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.     

Valuación con opciones reales de proyectos con flujos correlacionados con fundamentales económicos y con saltos extremos Viabilidad del caso COMERCI UCB

This paper extends the method of discounted cash flows to value investment projects through incorporating real options. It is assumed the cash flows generated by the firm are correlated with macroeconomic fundamentals, particularly with the interest rate. It is also assumed that the cash flows have jumps whose size is given by an extreme value distribution. The flows are viewed as a portfolio of real options. The options arise from a stochastic dynamic optimization process where the investor (the entrepreneur) seeks to maximize his/her total profit discounted, subject to the wealth he/she possesses. This wealth includes the investment project, a risk-free bond, and a set of real options associated with the project.     

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.     

Kritische Betrachtung marktorientierter Kapitalkostenbestimmung bei der Bewertung von Versicherungsunternehmen

Increasingly modern discounted cash flow approaches are used for valuing insurance companies. An essential feature of these approaches is the discounting of prospective cash flows with an interest rate deduced from capital markets. Due to its generality and objectivity such an interest rate is preferred. However this article demonstrates that operationalizing this interest rate is highly subjective, preventing the goal of objectivity from being achieved.     

Credit ratings and convertible bond prices: a simulation-based valuation

This study presents a simulation-based model of convertible bond prices under the assumption of stochastic interest rates. The model is developed such that the convertible bond price explicitly depends on the credit rating at the time of issuance. Key ideas explored in this study include terminating the simulated sample path immediately when the issuer defaults on the bond at time t, which is the same as the investor and the issuer optimally exercising their options and discounting the resulting cash flows at a risk-free rate. In turn, the defaulted group of sample paths belongs to the bottom xth percentile of the realized stock prices at each time, which is exogenously given by the cumulative or marginal default probability of a firm that has the same rating as the issuer. Upon calibrating the model, we can see that the moneyness of convertible bonds is strongly responsible for influencing the convertible bond price when the rating changes. Furthermore, the effects of stochastic interest rates are shown to be possibly significant when the interest rate risk’s market price is not zero.     

A Simple Approach to Valuing Risky Fixed and Floating Rate Debt

We develop a simple approach to valuing risky corporate debt that incorporates both default and interest rate risk. We use this approach to derive simple closed-form valuation expressions for fixed and floating rate debt. The model provides a number of interesting new insights about pricing and hedging corporate debt securities. For example, we find that the correlation between default risk and the interest rate has a significant effect on the properties of the credit spread. Using Moody's corporate bond yield data, we find that credit spreads are negatively related to interest rates and that durations of risky bonds depend on the correlation with interest rates. This empirical evidence is consistent with the implications of the valuation model.     

A Bayesian Approach to Real Options: The Case of Distinguishing between Temporary and Permanent Shocks

Traditional real options models demonstrate the importance of the “option to wait” due to uncertainty over future shocks to project cash flows. However, there is often another important source of uncertainty: uncertainty over the permanence of past shocks. Adding Bayesian uncertainty over the permanence of past shocks augments the traditional option to wait with an additional “option to learn.” The implied investment behavior differs significantly from that in standard models. For example, investment may occur at a time of stable or decreasing cash flows, respond sluggishly to cash flow shocks, and depend on the timing of project cash flows.     

Using Corporate Inflation Protected Securities to Hedge Interest Rate Risk

In the first half of 2008, rising inflation became a concern, but by the fall the focus was on deflation. Such shifts in the outlook for inflation represent a significant risk for some companies, particularly those whose revenues and profits are negatively affected by increases in inflation and rates. For such companies, the use of long‐term fixed‐rate debt will provide at least a partial hedge against increased rates. Less widely appreciated is that even companies whose profits move up and down with inflation face considerable risk from fluctuations in interest rates. Conventional wisdom holds that floating‐rate debt hedges this risk. But this article argues that floating‐rate debt still leaves a company exposed to increases in real interest rates. Inflation‐sensitive companies such as utilities can use corporate inflation‐protected securities (CIPS) to hedge their real interest rate risk as well as inflation risk. In addition to its hedging benefits, CIPS also have the potential to reduce borrowing costs by satisfying growing investor demand for high‐quality securities that provide inflation protection (including demand sources like the recent restoration of French savings accounts to inflation).     

Swap Rates and Credit Quality

This article presents a model for valuing claims subject to default by both contracting parties, such as swaps and forwards. With counterparties of different default risk, the promised cash flows of a swap are discounted by a switching discount rate that, at any given state and time, is equal to the discount rate of the counterparty for whom the swap is currently out of the money (that is, a liability). The impact of credit-risk asymmetry and of netting is presented through both theory and numerical examples, which include interest rate and currency swaps.     

FINANCING INNOVATIONS AND CAPITAL STRUCTURE CHOICES

The last two decades have seen a stream of innovation in financial markets, especially in corporate bonds. Some of these innovations—notably, hybrid debt—have provided firms with more flexibility in designing cash flows on borrowings, allowing them to match cash flows on financing more closely to cash flows on assets. In so doing, the use of such innovative securities has increased corporate debt capacity and hence firm value.
But if such changes have been mostly good news for corporate treasurers, the relentless torrent of innovation has sometimes resulted in firms issuing these new securities for the wrong reasons. Some have done so to take advantage of loopholes in the way ratings agencies and regulatory agencies define debt and equity—and others to exploit perceived pricing anomalies—without considering the effect of such securities on the firm's overall risk profile. In this context, it is worth noting that as corporate bonds have become more complex, investment bankers have made themselves indispensable to the process by providing pricing as well as selling support. This article aims to help managers distinguish when financing with complex securities serves their company's interests, and when it can end up hurting them.     

A simplified approach to measuring bond duration

Because interest rates vary over time, the realized return on a fixed-income investment will depend on the price at which the instrument is ultimately liquidated and the rate at which interim cash flows are reinvested. This variation in realized return, known as interest-rate risk, should be addressed by both individual and institutional investors. Tools for measuring the impact and adjusting for the effects of interest rate changes on fixed-income instrument performance have long been available with duration and its companion adjustment factor, convexity. In this article, a simplified alternative to the traditional complex duration calculation is developed and demonstrated. Thus, anyone who can calculate a bond price can quickly estimate the interest rate risk associated with a bond as well as calculate the expected bond price change for a given change in market yield-to-maturity.     

Pitfalls in Levering and Unlevering Beta and Cost of Capital Estimates in DCF Valuations1

The “levering” and “unlevering” of estimates of beta and various costs of capital are routine steps in estimating the discount rates used in DCF valuations. But as the authors demonstrate by reviewing the existing research on the subject, the levering and unlevering formulas that are most commonly used in practice are not appropriate for valuing many companies. They also illustrate the shortcomings of—and substantial valuation errors that can result from—the common practices of assuming that the betas of securities like debt and preferred stock are equal to zero and ignoring the effects of equity‐linked securities such as employee stock options, warrants, and convertible debt. The authors offer alternative levering formulas that are more appropriate for valuing most companies than—and as readily implemented as—the formulas commonly used today. They also provide a relatively easy way to estimate betas for debt and preferred stock that can be used in the levering and unlevering formulas. The authors discuss how properly to account for equity‐linked securities such as employee stock options, warrants, and convertible debt while demonstrating the potential importance of ignoring such equity‐linked securities in the levering and unlevering formulas. Finally, the authors show why it is appropriate to standardize the treatment of contractual obligations such as leases across comparable companies in order to get consistent estimates of the unlevered cost of capital.     

Valuing Fixed-Income Options and Mortgage-Backed Securities with Alternative Term Structure Models

To value mortgage-backed securities and options on fixed-income securities, it is necessary to make assumptions regarding the term structure of interest rates. We assume that the multi-factor fixed parameter term structure model accurately represents the actual term structure of interest rates, and that the values of mortgage-backed securities and discount bond options derived from such a term structure model are correct. Differences in the prices of interest rate derivative securities based on single-factor term structure models are therefore due to pricing bias resulting from the term structure model. The price biases that result from the use of single-factor models are compared and attributed to differences in the underlying models and implications for the selection of alternative term structure models are considered.     

Valuation of a Pharmaceutical Licensing Contract

It is quite common for boutique pharma companies, biotech firms, and university labs to license their intellectual property (a new compound) to large pharmaceutical companies. In such cases, the big pharma companies finance and manage the R&D process and, if successful, market the drugs. In exchange for use of their intellectual property, the outlicensing organizations receive licensing contracts that promise some combination of fixed payments, event‐specific milestone payments, and revenue‐ or profit‐based royalties. The authors show how to estimate the expected present value of the future cash flows promised by such licensing deals. The complicating factor in such valuations is that the licensing contracts are essentially derivative contracts written on drugs in development, which as the authors showed in a paper published in this journal a year ago, are themselves compound options on marketed drugs. The authors use the valuation example from the earlier paper, along with a proposed licensing deal, and walk the reader through the process of valuing the licensing deal's cash flows.     

Valuing mortgage loan servicing

We develop an intertemporal model for valuing mortgage loan servicing contracts. The model includes a stochastic short-term interest rate and realized inflation rate which jointly determine the current mortgage coupon rate, the mortgagor's prepayment decision, the servicer's future net cash flows, and the rate at which to discount these future cash flows. Several potential uses of the model for institutions that service mortgages and trade servicing portfolios are illustrated by the application of the model to servicing fixed-rate mortgages and adjustable-rate mortgages. The model also is applicable to regulatory issues and to the servicing of other types of loans.The authors gratefully acknowledge support from the Federal Home Loan Bank Board, Washington, D.C., the Purdue Research Foundation, West Lafayette, Indiana, and the Richard D. Irwin Foundation, Homewood, Illinois.     

The value relevance of cash flows, current accruals, and non-current accruals in the UK

Cash flow statements have a longstanding history as mandated financial statement disclosures, having replaced funds flow statements. The usefulness of such disclosures with respect to one of the main purposes of financial statements—providing information relevant to the assessment of future cash flows and their uncertainty, and the market value of firms—is still subject to debate. This study investigates whether various partitions of earnings involving combinations of a cash flow measure of performance and measures of current accruals and non-current accruals improve the ability to explain market values in the UK relative to using earnings alone. Using a valuation model-based methodology, and employing a UK sample of non-financial firms for the years 1993 to 2007, our results suggest strong support for the assertion that cash flows can have incremental value relevance relative to either earnings or funds flows. By implication, cash flows can have separate value relevance from total and, in particular, current accruals. There is slightly less consistent evidence that current and non-current accruals can have separate value relevance but, nonetheless, the results are still strongly in favour in this respect. Generally, the main source of increase in explanatory power for market values is the separate inclusion of our cash flow measure in the estimated regressions. As a consequence, we conclude that the statement of cash flows in the UK provides information useful to UK investors in valuing firms. Further, requiring a cash flow statement, as opposed to a funds flow statement, improves the information content of financial statements in the UK.     

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.     

Accruals,cash flows,and aggregate stock returns

This paper examines whether the firm-level accrual and cash flow effects extend to the aggregate stock market. In sharp contrast to previous firm-level findings, aggregate accruals is a strong positive time series predictor of aggregate stock returns, and cash flows is a negative predictor. In addition, innovations in accruals are negatively contemporaneously correlated with aggregate returns, and innovations in cash flows are positively correlated with returns. These findings suggest that innovations in accruals and cash flows contain information about changes in discount rates, or that firms manage earnings in response to marketwide undervaluation.     

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.     

Debt in industry equilibrium

This article shows (1) how entry and exit of firms in a competitiveindustry affect the valuation of securities and optimal capitalstructure, and (2) how, given a trade-off between tax advantagesand agency costs, a firm will optimally adjust its leveragelevel after it is set up. We derive simple pricing expressionsfor corporate debt in which the price elasticity of demand forindustry output plays a crucial role. When a firm optimallyadjusts its leverage over time, we show that total firm valuecomprises the value of discounted cash flows assuming fixedcapital structure, plus a continuum of options for marginalincreases in debt.