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# Adjusted Present Value (APV) Approach

The adjusted present value (APV) method is a model that shows how the value of a project to the levered firm (the adjusted present value) is equal to the value of the project to an unlevered firm (NPV) plus the net present value of the financing side effects (NPVF), or the net present value of financing. As a formula:

There are four major considerations for the APV method: the tax subsidy to debt, the cost of financial distress, the cost of issuing new securities, and the subsidies to debt financing. While each of these four factors are important when calculating the NPVF, the tax subsidy to debt is by far the most important. In practice questions, we typically look most closely at the tax subsidy to debt when calculating NPVF.

Tax subsidy to debt: For perpetual debt (that is, assuming that the firm maintains the same capital structure, simply rolling over its current debt into new borrowing) the value for the tax subsidy is equal to TCB (where TC is the corporate tax rate times, and B is the value of debt).

Costs of financial distress: The chance of the firm entering financial distress implies costs, which lower the value of the financing side effects.

Costs of issuing new securities: Those who participate in helping a firm issue new securities must be compensated for their time and effort, a cost that lowers the value of financing.

Subsidies to debt financing: Often corporations are encouraged to undertake projects by governments by being offered loans at interest rates below market value. The lower cost of borrowing is a subsidy that increases the value of financing.

Using the Formula:

NPV: We use ro, the expected return to equity of an unlevered firm, and the unlevered cash flows (the expected cash flows after tax, but before interest payments), to calculate NPV. If it is not given in the question, we can find the expected return to an unlevered firm by taking the observed beta of the levered firm (Bequity), and finding the corresponding beta for the firm if it was all equity (Basset). We can then plot the asset beta on the security market line to find the expected return of the firm if it was all equity.

NPVF: The present value of the financing side effects can typically simply be found by finding the tax shield from the debt financing of the project, calculated in perpetuity.

NPVF = TCB

Therefore,

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