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.     

How Do Investment Banks Value Initial Public Offerings (IPOs)?

Abstract:  We investigate the valuation and the pricing of initial public offerings (IPOs) by investment banks for a unique dataset of 49 IPOs on Euronext Brussels in the 1993–2001 period. We find that for each IPO several valuation methods are used, of which Discounted Free Cash Flow (DFCF) is the most popular. The offer price is mainly based on DFCF valuation, to which a discount is applied. Our results suggest that DDM tends to underestimate value, while DFCF produces unbiased value estimates. When using multiples, investment banks rely mostly on future earnings and cash flows. Multiples based on post-IPO forecasted earnings and cash flows result in more accurate valuations.     

The Incremental Information Content of Earnings and Cash Flows from Operations Affected by Their Extremity

Previous returns studies have shown that extreme earnings and extreme cash flows from operations are less informative than moderate (i.e., less extreme) earnings and moderate cash flows. Studies also report that cash flows supplement to earnings in firm valuation by showing a higher association of cash flows with returns when earnings are extreme than when earnings are moderate. We propose that this supplementary role of cash flows is affected by cash flows extremity. Using data from the US capital markets, we find that the supplementary role of cash flows exists only when cash flows are not extreme. We also investigate the supplementary role of earnings to cash flows and search for a higher association of earnings with returns when cash flows are extreme than when cash flows are moderate. Similar to results on cash flows, our findings show that the supplementary role of earnings exists only when earnings are not extreme. Our results imply that investors and researchers should consider both earnings and cash flows extremity when assessing the information content of these variables.     

Real and Financial Industry Booms and Busts

We examine how product market competition affects firm cash flows and stock returns in industry booms and busts. Our results show how real and financial factors interact in industry business cycles. In competitive industries, we find that high industry-level stock market valuation, investment, and financing are followed by sharply lower operating cash flows and abnormal stock returns. Analyst estimates are positively biased and returns comove more. In concentrated industries these relations are weak and generally insignificant. Our results are consistent with participants in competitive industries not fully internalizing the negative externality of industry competition on cash flows and stock returns.     

The evolution of financial constraints

We demonstrate that the severity of financial constraints has declined over time for two reasons: (i) improved access to external funds as evidenced by a decreased reliance on internal cash flows, and (ii) an inward shifting investment frontier with reduced investment opportunities. The decline in financial constraints coincides with the documented diminishing sensitivity of investment to cash flows, yet we show that cash flows remain a determining factor in helping constrained firms overcome restricted access to external capital. There is a flight-to-quality during economic shocks, where the adverse effects following periods of tightened credit are particularly pronounced for smaller firms, with larger firms appearing largely unaffected.     

Strategic Decision Making of the Firm Under Asymmetric Information

This paper develops a simple signaling model whereby high valuation firm uses levels of investment, debt and dividends to convey information to the market regarding its valuation. Conditions are determined under which investment, debt and dividends are employed in a separating Nash equilibrium. Unlike many other signaling models where the source of asymmetric information concerns only the mean of the firms' cash flow, our model allows for two sources of asymmetric information: the mean and the variance of the cash flow. This paper finds that the choice of signals depends on the relative importance of these two sources of informational asymmetry. For example, we show that high valued firms signal their values by decreasing their debt if the source of asymmetric information is mainly driven by the variance of the cash flows. This latter result differs from the debt signaling models found in the literature. The findings of this paper are consistent with extensive empirical evidence.     

An axiomatic approach to the valuation of cash flows

We model a stream of cash flows as an optional stochastic process, and value the cash flows by using a continuous and strictly positive linear functional. By applying a representation theorem from the general theory of stochastic processes we are able to study this valuation principle, as well as properties of the stochastic discount factor it implies. This approach to valuation is useful in the non-presence of a financial market, as is often the case when valuing cash flows arising from insurance contracts and in the application of real options.     

The Role of Real Options in Capital Budgeting: Theory and Practice1

Most discussions of capital budgeting take for granted that discounted cash flow (DCF) and real options valuation (ROV) are very different methods that are meant to be applied in different circumstances. Such discussions also typically assume that DCF is “easy” and ROV is “hard”—or at least dauntingly unfamiliar—and that, mainly for this reason, managers often use DCF and rarely ROV. This paper argues that all three assumptions are wrong or at least seriously misleading. DCF and ROV both assign a present value to risky future cash flows. DCF entails discounting expected future cash flows at the expected return on an asset of comparable risk. ROV uses “risk‐neutral” valuation, which means computing expected cash flows based on “risk‐neutral” probabilities and discounting these flows at the risk‐free rate. Using a series of single‐period examples, the author demonstrates that both methods, when done correctly, should provide the same answer. Moreover, in most ROV applications—those where there is no forward price or “replicating portfolio” of traded assets—a “preliminary” DCF valuation is required to perform the risk‐neutral valuation. So why use ROV at all? In cases where project risk and the discount rates are expected to change over time, the risk‐neutral ROV approach will be easier to implement than DCF (since adjusting cash flow probabilities is more straightforward than adjusting discount rates). The author uses multi‐period examples to illustrate further both the simplicity of ROV and the strong assumptions required for a typical DCF valuation. But the simplicity that results from discounting with risk‐free rates is not the only benefit of using ROV instead of—or together with—traditional DCF. The use of formal ROV techniques may also encourage managers to think more broadly about the flexibility that is (or can be) built into future business decisions, and thus to choose from a different set of possible investments. To the extent that managers who use ROV have effectively adopted a different business model, there is a real and important difference between the two valuation techniques. Consistent with this possibility, much of the evidence from both surveys and academic studies of managerial behavior and market pricing suggests that managers and investors implicitly take account of real options when making investment decisions.     

The Equilibrium Valuation of Risky Discrete Cash Flows in Continuous Time

This paper values a contingent claim to discrete stochastic cash flows generated by a Poisson arrival process with a randomly varying intensity parameter. In the most general case, both the size and the arrival intensity of cash flows may correlate wih state variables in a continuous time economy. Assuming the conditions of an intertemporal capital aset pricing model, solutions for the value of the contingent claim can be found using various techniques. The paper suggests immediate applications to the valuation of insurance contracts, the decision to build a firm with unknown future investment opportunities, and the pricing of mortgage-backed securities.     

What drives investment–cash flow sensitivity around the World? An asset tangibility Perspective

Motivated by ongoing debates on investment–cash flow sensitivity (ICFS) and its documented decline and disappearance in the U.S., we investigate the determinants of ICFS. Using firm-level data across 41 countries for the 1993–2013 period, we document an important role of asset tangibility in explaining the patterns in ICFS. Asset tangibility affects ICFS through two channels: investment intensity and cash flow persistence. As the share of tangible capital, investment and cash flow persistence has fallen in developed economies, ICFS has declined. In contrast, as developing economies operate with more tangible capital, have higher investment rates and more persistent cash flows, their ICFS is more stable. The results support our explanation of ICFS as a reflection of capital (investment) intensity and income predictability, rather than a measure of financial constraints.     

The Usefulness of Book-to-Market and ROE Expectations for Explaining UK Stock Returns

Abstract:  The fundamental valuation perspective on stock returns suggests that book-to-market will be positively related to returns if market value of equity equals future expected cash flows discounted at the expected return and book value proxies for future cash flows. Building on this perspective, we develop a log linear model which includes expectations of future BM and ROE in addition to current BM as explanatory variables for future stock returns. We show that these three variables explain a significant part of UK cross-sectional stock returns and that they remain highly statistically significant after including additional risk proxy variables. This supports relevance of fundamental valuation based firm characteristics for explaining stock returns and indicates their potential usefulness for predicting future stock returns.     

Capital Cash Flows,APV and Valuation

This paper examines three different methods of valuing companies and projects: the adjusted present value (APV), capital cash flows (CCF) and weighted average cost of capital (WACC) methods. It develops the appropriate WACC and beta leveraging formulae appropriate for each valuation model, so that given a particular valuation model the correct APV and CCF values can be determined from the WACC value and vice versa. Further it goes on to show when the perpetuity formulae give poor estimates of the value of individual cash flows, even though the overall values are correct. The paper cautions that the APV and CCF models require more information than is currently known, such as the value of the corporate use of debt, and consequently can give misleading results, particularly in sensitivity analyses.     

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.     

Do prices reflect market fundamentals in real estate markets?

The purpose of this article is to examine prices on land and REIT shares for possible evidence of deviations from market fundamentals, the underlying economic forces. Models of market fundamentals are developed from the intertemporal capital asset pricing model so that risk aversion and a stochastic investment opportunity set can be incorporated in the analysis. The approach in this article is to compare ex post values of actual discounted cash flows with prices and to test whether the price series are unbiased predictors of the future discounted cash flows. Several tests of the relationship are presented, and the results suggest that prices of real estate investment trusts and prices of farm land do not always reflect fundamental value.     

Dynamic Effects of Information Disclosure on Investment Efficiency

This paper studies how information disclosure affects investment efficiency and investor welfare in a dynamic setting in which a firm makes sequential investments to adjust its capital stock over time. We show that the effects of accounting disclosures on investment efficiency and investor welfare crucially depend on whether such disclosures convey information about the firm's future capital stock (i.e., balance sheet) or about its future operating cash flows (i.e., earnings). Specifically, investment efficiency and investor welfare unambiguously increase in the precision of disclosures that convey information about the future capital stock, since such disclosures mitigate the current owners' incentives to underinvest. In contrast, when accounting reports provide information about future cash flows, the firm can have incentives to either under‐ or overinvest depending on the precision of accounting reports and the expected growth in demand. For such disclosures, investment efficiency and investor welfare are maximized by an intermediate level of precision. The two types of accounting disclosures act as substitutes in that the precision of capital stock disclosures that maximizes investment efficiency (and investor welfare) decreases as cash flow disclosures become more informative and vice versa.     

Cost of capital equations under the Australian imputation tax system

Since the introduction of the Australian imputation tax system, there have been problems both in the measurement of the market value of franking (imputation tax) credits and in their application to estimating cash flows and the cost of capital. In the present paper, we provide a convenient and robust resolution to the above problems in the context of an internally consistent set of equations for the cost of capital, asset valuation and the capital asset pricing model (CAPM). The equations apply under both classical and imputation tax systems and under differential taxation of dividends, capital gains and interest. The simple form of the CAPM presented here is shown to encompass more complex versions of the CAPM, which attempt to accommodate the effect of personal taxes. The valuation equations require an estimate of the market value of $1 of the firm's dividends, within which is embedded the market value of the imputation tax credits. Separate estimates of the value of imputation tax credits, or Officer's gamma factor, are not required.     

The role of accruals and cash flows in explaining security returns: Evidence from New Zealand

This paper empirically examines the relative and incremental information content of earnings and cash flows and the role of firm-specific contextual factors in moderating information content in New Zealand. Accounting earnings are considered to be the premier information source for decision making and a substantial volume of literature, primarily in the United States, shows that earnings provide superior information to that of cash flows. However, significant reporting differences in New Zealand warrant and investigation of the role of earnings and cash flows to explain security returns. Results show that (a) earnings have higher explanatory power than cash flows, although the difference is not statistically significant, and (b) both earnings and cash flows have incremental information content for stock returns. Further analysis shows that the valuation role of earnings and cash flows is moderated by firm-specific factors.     

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.     

Organizational Capital and Investment‐Cash Flow Sensitivity: The Effect of Management Quality Practices

This paper examines the influence of organizational capital, as evident in management quality practices, on the response of firm investment to internal cash flows. We provide novel and strong evidence that investment sensitivity to internal cash flows decreases in the presence of superior management practices. We also find that superior management practices reduce the firm's financing frictions, evident in lower capital constraints. Our results are robust to numerous tests. Overall, our findings suggest that intangible organizational capital is important for investment decisions and that superior management practices contribute to value‐maximizing behavior.     

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.