Risk Analysis

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Adjusted Present Value Normal NPV calculation:
NPV = −investment + CFN CF1 CF2 + +L+ 2 (1 + WACC) (1 + WACC) (1 + WACC) N

where, in a simple situation:     equity debt WACC =     equity + debt (cos t of equity ) +  equity + debt (cos t of debt )(1 − tax rate )      Using debt for financing has a tax advantage in that interest payments are tax deductible. This tax deductibility is a source of value for the firm. In the normal NPV calculation, this additional value is accounted for in the WACC. However, in many cases the capital structure of the project may change over time. In other cases the tax rate faced by the firm may be expected to change over time (as firm goes from loss to profit, or special tax subsidies expire etc.). In other cases, the firm may be able to obtain subsidized financing from a government agency for the project. In all of these circumstances, these types of things mean that the WACC for the project will change, and may even change each year of the project’s life. Incorporating these types of factors into an NPV-WACC calculation is possible, but very complicated. The normal assumption is that the WACC is the same for each cashflow and each year of the project. These more complicated situations are more easily handled by using Adjusted Present Value (APV). APV is based on the following: APV = NPV of project assuming it is all equity financed + NPV of financing effects Essentially, APV breaks the total value of the project into parts: one part is the value assuming no debt is used, and then you add on the extra value created from using debt in the capital structure.

Consider an example: A firm is considering a project that will last 5 years. It will generate cashflows of $9 million annually. The initial investment required in the project is $28 million. Assume that the cost of equity for the project is 20% if the project is 100% equity financed.1 For the project, the firm will be able to obtain some short term debt...
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