On the relation between expected returns and implied cost of capital

We examine the relation between implied cost of capital and expected returns under an assumption that expected returns are stochastic, a property supported by theory and empirical evidence. We demonstrate that implied cost of capital differs from expected return, on average, by a function encompassing volatilities of, as well as correlation between, expected returns and cash flows, growth in cash flows, and leverage. These results provide alternative explanations for findings from empirical studies employing implied cost of capital on the magnitude of the market risk premium; predictability of future returns; and the relations between cost of capital and a host of firm characteristics, such as growth, leverage, idiosyncratic risk and the firm’s information environment.     

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.     

The impact of opacity on bank valuation during the global financial crisis: A channel analysis

Prior literature suggests that opacity in the banking industry is mainly caused by a lack of informativeness in the assessment of the quality of bank assets. Examining a sample of bank holding companies in the United States, we find that there is a negative relationship between opacity and bank valuation during the 2007–2009 global financial crisis. We further attempt to identify two potential channels through which opacity negatively affects bank valuation during the financial crisis: a cash flow channel and an expected return channel. We show that one channel flows from bank profitability, measured by return on equity and return on assets, confirming a cash flow channel, whereas an expected return channel, proxied by the implied cost of capital, only works for small banks. Overall, this study sheds light on the relationship between in-transparency and bank value discount during a global recession.     

Climate risk: The price of drought

We document a significant positive relation between drought risk and the cost of equity capital. Our estimation shows that the cost of equity capital is 92 basis points higher for firms affected by severe drought conditions. We provide evidence that when firms are affected by droughts, firms with higher local institutional holdings exhibit a higher cost of equity capital. This result supports the well-known local bias of institutional investors, and suggests that diversification cannot fully eliminate the loss in wealth caused by droughts. Consistent with theoretical predictions, we find that drought duration and drought intensity further increase a firm's risk premium. However, for firms with diversified cash flows/investments, geographically dispersed business operations, and high cash holdings, the impact of drought on the expected return is significantly lessened. Overall, our findings show that investors require a higher rate of returns on firms affected by droughts and offer implications on how firms can mitigate the impact of droughts on their cost of capital.     

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.     

New estimates of the cost of capital for pharmaceutical firms

Academic researchers, as well as pharmaceutical firms themselves, often use the Capital Asset Pricing Model (CAPM) to estimate a firm's cost of capital. But the CAPM implicitly assumes that cash flows follow a random walk. This assumption is inconsistent with our finding that large U.S.-based pharmaceutical firms' cash flow growth rates display either momentum or mean-reversion. We show that growth rate momentum implies: (1) the systematic risk of a project increases monotonically with time to maturity of the cash flows; and (2) longer duration projects require a higher cost of capital. One of the practical implications of our results is that the traditional CAPM underestimates the cost of capital for some pharmaceutical firms by as much as 2.8%. These findings are quite relevant for the policy debate about the high rates of return earned by pharmaceutical companies, which some claim are pure rents and are not necessary to attract investors. Our theoretical and empirical analysis shows that high returns are often required to compensate for the higher systematic risk of long-duration pharmaceutical cash flows.     

Capital Allocation in Financial Firms

This paper develops a theory of capital allocation in financial intermediaries where the cost of "risk capital" is a critical consideration. The implication for capital budgeting is that financial firms should use a modified NPV rule in which projects are valued by calculating the NPV of cash flows using marketdetermined discount rates and then subtracting a deadweight cost of capital that reflects the project's marginal contribution to firm-wide risk.
By taking account of deadweight costs—mainly monitoring and moral hazard costs associated with having too little equity capital as well as "free cash flow" agency costs and higher taxes associated with having too much—the capital allocation model predicts that financial firms will diversify across businesses with similar deadweight costs. Such diversification reduces the cost of risk capital for the individual businesses, thereby creating more profitable investment opportunities at the margin and enabling the businesses to operate on a larger scale. The authors note that their model has similarities to but also important differences from the standard applications of RAROC models.     

Accounting Information, Disclosure, and the Cost of Capital

In this paper we examine whether and how accounting information about a firm manifests in its cost of capital, despite the forces of diversification. We build a model that is consistent with the Capital Asset Pricing Model and explicitly allows for multiple securities whose cash flows are correlated. We demonstrate that the quality of accounting information can influence the cost of capital, both directly and indirectly. The direct effect occurs because higher quality disclosures affect the firm's assessed covariances with other firms' cash flows, which is nondiversifiable. The indirect effect occurs because higher quality disclosures affect a firm's real decisions, which likely changes the firm's ratio of the expected future cash flows to the covariance of these cash flows with the sum of all the cash flows in the market. We show that this effect can go in either direction, but also derive conditions under which an increase in information quality leads to an unambiguous decline in the cost of capital.     

Discounting expected values with parameter uncertainty

In valuing future cash flows, the standard practice is to take the current cash flow and then extrapolate at an expected growth rate, which can vary at different points in time. This practice stems from the standard way of dealing with time value of money problems under certainty. However, with uncertain cash flows, this practice underestimates the expected cash flows when the growth rates are serially correlated. As a result, both value and the equity cost, calculated as an internal rate of return, are biased low. Given the prevalence of serial correlation in the economy, this paper demonstrates how to incorporate the effects of serial correlation in a simple way and demonstrates by way of a simulation that the effects can be significant. As a result, it casts doubt on the usefulness of several standard valuation approaches and results.     

How to Create Value Without Earnings: The Case of Amazon

Investors and commentators often equate GAAP accounting metrics, especially earnings per share, with financial success. The reality, however, is that there is no simple, linear relationship between GAAP earnings and intrinsic value, which is defined as the present value of expected future cash flows. And adjustments of GAAP metrics, though admittedly subjective, are often required to understand the economic reality of a business. http://Amazon.com Inc. provides a case study that throws into sharp relief the need to look beyond GAAP in order to analyze underlying fundamentals and value. In this paper, the authors argue that Amazon has done a superb job of building shareholder wealth, all the while reporting low and declining operating and net income margins. The article provides a framework for thinking about Amazon's underlying profitability that is based on the concept of return on capital in relation to the cost of capital, and shows how that profitability has been masked by GAAP accounting. The authors demonstrate that the company is now investing very large amounts of capital with the expectation of earning rates of return well above its cost of capital. And their analysis suggests that if such investment can continue over the long term, Amazon's current market value of $140 billion can be readily justified.     

A theory of risk disclosure

In this paper, we consider the price effects of risk disclosure. We develop a model in which investors are uncertain about the variance of a firm’s cash flows and the firm releases an imperfect signal regarding this variance. In our model, uncertainty over the riskiness of a firm’s cash flows leads to a variance uncertainty premium in its price. We demonstrate that risk disclosure decreases the firm’s cost of capital by reducing this premium and that the market response to risk disclosure is small when the expected level of risk is high. Moreover, we find that firms acquire and disclose more risk information when their cash flow risk is greater than expected. Finally, we demonstrate that in a multi-asset setting, only risk disclosure concerning systematic risks will impact the cost of capital.     

THE COST OF CAPITAL OF A COMPANY UNDER AN IMPUTATION TAX SYSTEM

One of the issues arising out of the introduction of an imputation tax for companies in Australia is the effect it is likely to have on the definition and measurement of a company's cost of capital. Insofar as there is a difference between the value of a dollar of franked relative to unfranked dividends, conventional definitions for the cost of capital are inappropriate and new definitions are required. This has implications for the measurement of a company's cost of capital and for the definition of net cash flows that are used in conjunction with the cost of capital. This paper sets out these definitions and an approach for measuring the cost of capital. The new definition of the cost of capital replaces the effective company tax rate T with T(l - γ) where γ is the value of personal tax credits. Further, the definition of the risk premium in the capital asset pricing model requires an adjustment for the capitalized value of personal tax credits to maintain consistency between the cost of capital and cash flows which are defined on an after-company tax but before-personal tax basis.     

Explaining the accrual anomaly by market expectations of future returns and earnings

This study examines the accrual anomaly under the framework of the Campbell [Campbell, J.Y. (1991). A variance decomposition for stock returns. Economic Journal 101 (405), 157-179.] model. The Campbell (1991) model shows that realized asset returns are a joint function of 1) expected returns, 2) revisions in market expected future returns (i.e., return news), and 3) revisions in market expected future cash flows (i.e., cash flow news). The current study adopts the Easton [Easton, P. (2004). PE ratios, PEG ratios, and estimating the implied expected rate of return on equity capital. The Accounting Review 79 (1), 73-96.] model to estimate proxies for expected returns, return news, and cash flow news. The results show that firms with low accruals have lower expected returns than firms with high accruals, which is contradictory to prior research that argues that firms with low accruals are more risky. However, investors underestimate (overestimate) future earnings growth, a proxy for cash flow growth, for low (high) accrual firms. Further analysis demonstrates that earnings news (proxy for cash flow news) plays a major role in explaining abnormal returns associated with the accrual anomaly.     

Understanding Stock Price Volatility: The Role of Earnings

In an efficient capital market, asset prices vary when investors change their expectations about cash flows, discount rates, or both. Using dividends to measure cash flows, previous research shows that the aggregate dividend‐price ratio varies due to changes in expected discount rates (returns) rather than expected cash flows. In contrast, using accounting earnings instead of dividends as a measure of cash flows, this paper shows that as much as 70% of the variation in the dividend‐price ratio can be explained by changes in expected earnings. Moreover, the paper documents a significant negative correlation between expected returns and expected earnings, suggesting that variations in a common factor to both may generate significant price volatility. The results are consistent with the dividend‐policy irrelevance hypothesis.     

The term structures of equity and interest rates

This paper proposes a dynamic risk-based model capable of jointly explaining the term structure of interest rates, returns on the aggregate market, and the risk and return characteristics of value and growth stocks. Both the term structure of interest rates and returns on value and growth stocks convey information about how the representative investor values cash flows of different maturities. We model how the representative investor perceives risks of these cash flows by specifying a parsimonious stochastic discount factor for the economy. Shocks to dividend growth, the real interest rate, and expected inflation are priced, but shocks to the price of risk are not. Given reasonable assumptions for dividends and inflation, we show that the model can simultaneously account for the behavior of aggregate stock returns, an upward-sloping yield curve, the failure of the expectations hypothesis, and the poor performance of the capital asset pricing model.     

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.     

AN EMPIRICAL TEST OF AN EX-ANTE MODEL OF THE DETERMINATION OF STOCK RETURN VOLATILITY

The assumption that changing expected cash flows and discount factors affect a security's return is at the foundation of many financial models. This study examines empirically the hypothesis that expected stock return variability is a function of cash flow and discount rate uncertainty. Maximum likelihood estimation techniques and expectational data are employed. Strong, positive relationships are found, verifying the foundations of the ex-ante models with ex-ante data and providing a better understanding of security markets by explaining, in part, the causes of expected stock price variability.     

A Note on The Cost of Capital and Investment Evaluation For Companies Under the Imputation Tax

The 25 May, 1988, Statement of the Federal Treasurer indicated that superannuation funds are to be taxed at 15% from 1 July, 1988. Also, it has become increasingly clear that the cost of tax arbitrage is not so great that it is going to inhibit or prevent those receiving franked dividends, such as offshore investors, from selling the tax credits associated with such dividends. The net result is that franked dividends have the potential for benefitting all investors irrespective of their tax status. The outcome could substantially reduce company tax for Australian companies which in turn can be expected to have an effect on their before-tax cost of capital and on the after-tax cash flows but not on their before-tax cash flows or their after-tax cost of capital. This effect will increase the value of companies paying franked dividends.     

Types of investor uncertainty and the cost of equity capital

We jointly test the effects of two types of investor uncertainty, one related to future firm performance and unrelated to accruals (cash flow uncertainty) and one directly related to accrual estimation errors (accounting quality uncertainty). Distinct from prior studies, our uncertainty estimates are based on a matched‐firm design that minimizes the mechanical relationship between the two uncertainty variables. We find a strong negative relationship between cash flow uncertainty and multiple estimates of the cost of equity capital. With respect to accounting quality uncertainty, we find a strong positive association with both expected stock returns and implied costs of equity, but only in settings that control for cash flow uncertainty. Collectively, our results suggest the need to consider different types of investor uncertainty when examining how investor uncertainty affects the cost of equity capital.