## Steps in the Adjusted Present Value approach

In the Adjusted Present Value approach, we assume that the primary benefit of borrowing is a tax benefit, and that the most significant cost of borrowing is the added

23 The normal range for long term interest rates in the United States for the last 40 years has been between 4 and 8%. There was a short period between 1978 and 1982 when long term interest rates were much higher.

risk of bankruptcy. To estimate the value of the firm, with this assumption, we proceed 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. Step 1: Estimate the value of the firm with no debt: The first step in this approach is the estimation of the value of the unlevered firm. This can be accomplished by valuing the firm as if it had no debt, i.e., by discounting the expected after-tax operating cash flows at the unlevered cost of equity. In the special case where cash flows grow at a constant rate in perpetuity,

Value of Unlevered Firm = FCFFo (1+g)/(pu - g) where FCFF0 is the current after-tax operating cash flow to the firm, pu is the unlevered cost of equity, and g is the expected growth rate. The inputs needed for this valuation are the expected cashflows, growth rates and the unlevered cost of equity. To estimate the latter, we can draw on our earlier analysis and compute the unlevered beta of the firm -

where

Punlevered = Unlevered beta of the firm, Pcurrent = Current equity beta of the firm, t = Tax rate for the firm and D/E = Current debt/equity ratio. This unlevered beta can then be used to arrive at the unlevered cost of equity. Alternatively, we can take the current market value of the firm as a given and back out the value of the unlevered firm by subtracting out the tax benefits and adding back the expected bankruptcy cost from the existing debt.

Current Firm Value = Value of Unlevered firm + PV of tax benefits - Expected Bankruptcy cost

Value of Unlevered firm = Current Firm Value - PV of tax benefits + Expected Bankruptcy costs

Step 2: Estimate the present value of tax benefits from debt: The second step in this approach is the calculation of the expected tax benefit from a given level of debt. This tax benefit is a function of the tax rate of the firm and is discounted at the cost of debt to reflect the riskiness of this cash flow. If the tax savings are viewed as a perpetuity, Value of Tax Benefits =[ Tax Rate * Cost of Debt * Debt] / Cost of Debt = Tax Rate * Debt

The tax rate used here is the firm's marginal tax rate, and it is assumed to stay constant over time. If we anticipate the tax rate changing over time, we can still compute the present value of tax benefits over time, but we cannot use the perpetual growth equation cited above.

Step 3: Estimate the expected bankruptcy costs as a result of the debt: The third step is to evaluate the effect of the given level of debt on the default risk of the firm and on expected bankruptcy costs. In theory, at least, this requires the estimation of the probability of default with the additional debt and the direct and indirect cost of bankruptcy. If na is the probability of default after the additional debt and BC is the present value of the bankruptcy cost, the present value of expected bankruptcy cost can be estimated-

PV of Expected Bankruptcy cost = Probability of Bankruptcy * PV of Bankruptcy Cost

This step of the adjusted present value approach poses the most significant estimation problem, since neither the probability of bankruptcy nor the bankruptcy cost can be estimated directly. There are two basic ways in which the probability of bankruptcy can be estimated indirectly. One is to estimate a bond rating, as we did in the cost of capital approach, at each level of debt and use the empirical estimates of default probabilities for

Bankruptcy Cost: This is the cost associated with going bankruptcy. It includes both direct costs (from going bankrupt) and indirect costs (arising from the perception that a firm may go bankrupt).

each rating. For instance, table 8.18, extracted from a study by Altman and Kishore, summarizes the probability of default over ten years by bond rating class in 1998.24 Table 8.18: Default Rates by Bond Rating Classes

 Bond Rating Default Rate

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