*Extensions on the WACC Approach*The weighted average cost of capital approach, where the optimal debt ratio is assumed to be the one at which the cost of capital is minimized works if:

(a) operating income and cash flows are unaffected by leverage

(b) firms maintain a market value debt ratio over time

(c) firms do not have any other constraints that may prevent them from moving to the optimal, including regulatory or legal limits.

To the extent that these assumptions are unreasonable, the cost of capital approach may have to be modified. One obvious extension is to make the operating income a function of the firm's default risk (or rating), and choosing the debt ratio that maximizes firm value (rather than minimizing operating income). Similarly constraints imposed by regulators, managment or lenders can be built into the process. The most difficult assumption to overcome is the assumption of a constant market debt ratio. To the degree that this makes users uncomfortable, the adjusted present value approach may provide a more realistic solution.*Building in Constraints*The simplest way to build in constraints is to stay within the framework of the cost of capital approach, and view minimizing the cost of capital, subject to the constraint, as the objective function. For instance, one very common constraint imposed by regulators, bondholders and managers is a constraint that the book value debt ratio not exceed a specified number. Since the analysis we have done so far has focused on market value debt ratios, there is the risk that the book value constraint may be violated. There are two solutions:

1. The first is to do the entire analysis using book value of debt and equity, looking for the optimal debt ratio. Since the approach we have described is driven by cash flows, the optimal dollar debt that is computed should not be affected significantly by doing this.

2. The second and more general approach (since it can be used to analyze any kind of constraint) is to keep track of the book value debt ratio in the traditional analysis, and view the optimal capital structure as the one the minimizes the cost of capital subject to the book value debt ratio being lesser than the specified constraint.

*Applying Cost of Capital Approach to Financial Service Firms*There are several problems in applying the cost of capital approach to financial service firms, such as banks and insurance companies. The first is that the interest coverage ratio spreads, which are critical in determining the bond ratings, have to be estimated separately for financial service firms; applying manufacturing company spreads will result in absurdly low ratings for even the safest banks, and very low optimal debt ratios. The solution is to use interest coverage ratios tailored for financial service firms, rather than the manufacturing firm ratios.

The second is a measurement problem that arises partly from the difficulty in estimating the debt on a financial service company’s balance sheet. Given the mix of deposits, repurchase agreements, short term financing and other liabilities that may show up on the balance sheet, one solution may by to focus only on long term debt, defined tightly, and to use interest coverage ratios defined consistently.

The third problem is that financial service firms may find their operating income affected by their bond rating; as the rating drops, the operating income might drop too. The solution is to make the operating income a function of the bond ratings.

Finally, minimizing cost of capital in a bank has to work within the constraints on book capital ratios imposed by regulatory authorities.*Normalizing Earnings: Some Simple Approaches*In estimating optimal debt ratios, it is always more advisable to use normalized operating income, rather than current operating income. Most analysts normalize earnings by taking the average earnings over a period of time (usually 5 years). Since this holds the scale of the firm fixed, it may not be appropriate for firms which have changed in size over time. The right way to normalize income will vary across firms:

1. For cyclical firms, whose current operating income may be overstated (if the economy is booming) or understated (if the economy is in recession), the operating income can be estimated using the average operating margin over an entire economic cycle (usually 5 to 10 years)

Normalized Operating Income = Average Operating Margin (Cycle) * Current Sales

2. For firms which have had a bad year in terms of operating income, due to firm-specific factors (such as the loss of a contract), the operating margin for the industry in which the firm operates can be used to calculate the normalized operating income:

Normalized Operating Income = Average Operating Margin (Industry) * Current Sales

The normalized operating income can also be estimated using returns on capital across an economic cycle (for cyclical firms) or an industry (for firms with firm-specific problems), but returns on capital are much more likely to be skewed by mismeasurement of capital than operating margins.

*Getting Inputs for Expected Bankruptcy Cost for Adjusted Present Value Approach*Of the three inputs needed for the APV approach - the unlevered firm value, tax benefits and the expected bankruptcy costs - the expected bankruptcy cost is the most difficult to estimate. 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 p

_{a}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 as follows–

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

= p_{a}BC

There are two basic ways in which the probability of bankruptcy can be indirectly estimated. 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 each rating. The other approach is to use a statistical approach, such as a probit, to estimate the probability of default, based upon the firm’s observable characteristics, at each level of debt.

The bankruptcy cost can be estimated, albeit with considerable noise, from studies that have looked at the magnitude of this cost in actual bankruptcies. It will vary across firms, depending upon the magnitude of indirect bankruptcy costs. Combining the results of Warner on direct bankruptcy cost and Shapiro on indirect bankruptcy cost may provide a measure of the total bankruptcy costs faced by firms.

*Minimizing WACC versus Adjusted Present Value Approaches*Both approaches require heroic assumptions at some stage in the analysis. The cost of capital approach is based upon the assumption that the market debt ratio will be maintained over the long term, and that the savings from reducing cost of capital (though implicit) will be weighted as heavily as explicit savings. The adjusted present value approach, by focusing on a dollar debt figure, avoids the problems associated with targeting debt ratios, but it runs aground on estimation problems. If it is difficult to estimate costs of equity and debt at different debt ratios, it is even more difficult to estimate the probabilities of bankruptcy and bankruptcy cost

*Building a Cross-Sectional Regression*To build a cross sectional regression for the debt ratio, we began with the benefits and costs of debt in the abstract - the tax benefit and the added discipline on the plus side, and the bankruptcy costs, agency costs and lost flexibility on the minus side. We then looked for measurable proxies for each variable. For the tax benefit, this could be the tax rate or the existence of other tax deductions (such as depreciation). For added discipline, this could be the percent of stock held by manageers. Presumably, firms with significant insider holdings do not need the discipline of debt. For bankruptcy costs, this could be the variability in opeating income; firms with high variability will have higher bankruptcy risk. (Measures such as ratings cannot be used, since they might reflect the current borrowings of the firm). For agency costs, this could be the type of and the liquidity in the assets owned by the firm. Firms with tangible and liquid assets should have fewer agency costs than firms without these assets. Finally, for flexibility, the proxy may be the magnitude of and uncertainty about future investment needs.

It is conceivable that we could explain more of the difference in debt ratios by throwing in other variables into the regression, but kitchen-sink regressions are dangerous and may not be very useful in coming up with predicted debt ratios.