EQUIVALENCE OF CASH FLOWS WHEN COMPOUNDING OCCURS LESS FREQUENTLY THAN THE CASH FLOWS

A method for determining the equivalent cash flow when compounding occurs less frequently than the cash flow is presented. Existing methods for determining the equivalence of cash flows ignore the time value of money and, hence, are not satisfactory. A prorated simple interest is used for calculating the interest within the compounding period. An example utilizing the proposed method is presented.     

Probability Distribution of the Project Payback Period Using the Equivalent Cash Flow Decomposition

For stochastic cash flows, probabilistic approaches to determine a complete distribution of payback period are very limited. The payback analysis based on the net present value (NPV) has several advantages. For annual cash flows, however, the NPV-based method does not provide a complete payback distribution. This article proposes a new technique, the equivalent cash flow decomposition (ECFD), which converts an annual cash flow into an equivalent subannual cash flow at a desired level of precision. The ECFD technique can be used in conjunction with any probabilistic cash flow technique. This article demonstrates that the ECFD technique overcomes the discontinuity limitation of the conventional NPV-based payback period method and generates a complete distribution of the payback period of annual cash flows. Examples indicate that the proposed method is robust with the accuracy comparable to Monte Carlo simulation.     

INDUSTRIAL TECHNOLOGIES FOR DEVELOPING ECONOMIES By Jack Baranson Frederick A.Praeger

The finding of the present value and the equivalent annual amount for cash flow sequences which vary with time as polynomials of the second or third degree are presented. This is accomplished through the introduction of additional compound interest factors, which are easily computed, and represent an extension and generalization of the well-known uniform gradient factors. A numerical example is provided.     

Fuzzy Decision Analysis for Alternative Selection Using a Fuzzy Annual Worth Criterion

Very often, in industry, discounted cash flow techniques are applied for analyzing and selecting investment alternatives under consideration. These techniques are usually based on the data under certainty or risk. In reality, however, the decision makers are often facing the situation of vague cash flows and discount rates, or even uncertain durations, when evaluating and selecting potential investments. Fuzzy set theory has the capability of capturing vague data and allows mathematical operations. This article proposes a fuzzy equivalent uniform annual worth (fuzzy EUAW) method to assist practitioners in evaluating investment alternatives utilizing the theory of fuzzy sets. Triangular fuzzy numbers (TFNs) are used throughout the analysis to represent the uncertain cash flows and discount rates. Further, fuzzy capital recovery factors and fuzzy sinking fund factor are derived. Using these two factors, the fuzzy equivalent annual worth of each investment alternative can be found. By ranking these fuzzy numbers with the integral value, the optimal investment alternative is selected. A numerical example is provided to illustrate the results of the alternative selection.     

FREE CASH FLOW (FCF), ECONOMIC VALUE ADDED (EVA™), AND NET PRESENT VALUE (NPV):. A RECONCILIATION OF VARIATIONS OF DISCOUNTED-CASH-FLOW (DCF) VALUATION

The paper assists the user of DCF methods by clearly setting forth the relationship of free-cash-flow (FCF) and economic value added (EVA?) concepts to each other and to the more traditional applications of DCF thinking. We follow others in demonstrating the equivalence between EVA and NPV, but our approach is more general in that it links the problems of security valuation, enterprise valuation, and investment project selection. Additionally, our approach relates more directly to use of standard financial accounting information. Beginning with cash budget identity, we show that the discounting of appropriately defined cash flows under the free-cash-flow valuation approach (FCF) is mathematically equivalent to the discounting of appropriately defined economic profits under the EVA? approach. The concept of net operating profit after-tax (NOPAT), found by adding after-tax interest payments to net profit after taxes, is central to both approaches, but there the computational similarities end. The FCF approach focuses on the periodic total cash flows obtained by deducting total net investment and adding net debt issuance to net operating cash flow, whereas the EVA? approach requires defining the periodic total investment in the firm. In a project valuation context, both FCF and EVA? are conceptually equivalent to NPV. Each approach necessitates a myriad of adjustments to the accounting information available for most corporations.     

DERIVATION OF AN INTERTEMPORAL CORRELATION COEFFICIENT MODEL BASED ON CASH FLOW COMPONENTS AND PROBABILISTIC EVALUATION OF A PROJECT'S NPV

If the first two moments (mean and variance) of the net present value (NPV) are known, various probabilistic information of possible NPV can be derived. However, in general, it is practically impossible to estimate the variance of lengthy investment projects due to difficulties in estimating all the intertemporal correlation coefficients between cash flows of two different periods. In this paper, we derive an estimation model for the intertemporal coefficients based on cash flow components and show how the model, under a certain assumption, can be used for estimating and deriving probabilistic information.     

ALTERNATIVE MODELS FOR FINDING CUMULATIVE PAID CAPITAL AND REMAINING BALANCE FOR A UNIFORM SERIES OF CASH FLOWS

The purpose of this paper is to propose models for finding the cumulative amount of paid capital up to a certain point in time for a discrete uniform series of cash flows, and also the unpaid capital amount of a similar séries of cash flows. An exponential model for finding the present worth for a séries of cash flows that is increasing exponentially is used to find the sum of paid capital. The second model that is used for finding the unpaid capital is developed based on the first model. The major advantages of the first model over the existing models is that it provides a direct tool for finding the cumulative amount of paid capital or unrecovered investment. The proposed models are easy to use since they are independent of finding the amount of the cash flow A. The cumulative paid interest up to a certain point in time can be found by subtracting the total repaid capital from the amount of total paid money up to that point.     

APPLICATION OF CHANCE-CONSTRAINED PROGRAMMING TO CAPITAL RATIONING PROBLEMS WITH ASYMMETRICALLY DISTRIBUTED CASH FLOWS AND AVAILABLE BUDGET

Most applications of chance-constrained programming are based on either normally distributed random variables or random variables with symmetric distributions such as uniform, which can be approximated rather accurately by the normal distribution. In this paper we study pure capital rationing with selection of the best project mix when cash flows and available budget are random variables with asymmetric distributions. We show that solutions obtained by chance-constrained programming using normality approximation for asymmetrically distributed random variables fail to satisfy budget constraints when cash outflows are skewed to the left, indicating that realized cash outflows are more likely to be higher than expected.     

DISCOUNT RATE VALUE AND CASH FLOW DEFINITION: A NEW RELATIONSHIP AND ITS IMPLICATIONS

This article uses different standpoints to approach the question of the consistency of project valuation methods. It shows that the NPV of a project can be obtained by discounting adjusted operating cash flows at a different rate from the risk-adjusted discount rate which should normally be used. Each of the conventional project valuation methods (standard WACC, equity residual, Arditti-Levy, APV) accordingly corresponds to a specific choice of the discount rate. Thus the convergence of these methods is obvious when the risk-adjusted discount rate integrates a debt ratio equal to the one of the project. Moreover, we obtain the Modigliani-Miller relationship generalized to the case of a project of any duration.     

Letter From the Editor

This paper Identifies situations in which the widely recommended procedures for evaluating mutually exclusive projects with unequal lives may result in incorrect project rankings. These situations arise from the failure of conventional techniques to place alternatives on an appropriate equivalent-risk basis and may occur whether a net present value or equivalent annual annuity approach is utilized. We develop alternative discounted cash flow procedures which correctly reflect the nature of risk. In so doing, we address the following important issues: 1) the choice of the discount rate to be used in calculating the net present value of a series of replications of a project: 2) the choice of a discount rate for calculating the equivalent annual annuity for a series of replications: and 3) the selection of an appropriate common-life horizon for comparison of alternative projects.     

A review of: “PROJECT MANAGEMENT IN MANUFACTURING AND HIGH TECHNOLOGY OPERATIONS” by Adedeji B. Badiru,John Wiley and Sons,Inc., New York, 1988, xxii + 319 pp., ISBN 0471-62892-1, List $44.95.

The conventional approach to considering working capital cash flows in capital budgeting is to omit them or include some ad hoc figures at the initiation and termination of the project. The authors argue for an endogenous system of estimating relevant working capital cash flows on a periodic basis. Otherwise, the present value of working capital cash flows is biased against the project's acceptance. Examples of calculating working capital cash flows as related to changes in annual sales are presented for three time patterns of sales and contrasted to the conventional method. An empirical study of the linear relationship of net working capital and sales revenue of 770 companies is reported, and an alternative cash flow model is offered thai includes working capilal cash flows.     

A Cash Flow Model of Rational Housing Tenure Choice*

This paper develops a model of housing costs in a cash flow framework. The cash flow approach allows both the consumption and investment aspects of tenure choice to be analyzed. By solving the model for the rental flow equivalent to any owning situation, we can determine whether or not a household would buy or rent from an economic perspective. The results are very sensitive to the household's income, the expected duration of occupancy, the mortgage interest rate, and inflation expectations. The results suggest that “rule-of-thumb” generalizations about tenure choice are often ill-founded, and that studies of tenure choice need to explicitly consider the interaction of income, taxes, length of occupancy and expectations.     

企业要利润更要现金流

论述了现金流对企业生存发展的重要意义.针对电力企业应收电费存在巨额拖欠,导致部分售电收入的现金流无法回流的现象,提出有效的解决途径,并阐述了加强现金流管理还应关注的其他重要方面,以提高电力企业的现金盈利能力和可持续发展能力.     

ENGINEERING ECONOMY CASES

This note extends the Initial partial-mean concept for present worth analysis of risk by Buck and Askin (1986) to a two random variable case where the magnitude of a single cash flow Is a random variable, and the time duration is a random variable with uniform distribution. This extension leads to the calculation of the expected magnitude of a project loss given that the loss occurs. Computational formulas and numerical Illustrations are presented.     

On delineating supply chain cash flow under collectionrisk

The credit terms for accounts receivable (AR) offered by sellers to buyers not only create a time lag between supply chain physical flow and cash flow, but also increase the collection risk contributed by late collection and default. Previous studies describing the relationship between the two major supply chain flows did not consider the collection risk, which poses a serious challenge to companies with limited cash resources when seeking growth opportunities in sales. This study first delineates the relationship between the two flows during a growth period without imposing any constraints. A stochastic optimization model is then developed to observe the managerial implications of cash flow risk under tight cash constraints.     

优秀企业的现金流量状况分析

企业现金流量管理是企业财务管理的重要内容,现金流量和利润是不同的两个概念。一个优秀的企业应该有良好的成长性及持续地获利能力,企业现金流量状况能够很好地反映这些。而企业在不同时期的现金流量呈现出不同的特点,对优秀企业现金流量不同时期的不同状况进行分析,对企业根据自身特点安排各项活动有重要作用。     

Present Worth of Interest Tax Credits

The widely used concept of a cash flow per project in capital budgeting has serious weaknesses when resources are shared by different projects. Accordingly, the concept of cash flow per project is not used herein. Instead, the project portfolio approach is used in which costs are considered only in the acquisition and utilization of resources; when these costs actually occur. The main conclusion from this approach is that better capital budgeting decisions can be made if the concept of cash flow per project is avoided when resources are shared.     

Return Risk and Cash Flow Risk with Long-term Riskless Leases in Commercial Real Estate

This paper presents a conceptual analysis of some of the key fundamentals that underlie the risk characteristics of commercial real estate returns. In particular, the relationship between the property's return risk and its cash flow risk is explored. This relationship is important because it is the return risk that should matter most to investors, yet it is the cash flow risk or market risk about which we may have the most objective information and the most intuition. This is because real estate assets are generally unsecuritized and trade too infrequently to observe time series of returns (including appreciation) that could be used to directly study the risk characteristics of the returns. By explicitly incorporating the possibility of cash flows governed by riskless long-term leases, this paper also explores the relationship between lease term and both cash flow risk and return risk.     

Risikomanagement und -controlling bei Offshore-Windenergieanlagen

In this paper we provide an overview of the various terms and methods used in risk management and risk controlling. Further, we identify and discuss internal and external risks of offshore wind power plants (WPP) and demonstrate for the concrete example of a fictitious 400 MW offshore wind park in the North Sea the use of the discounted cash flow (DCF) method. The offshore risks involved are considered as part of the different components of the free cash flow, which form the basis for the DCF evaluation, by using a Monte Carlo simulation. The latter contains assumptions for the distribution of each cash flow component, which are based on a detailed consideration of the risk bearings. We use the cash flow at risk (CFaR), with the DCF as the risk-carrying target variable, as a quantitative risk measure for the simulated DCF evaluation. The CFaR enables us to draw a conclusion regarding the risk distribution of the DCF. According to the fictitious offshore wind park studied, the CFaR obtained provides evidence that the investment project investigated is indeed economically viable.     

On The Park-Thuesen Index and the Value of Earlier Uncertainty Resolution

In practice, engineering economic analysis involves uncertainty about future cash flows. To deal quantitatively with imprecision or uncertainty, fuzzy set theory is primarily concerned with vagueness in human thoughts and perceptions. As an alternative to conventional cash flow models where cash flows are defined as either crisp numbers or risky probability distributions, we propose an engineering economic decision model in which the uncertain cash flows and discount rates are specified as triangular fuzzy numbers. The present worth formulation of this fuzzy cash flow model is derived. The result of the present worth is also a fuzzy number with nonlinear membership function. The present worth can be approximated by a triangular fuzzy number. Deviation between exact present worth and its approximate form is examined. Finally, the fuzzy project selection is performed by applying different dominance rules. To demonstrate the application of the fuzzy present worth function, a comprehensive numerical example is presented.