There is no argument that WACC is the most widely used method to asses the overall cost of capital to judge business whether it is profitable or not. However WACC has also limitations and its calculations are bound to equity and debt financing and their calculated ratios. When projects have side effects which have other contributions on cost of capital, the APV model is more handy.

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). This is because an assumption is made as the company is all financed through equity and leverage is zero at start. Then separate adjustments are made for all other side effects (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 Mechanics of APV Valuation

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.

In brief, we estimate the value of the firm in three steps. We begin by estimating the value of the firm with no leverage. We then consider the present value of the interest tax savings generated by borrowing a given amount of money. Finally, we evaluate the effect of borrowing the amount on the probability that the firm will go bankrupt, and the expected cost of bankruptcy.

#### Cost of Capital versus APV Valuation

In the cost of capital approach, the effects of leverage show up in the cost of capital, with the tax benefit incorporated in the after-tax cost of debt and the bankruptcy costs in both the levered beta and the pre-tax cost of debt. Will the two approaches yield the same value? Not necessarily. The first reason for the differences is that the models consider bankruptcy costs very differently, with the adjusted present value approach providing more flexibility in allowing you to consider indirect bankruptcy costs. To the extent that these costs do not show up or show up inadequately in the pre-tax cost of debt, the APV approach will yield a more conservative estimate of value. The second reason is that the APV approach considers the tax benefit from a dollar debt value, usually based upon existing debt. The cost of capital approach estimates the tax benefit from a debt ratio that may require the firm to borrow increasing amounts in the future. For instance, assuming a market debt to capital ratio of 30% in perpetuity for a growing firm will require it to borrow more in the future and the tax benefit from expected future borrowings is incorporated into value today.

There are many who believe that adjusted present value is a more flexible way of approaching valuation than traditional discounted cash flow models. This may be true in a generic sense, but APV valuation in practice has significant flaws. The first and most important is that most practitioners who use the adjusted present value model ignore expected bankruptcy costs. Adding the tax benefits to unlevered firm value to get to the levered firm value makes debt seem like an unmixed blessing. Firm value will be overstated, especially at very high debt ratios, where the cost of bankruptcy is clearly not zero and, in some instances, the cost of bankruptcy is higher than the tax benefit of debt.

## No comments:

Post a Comment