is the effect of corporate income taxes on the firm’s decision. We know that the Internal Revenue Code treats Taxable Income as:

Thus, the Capital Budgeting Decision and the Capital Structure Decision cannot be treated separately.

There are two popular methods of considering the firm’s capital budgeting decision when the firm’s Income is subject to Corporate Tax.

 ADJUSTED PRESENT VALUE (APV) Adjust the Cash Flows to take into account the effect of Capital Structure

WEIGHTED AVERAGE COST OF CAPITAL (WACC) Adjust the discount rate to take into account the effect of Capital Structure

If done correctly, each of these methods will give the same answer. The only question is which is the most convenient to use.

The Adjusted Present Value Method

 1. Forecast the project’s expected after-tax cash flows assuming the project is financed entirely with equity!!!

2. Value the cash flows generated above, assuming the project is financed entirely with equity!!!

3. Add to the value obtained above the value generated as a result of the tax shield and other subsidies (or subtract costs) from the project’s financing decision.

Thus, the project is evaluated as if it were equity financed, and then an additional amount is added to allow for the tax (and other) subsidies from the financing decision.

The Weighted Average Cost of Capital Method

1. Forecast the project’s expected after-tax cash flows assuming the project is financed entirely with equity!!!

2. Value the cash flows generated above, by discounting them at a single risk-adjusted discount rate that varies with the optimal degree of debt financing
 

After-Tax Real Asset Cash Flows:
After-Tax Operating Cash Flows:
After-Tax Earnings Assuming the Firm Finances the Project with Equity Only.
 
 

Ignores:

Interest payments from debt financing and the Tax benefit from those interest payments.

DEFINITION:

  After-Tax Real Asset Cash Flows at time t {Y(t)*(1-T_c)}
 

EBIT
PLUS
+ depreciation and amortization (non-cash expenses)
+ Sales of capital assets
+ Realized capital losses

MINUS
- Change in working capital
- Capital expenditures
- Realized capital gains
- EBIT times the corporate tax rate.

+ Depreciation 600,000
- Working capital change (80,000)
+ Revenue from sale of asset 40,000
- Realized Capital Gain (10,000)

Real Cash Flow Before Taxes 1,640,000
Tax {1,090,000 times .34} (370,600)

After-Tax Real Cash Flow 1,269,400
 

Note that the Taxes Charged to the Project is not the true taxes Paid. In fact the actual tax payment will allow for an interest deduction. It is the VALUE of the tax savings from this interest deduction which is the subject of today’s lecture.

Note that in the Absence of taxes (and other frictions):
 

WACC is independent of capital structure. Thus, the appropriate discount rate to use for any project (regardless of how financed) would be the WACC if the comparison firm(s) were pure equity financed. That is:

So it doesn’t matter what the financing arrangements are.

Similarly with the Beta of the Project, relative to the Comparison firms:

Risk After Accounting For Taxes:

In contrast to the Perfect Capital Market setting, the firm’s capital structure will effect the observed Betas and thus the estimate of the comparison firm’s asset Betas.

                    ASSETS                                 LIABILITIES

MV of Oper. Assets(OA)                   Debt                 $1,000,000

                    $3,660,000                    Equity               $3,000,000

MV of Tax Assets(TA)
                    340,000

Total         $4,000,000                         Total               $4,000,000

Again, we can think of the firm’s total assets as a portfolio of two different kinds of assets, the operating assets (machines, buildings, growth opportunities) and the Tax Assets (the Tax benefit from leverage)

Then the firm’s Total Beta (b_A) is simply the weighted sum of the Betas of the Operating Assets (b_{OA) and the Tax Assets (}b_TXA).

So that:

            b_A = ((OA/D+E)) (b_{OA) + ((TXA/D+E)) (}b_TXA)

Also, you will recall that:

            b_A = b_{E (E/E+D) +} b_{D (D/D+E)}

_{Therefore, estimating the Operating Beta from the Betas of the Debt and Equity would be incorrect since the Observed Operating Beta (}b_{A) will include the impact of financing. Thus we need to "subtract out" the impact of leverage and taxes on our estimates of the firm’s operating beta. In fact, what we want to estimate is:}

      b_{OA the operating Beta of the firm if the firm were totally equity financed.}

_{Hamada:
Assuming:
            (1) All debt is perpetual and risk free
            (2) The Tax saving from debt is risk free and equal to: TcD:
Then:}
                b_{A = [(D + E+ TcD)/(D+E)]} b_OA

_{And we know that:}
                b_{A =} b_{E (E/E+D)}

_{Substituting for} b_{A and solving yields an expression for the relationship between} b_{E and} b_OA

                b_{E = [1 + (1-TC)(D/E)]} b_OA
or:
               b_OA= b_{E/[1 + (1-TC)(D/E)]}

_{Thus, we can get the unleveraged Beta from the Equity Beta and the leverage ration as well as the tax rate.}

_{The Widget Example :
Recall:
                                    Equity Beta         D/V         D/E}         b_OA

        _{Acme                         1.2                 .5             1
        Best                           1.0                 .3             3/7
        Consol.                      1.1                 .4             2/3}

_{Assume the Corporate Tax rate is 34%, then the asset betas become:}

            b_OA= b_{E/[1 + (1-TC)(D/E)]}

_{The Adjusted Present Value Method}

<sub>1. Estimate After-Tax Real Cash Flows, using the definition as the after tax cash flows that would exist if the firms were equity financed.
2. Estimate the</sub> b<sub>OA of the Comparison firms
3. Plug that into the CAPM for the appropriate Discount rate.
4. Find the NPV of the After-Tax Real Cash Flows
5. Add to this the Present Value of any Financing Subsidies</sub>
 

_{Benefits of the APV Method:}
 

_{Is quite versatile, and can handle complications like:}

• _{The possibility of a wealth transfer from bondholders to stockholders (or stockholders to bondholders) must also be considered.}
• _{Dynamic Debt Policy}
• _{Complicated Tax Considerations}
• _{Risky Debt and Risky Tax Shields}

_{The Weighted Average Cost of Capital Method (WACC)}

_{Recall that the WACC is the Firm’s Capitalization rate. Thus we can calculate the WACC as follows:}
 

            _{V =}

_{Note that the numerator here is the firm’s Operating Cash Flows:.}

_{When there are taxes, and a Corporate Tax Subsidy, the the numerator is not quite obvious:..}

_{What we want in the Numerator is the firm’s After-Tax Real Asset Cash Flows. Note very important: We do not want the tax subsidy resulting from the debt financing in the numerator. This will be accounted for by a reduction in the capitalization Rate.}
 

_{The After Tax WACC is defined as:}