Genetic Algorithms and Engineering Design

Viewing the future value of a cash flow stream as a polynomial in the compounding factor (being one plus the interest rate), this article uses Ruffini's rule in the synthetic division of a polynomial to provide insight linking several discounted cash flow analysis concepts. We use the polynomial remainder theorem to relate the concepts of divisor, quotient, and remainder to concepts in cash flow analysis—future value, present value, interest rate, account balance, and internal rate(s) of return—establishing a remainder theorem for the future value of a cash flow. Our exposition suggests that future value analysis is perhaps more direct and mathematically more transparent than attention paid to examining present value. This article extends previous work on the resolution of multiple rates of return when the interest rate used in our analysis equals an internal rate of return of the cash flow.     

A review of: “ENGINEERING ECONOMICS” by James L. Riggs,McGraw-Hill Book Company: New York, 1977, 609 pages, $19.50 list.

The relevance of corporate investment decisions lies in their impact on shareholder wealth. It not only depends on the investment project but also on the corporate dynamics that turns it into the sequence of shareholders’ capital contributions, dividends, and gross terminal value that constitutes the shareholders’ investment project (SIP). We develop a model to calculate the SIP cash flows and the values of its interim capitals following the average internal rate of return (AIRR) paradigm. The shareholders’ final value depends on two reinvestment rates that, respectively, capture the returns obtained by the retained cash flows and the dividends reinvested by shareholders. On this basis, we approach the analysis of value creation combining both reinvestment rates in the shareholders’ net present value (SNPV). This model enables us to obtain the AIRR of the SIP and a variant of it, the equity growth rate that embeds the impact of internal and external reinvestment on the shareholders’ final value.     

A NEW PERSPECTIVE ON MULTIPLE INTERNAL RATES OF RETURN

The most commonly cited drawback to using the internal rate of return to evaluate deterministic cash flow streams is the possibility of multiple conflicting internal rates, or no internal rate at all. We claim, however, that contrary to current consensus, multiple or nonexistent internal rates are not contradictory, meaningless or invalid as rates of return. There is, moreover, no need to carefully examine a cash flow stream to rule out the possibility of multiple internal rates, or to throw out or ignore “unreasonable” rates. What we show is that when there are multiple (or even complex-valued) internal rates, each has a meaningful interpretation as a rate of return on its own underlying investment stream.It does not matter which rate is used to accept or reject the cash flow stream, as long as one identifies the underlying investment stream as a net investment or net borrowing. When we say it does not matter which rate is used, we mean that regardless of which rate is chosen, the cash-flow acceptance or rejection decision will be the same, and consistent with net present value.     

Multiple Internal Rate of Return Revisited: Frequency of Occurrences

Research in multiple internal rate of return (MROR) has mainly focused on three areas: uniqueness, conditions where MROR occur, and solutions to MROR. In an attempt to solve for MROR, researchers have assumed that the occurrence of MROR is prevalent and thus a solution is direly needed. This article examines the probability that positive MROR would occur when variation is incorporated into the cash flow and the probability of getting positive MROR when multiple sign-change cash flow is generated. Results show that the probability of positive MROR occurring in multiple sign-change cash flows is relatively low and potentially a rare event.     

A Companion For NPV: The Generalized Relative Rate of Return

We show how to determine a unique rate, for a particular cash flow stream, that is used only whenever a project demands outside resources to compound the rates of the existing term structure precisely at those times. The net present value of the cash flow stream when discounted with the thus-modified term structure becomes zero. We therefore determine a vector of rates that belongs to the induced space of internal rates of return for that cash flow stream. The rate is applicable under discrete stochastic interest rate representations and provides maximum loan rates that may be contracted only when needed thus keeping a project financially autonomous. (Any investments required may be fully repaid by the project's own cash outflows).     

Valuation of projects with minimum revenue guarantees: A Gaussian copula–based simulation approach

This technical note presents a numerical simulation technique to perform valuations of infrastructure projects with minimum revenue guarantees (MRG). It is assumed that the project cash flows—in the absence of the MRG—can be described in a probabilistic fashion by means of a very general multivariate distribution function. Then, the Gaussian copula (a numerical algorithm to generate vectors according to a prespecified probabilistic characterization) is used in combination with the MRG condition to generate a set of plausible cash flow vectors. These vectors form the basis of a Monte Carlo simulation that offers two important advantages: it is easy to implement and it makes no restrictive assumptions regarding the evolution of the cash flows over time. Thus, one can estimate the distribution of a broad set of metrics (net present value, internal rate of return, payback periods, etc.). Additionally, the method does not have any of the typical limitations of real options–based approaches, namely, cash flows that follow a Brownian motion or some specific diffusion process or whose volatility needs to be constant. The usefulness of the proposed approach is demonstrated with a simple example.     

Characterizing the Real Roots for P,A, and F with Applications to Environmental Remediation and Home Buying Problems

Historically, work on multiple roots for the internal rate of return (PW = 0) equation focuses on tests for the root's uniqueness and interpreting the meaningfulness of computed roots. Instead, this article starts with problems that consist of P, A, and F cash flows. Then for all possible values of these cash flows, this article develops the boundary conditions for no, single, and multiple real roots of either positive or negative sign.

The results of characterizing these roots are applied to two examples as a foundation for conclusions about those multiple root problems and hypotheses about other problems with multiple roots. The first example is an important class of resource development projects that may require significant expenditures for environmental remediation at the conclusion of operation. The second example of buying versus leasing a home is often used to demonstrate the value of economic analysis to students.     

Duration Measures for Corporate Project Valuation

Sensitivity analysis is a very common exercise performed with the forecasting of project cash flows. In this article, a duration-type measure is generated that provides a single number for the assessment of project cash flows relative to changes in the discount rate (or adjusted for changes in a particular cash flow model parameter). The calculation is no more difficult than the duration measures that already exist for bonds. Yet, the calculation provides valuable insight that many times is lost when performing sensitivity analysis. Further, at a minimum, the measure provides a gauge for the consequences of misspecifiying the discount rate for a project.     

The IRR of a project with many potential outcomes

This article shows that the internal rate of return (IRR) of a project's expected cash flow stream is a weighted average of the IRRs offered by the project's (many) possible future outcomes, where the weights are calculated using the outcome probabilities and invested capital balances. Because the invested capital associated with a particular realization is a function of the Macaulay duration of the cash flows in that outcome, the weights depend on the outcome probabilities and the effective length of each cash flow stream.     

A Review of: “STATISTICS OF EXTREMES” By Emil J. Gumbel Columbia University Press New York, 1958 375 pp. $15.00

Standard procedures for evaluating future cash flows are to find an appropriate discount rate consistent with the cash flow's risk and then to derive a present value. While discounted cash flows seem appropriate for many instances, finding appropriate discount rates is often difficult, or discount rates may not exist when the risk is actually a function of a decision that requires the cash-flow valuation. We consider two approaches that have been suggested to alleviate this problem: the capital asset pricing model (CAPM) and the risk-neutral pricing arguments from option theory. We discuss the assumptions inherent in these models and show the results on the well-known news vendor model. Our option pricing results correspond to Singhal's [17] results using CAPM and a different valuation procedure for the option pricing model. We, however, derive a simpler expression that clearly illustrates differences from the standard form ignoring risk.     

对“全投资现金流量表”的修改意见

《建设项目经济评价方法与参数》已使用8年多,其对全投资现金流量表和内部收益率和净现值的现定存在一定问题,建议将全投资现金流量表改称项目现金流量表,并在现金汉出项中增加一项利息支出等。     

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.     

2006 IIE-EED Business Meeting Minutes

The duration measure of weighted average life has been applied in the capital budgeting literature as a measure of project liquidity. Duration is superior to payback methods because it considers both the timing and present value of the entire cash flow stream. However, the literature is ambivalent on the choice of discount rate in calculating project duration. For duration to properly serve as a project liquidity measure, the internal rate of return should be used to discount future cash flows. Examples show that using the firm's cost of capital to calculate duration fails to measure the time to recover initial project outlays in present value dollars.     

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.     

Nominal and Real Required Returns in Present Value Analysis

Present value analysis is complicated by uncertainty about future inflation. If it so happened that real cash flows did not depend on inflation and real required returns were close to zero, then inflation and required returns could be omitted from present value analysis. Unfortunately, they cannot. This paper shows that real cash flows are typically sensitive to inflation and that, outside of the 1950s and 1960s, real interest rates, have not been very stable or close to zero. There have consequently been many years when a neglect of inflation and interest rates would have caused substantial present-value errors. It is also argued that interest rates on Treasury and Corporate AAA bonds are only appropriate for virtually risk-free projects. An engineering project normally commands a substantial risk premium and the neglect of such premia can cause a large overestimate of a project's present value.     

Regulated prices and real options

This paper shows how the cash flows received by an unregulated firm operating in a workably competitive market can be replicated for a regulated firm. The only change to standard regulatory practice is that each time the regulated firm invests, the amount added to its rate base is the product of its capital expenditure and a multiplier, greater than one, that captures the reduction in value of the unregulated firm's growth options that occurs whenever the firm invests. The regulated firm is allowed to earn a rate of return equal to its weighted-average cost of capital, applied to this rate base. Four possible approaches to estimating the size of the multiplier are presented, each based on an established real-options investment model.     

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.     

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.     

确定建设项目或行业基准内部收益率的初步探讨

随着经济改革的不断深入，在项目经济评价中，国内所使用的基于20世纪80年代经济形势下测算发布的基准内部收益率指标，已经很难满足目前经济环境下的要求。文章力图从基准内部收益率的构成出发，寻求如何更合理地制定基准内部收益率的方法。