A Reconsideration of Tax Shield Valuation

A quarter‐century ago, Miles and Ezzell (1980) solved the valuation problem of a firm that follows a constant leverage ratio L = D/S. However, to this day, the proper discounting of free cash flows and the computation of WACC are often misunderstood by scholars and practitioners alike. For example, it is common for textbooks and fairness opinions to discount free cash flows at WACC with beta input β _S = [1 + (1 ? τ)L]β_u, although the latter is not consistent with the assumption of constant leverage. This confusion extends to the valuation of tax shields and the proper implementation of adjusted present value procedures. In this paper, we derive a general result on the value of tax shields, obtain the correct value of tax shields for perpetuities, and state the correct valuation formulas for arbitrary cash flows under a constant leverage financial policy.     

FINDING VALUE WHERE NONE EXISTS: PITFALLS IN USING ADJUSTED PRESENT VALUE

There are several conceptually "correct" methods for valuing firms and projects, including the weighted average cost of capital (WACC) approach, the flows to equity (FTE) method, and the adjusted present value (APV) or valuation-by-components method. The author examines the relative advantages of these frameworks and offers guidance as to when they are likely to be most useful. The key message is a caution to would-be users of APV: it is frequently unreliable and should be used only in conjunction with more conventional valuation frameworks. It works best in transactions that involve structured financings, such as leveraged buyouts and project and real estate financings. Even in these cases, however, its usefulness depends on theoretical concepts that in practical applications have a wide margin of error.
In general, WACC is a robust and appropriate valuation framework as long as the firm has a target debt ratio. The FTE method is most relevant for acquisitions and very large projects. The author shows how APV and FTE can be formulated to be consistent with the WACC valuation. The issue, however, is not whether the techniques can be made consistent through relatively complex adjustments by sophisticated users, but rather what happens when they are used in everyday applications by practitioners unfamiliar with the somewhat arcane valuation issues involved.     

Using APV (adjusted present value): a better tool for valuing operations

Anyone who learned valuation techniques more than a few years ago is probably due for a refresher course. For the past 25 years, managers have been taught that the best practice for valuing assets-that is, an existing business, factory, product line, or market position-is to use a discounted-cash-flow (DCF) methodology. That is still true. But the particular version of DCF that has been accepted as the standard-using the weighted-average cost of capital (WACC)-is now obsolete. Today's better alternative, adjusted present value (APV), is especially versatile and reliable. It will likely replace WACC as the DCF methodology of choice among generalists. Like WACC, APV is used to value operations, or assets-in-place-that is, any existing asset that will generate a stream of future cash flows. Timothy Luehrman explains APV and walks readers through a case example designed to teach them how to use it. He argues that APV always works when WACC does-and sometimes when WACC doesn't, because it requires fewer restrictive assumptions. And APV is less prone to yield serious errors than WACC is. But, most important, general managers will find that APV's power lies in the managerially relevant information it provides. APV can help managers analyze not only how much an asset is worth but also where the value comes from.     

TWO DCF APPROACHES FOR VALUING COMPANIES UNDER ALTERNATIVE FINANCING STRATEGIES (AND HOW TO CHOOSE BETWEEN THEM)

This is the sequel to the authors' 1989 article discussing the two basic discounted cash flow approaches for valuing debt-financed transactions and corporations: weighted average cost of capital (WACC) and adjusted present value (APV). The WACC method discounts all after-tax (but pre-interest) cash flows at the company's weighted average cost of capital. The APV method treats the value of a levered firm as the value of the same firm if financed entirely with equity plus the discounted value of the interest tax shields from the debt its assets will support. The authors argue that the WACC approach is more practical if the firm intends to hold its (market) leverage ratio relatively constant over time, but that the APV technique is the preferred method if the firm plans to reduce its leverage ratio according to a pre-determined schedule (as tends to be the case in highly leveraged transactions).     

Incorporating Competition into the APV Technique for Valuing Leveraged Transactions

According to a recent survey, the discounted cash flow approach is the valuation technique most widely used by companies evaluating acquisition targets. But because the DCF approach is inappropriate when the capital structure is changing during the forecast period, many analysts turn to the adjusted present value (APV) approach, which can easily accommodate a changing capital structure. Still, the finance literature has not shown how to incorporate assumptions about the effect of competition in the post-forecast period into an APV analysis.
This paper provides two new tools for calculating horizon values with changing leverage and competition. First, it provides a new model, based on more realistic assumptions, for valuing a growing annuity of free cash flows when ROIC is expected to decline due to competition. Second, it provides a model for valuing tax shields that correctly incorporates the impact of competition in the post-forecast period. When used together with the APV approach, these two new tools allow an analyst to estimate the value of a company with a changing capital structure that faces competition in the post-forecast period.     

Two Different Ways of Treating Corporate Cash in FCF Valuations—and the Importance of Getting the Cost of Capital Right

The methods for calculating free cash flow presented in texts on financial statement analysis and valuation appear to be very different from those in corporate finance texts, causing some confusion among academics as well as practitioners. Financial statement analysis and valuation texts generally begin by valuing just the enterprise operations—that is, the entity that engages in the firm's primary revenue‐generating activities—and then adding back the value of its cash holdings and other financial assets. The corporate finance approach is typically to value all the assets together, including financial assets that are not used in the production of the goods and services provided by the firm. Using a simple example, the authors show that the valuation of the equity ownership of the firm should be the same for both methods of calculating free cash flow, provided the analyst makes the appropriate adjustments to the method for calculating the cost of capital (WACC) used to discount forecasted free cash flows to a present value.     

The valuation of projects under the dividend imputation tax system

This paper proves that a modified weighted average cost of capital (“WACC”) valuation methodology is a rigorous and practicable method of valuing projects and companies under the Australian dividend imputation tax system. This methodology uses an effective tax rate in calculating both the discount rate and the ungeared after tax cash flow. A cash flow after effective corporate tax is shown to be equivalent to a cash plus value of imputation credit stream. Importantly, this valuation methodology is applicable to returns that are non-uniform and of finite duration. Also examined is the discounting of equity returns at the company's cost of equity capital. A worked example is presented to clarify and quantify the effects discussed.     

Beta Geared and Ungeared: Further Analysis of the Case of Active Debt Management

This paper extends previous work by Appleyard and Strong (1989) concerned with the implications of an active debt management policy (ADMP) for de-gearing a geared firm's equity beta. First, alternative derivations of the ADMP beta de-gearing formulae for an MM perfect capital market with corporation tax and for a world with corporation and personal taxes are presented. These derivations do not require the assumption of level perpetuity expected cash flows and therefore indicate a broader basis for the ADMP beta de-gearing formulae than previously demonstrated. Secondly, possible investor valuation errors from use of a PDMP (passive debt management policy) valuation methodology to value firms pursuing an ADMP are analysed in the context of an MM perfect capital market with corporation tax. Given constant (or zero) growth in the firm's expected unlevered cash flows, this analysis indicates that degearing errors from use of the PDMP beta de-gearing formula will only be associated with valuation errors if there is a change in the firm's target debt ratio and that the significance of such valuation errors will be largely dependent on the expected growth rate.     

What's it worth? A general manager's guide to valuation

Behind every major resource-allocation decision a company makes lies some calculation of what that move is worth. So it is not surprising that valuation is the financial analytical skill general managers want to learn more than any other. Managers whose formal training is more than a few years old, however, are likely to have learned approaches that are becoming obsolete. What do generalists need in an updated valuation tool kit? In the 1970s, discounted-cash-flow analysis (DCF) emerged as best practice for valuing corporate assets. And one version of DCF-using the weighted-average cost of capital (WACC)-became the standard. Over the years, WACC has been used by most companies as a one-size-fits-all valuation tool. Today the WACC standard is insufficient. Improvements in computers and new theoretical insights have given rise to tools that outperform WACC in the three basic types of valuation problems managers face. Timothy Luehrman presents an overview of the three tools, explaining how they work and when to use them. For valuing operations, the DCF methodology of adjusted present value allows managers to break a problem into pieces that make managerial sense. For valuing opportunities, option pricing captures the contingent nature of investments in areas such as R&D and marketing. And for valuing ownership claims, the tool of equity cash flows helps managers value their company's stake in a joint venture, a strategic alliance, or an investment that uses project financing.     

Discounting Mean Reverting Cash Flows with the Capital Asset Pricing Model

Discounting cash flows requires an equilibrium model to determine the cost of capital. The CAPM of Sharpe and the intertemporal asset pricing model of Merton (1973) offer a theoretical justification for discounting at a constant risk adjusted rate. Two problems arise with this application. First, for mean reverting cash flows the risk adjustment is unknown, and second, if the present value is compounded forward then the distribution of future wealth is likely right skewed. I develop equilibrium discount rates for cash flows whose level or growth rate is mean reverting. Serial correlation also largely eliminates the skewness problem.     

Adapting the APV valuation methodology and the beta gearing formula to the dividend imputation tax system

This paper adapts the APV valuation methodology and the formula for gearing beta to the Australian dividend imputation tax system. The APV formulation is shown to be able to be applied in the dividend imputation tax system by simply replacing the statutory tax rate with an effective tax rate in the calculation of the “cash flows”. The effect of the dividend imputation tax system on a company's value is shown to be easily bounded using the APV formulation by making the extreme assumption that imputation credits are either: fully distributed and fully valued by the market; or that they are worthless. This paper also quantifies the effect of changing the assumed value of imputation credits on: (i) the value of the interest tax shield of debt; and (ii) the levered, or equity, beta.     

Risk-adjusted discount rates and capital budgeting under uncertainty

This paper is concerned with the valuation of multiperiod cash flows in a world where prices are determined according to the Sharpe-Lintner-Black model of capital market equilibrium. We find that the current market value of any future net cash flow is the current expected value of the flow discounted at risk-adjusted discount rates for each of the periods until the flow is realized. The discount rates are known and non-stochastic, but the rates for the different periods preceding the realization of a cash flow need not to be the same, and the rates relevant for a given period can differ across cash flows. The risk adjustments in the discount rates arise because of uncertainties about reassessments through time of the expected value of a flow and the relationships between these reassessments and the corresponding reassessments of the expected cash flows of all firms.     

Implementing Fischer Black's Simple Discounting Rule

Corporate managers typically estimate the value of capital projects by discounting the project's expected future net cash flows at the cost of capital. The capital asset pricing model (CAPM) is generally used to estimate that cost. But, as anyone who has worked on the finance or business development staff of a public company can attest, there are major challenges in applying the CAPM, including largely unresolved questions about what constitutes the “market portfolio,” how to estimate market risk premiums, and how to estimate the betas of projects. In a short article published in Financial Management in 1988, Fischer Black proposed a valuation “discounting rule” that avoids all these problems—one that involves discounting a relatively certain (as opposed to an expected or average) level of operating cash flows at the risk-free rate. But Black's article does not address the question of how to calculate these “certainty equivalent” or “conditional” cash flows. In this article, the authors propose a way of implementing Black's rule that involves estimating the “conditional” cash flows in a three-step procedure:

• • Find a benchmark security that correlates with the project's cash flows;
• • Estimate the percentiles of the distribution in which the benchmark return equals the risk-free rate over different investment horizons;
• • Use information from corporate managers to assess the cash flows that define the same percentiles in the cash flow distributions.

As the authors point out, the virtue of Black's rule is that it shifts the focus of the analyst away from the assessment of discount factors and puts it squarely on the more challenging, and arguably more relevant, problem of estimating the project's cash flows.     

Valuation in Emerging Markets: A Simulation Approach

Most of the foundations of valuation theory have been designed for use in developed markets. Because of the greater, and in some cases different, risks associated with emerging markets (although recent experience might suggest otherwise), investors and corporate managers are often uncomfortable using traditional methods. The typical way of capturing emerging-market risks is to increase the discount rate in the standard valuation model. But, as the authors argue, such adjustments have the effect of undermining some of the basic assumptions of the CAPM-based discounted cash flow model. The standard theory of capital budgeting suggests that estimates of unconditional expected cash flows should be discounted at CAPM discount rates (or betas) that reflect only “systematic,” or “nondiversifiable,” market-wide risks. In practice, however, analysts tend to take what are really estimates of “conditional” expected cash flows—that is, conditional on the firm or its country avoiding a crisis—and discount them at higher rates that reflect not only systematic risks, but diversifiable risks that typically involve a higher probability of crisis-driven costs of default. But there is almost no basis in theory for the size of the increases in discount rates. In this article, the authors propose that analysts in emerging markets avoid this discount rate problem by using simulation techniques to capture emerging-market risks in their estimates of unconditional expected cash flows—in other words, estimates that directly incorporate the possibility of an emerging-market crisis and its consequences. Having produced such estimates, analysts can then discount them using the standard Global CAPM.     

Quantifying time value errors

Time valuation of cash flows is an essential part of personal financial planning and management. Many financial arrangements are priced according to a cash-flow valuation model. Expected cash flows associated with a stock or bond are discounted at an appropriate risk-adjusted rate in order to determine the fair value of the financial asset. Home mortgage loans are priced according to the discounted value of the future principal and interest cash flows. Yet, despite the importance of the discounted cash flow methodology in pricing assets, computational errors are often made when discount factors are not calculated precisely. This article attempts to quantify the magnitude of the error when the mathematical function for present value is ignored and interpolation is used instead to determine the discount factor.     

Cash Flow Sensitivity of Investment

Investment cash flow sensitivity is associated with both underinvestment when cash flows are low and overinvestment when cash flows are high. The accessibility of external capital is positively correlated with cash flows, intensifying investment cash flow sensitivity. Managers actively counteract the variations in internal and external liquidity by accumulating working capital when liquidity is high and draining it when liquidity is low. These results imply that cash flow sensitive firms face financial constraints, which are binding in low cash flow years. Traditional indicators of financial constraints, such as size and dividend payout, successfully distinguish firms that may potentially face constraints, but are less successful in distinguishing between periods of tight and relaxed constraints. These periods are much more clearly separated by the KZ index, which, on the other hand, is less successful in identifying firms that are likely to face liquidity constraints.     

Capital Project Analysis When Cash Flows Evolve as a Continuous Time Branching Process

Optimal capital budgeting criteria now exist for a variety of applications when project cash flows (or present values) evolve in terms of the well-known geometric Brownian motion. However, relatively little is known about the capital budgeting procedures that ought to be implemented when cash flows are generated by stochastic processes other than the geometric Brownian motion. Given this, our purpose here is to develop optimal investment criteria for capital projects with cash flows that evolve in terms of a continuous time branching process. Branching processes are compatible with an empirical phenomenon known as 'volatility smile'. This occurs when there are systematic fluctuations in the implied volatility of a capital project's cash flows as the cash flow grows in magnitude. A number of studies have shown that this phenomenon characterizes the cash flow streams of the capital projects in which firms typically invest. We implement optimal capital budgeting procedures for both the continuous time branching process and the geometric Brownian motion using cost and revenue data for the Stuart oil shale project in central Queensland, Australia. This example shows that significant differences can arise between the optimal investment criteria for cash flows based on a branching process and those based on the geometric Brownian motion. This underscores the need for the geometric Brownian motion broadly to reflect the way a given capital project's cash flows actually evolve if serious errors in valuation and/or capital budgeting decisions are to be avoided.     

Personal Taxation in Firm Market Valuation: Theory and Test*

In this paper, I extend Ohlson's 1995 firm market valuation model to incorporate personal taxes: the taxes on dividends and the taxes on capital gains. Without personal taxes, firm market value can be expressed as the present value of future benefits received by the shareholders (dividends, in this case). With personal taxes, the benefits received by the shareholders should be classified into three categories (due to their different tax treatments): dividends, share repurchases, and new share issues (i.e., contributed capital). The extended model shows the effects of personal taxation on firm market valuation: retained earnings are valued less than contributed stocks, both dividends taxes and capital gains taxes affect retained earnings valuation and firm market value, and firms choose cash distribution methods (paying dividends and repurchasing shares) to increase their retained earnings valuation, therefore increasing their market value. An empirical test using a sample from the Disclosure Select Canada and Financial Post Card data bases for the years 1995‐98 supports these personal tax effects.     

Estimating cost of capital in firm valuations with arithmetic or geometric mean – or better use the Cooper estimator?

We test the extent and determinants of bias effects of the arithmetic as well as the geometric mean estimator and the estimator of Cooper [1996. Arithmetic versus geometric mean estimators: Setting discount rates for capital budgeting. European Financial Management 2 (July): 157–67] regarding discount rate estimation for firm valuation by way of a bootstrap approach for 13 different countries. The Cooper estimator is superior to both the geometric and the (conventional) arithmetic mean estimator. However, a ‘truncated’ version of the arithmetic mean estimator leads generally to better estimation outcomes than the Cooper estimator. This means that, in order to reduce problems of upward-biased firm value estimates, expected cash flows beyond a certain time horizon are completely neglected in terminal value estimation. Such an approach seems particularly reasonable for the valuation of young growth companies as well as for companies from quickly developing countries such as Brazil, China, or Thailand, because the bias in terminal value estimation is increasing in the growth rate of future expected cash flows.