Adjusted present value (APV) is similar to NPV. The difference is that is uses the cost of equity as the discount rate (rather than WACC). Separate adjustments are made for the effects financing (e.g. the tax advantages of debt).
As usual with DCF models of this sort, the calculation of adjusted present value is straightforward but tedious.
The first step in calculating an APV is to calculate a base NPV using the cost of equity as the discount rate. This may be the same as the company's cost of equity. In some cases it may be necessary to recalculate it by estimating a beta and using CAPM. This is most likely when assessing a project or business that is very different from a company's core business.
Once the base NPV has been calculated, the next step is to calculate the NPV of each set of cash flows that results from financing. The most obvious of these are the tax effects of using debt rather than equity. These can be discounted either at the cost of debt or at a higher rate that reflects uncertainties about the tax effects (e.g. future tax rates, whether the company as a whole will be profitable and paying tax). The NPV of the tax effects is then added to the base NPV.
If there are other effects of financing, then these are also added or subtracted, and the end result is the APV.
Given capital structure irrelevance, the savings from financing should be balanced by changes in the required return on equity with changes in capital structure. This usually makes a simple NPV with the WACC as the discount rate preferable.