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.     

Duration and the Risk Adjustment of Discount Rates for Capital Budgeting

Capital budgeting applications frequently necessitate the use of a discounting methodology to allow for time value of money, supplemented by payback calculation to assess liquidity risk. This paper explains how both concerns can be addressed in a single process by using duration measure in making discount rate adjustments which allow for the timing of the expected cash flows.     

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.     

A NOTE ON BIAS IN CAPITAL BUDGETING INTRODUCED BY STOCHASTIC LIFE

This note extends work by Young and Contreras and by Rosenthal on the present worth of cash flows under uncertain timing. In capital budgeting analysis, the use of the expected life of a project instead of the life distribution of the project biases the estimate of its expected net present value. In most situations the bias results in an overestimate of the expected net present value of the project. When the exact life distribution is unknown, the bias can be approximated by Taylor series expansion. The sensitivity of the bias to the discount rate, to cash flow patterns, and to income taxes is also investigated.     

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.     

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.     

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.     

Integrating Real Options with Managerial Cash Flow Estimates

This article presents a real options model that fits managerial cash flow estimates (optimistic, likely, and pessimistic projections) to a continuous geometric Brownian motion (GBM) cash flow process with changing growth and volatility parameters. The cash flows and the value of a project are correlated to a traded asset, so the real option is priced under the risk-neutral measure with a closed-form solution. The analysis is extended to a sequential compound call option for investments over multiple periods. If the project is correlated to the market, then some of the risk may be mitigated by a delta-hedging strategy. A numerical example shows that the effect of the correlated asset on the real option value is significant, and the relationship between the volatility of the project and the real option value is not analogous to the typical relationship found in financial option pricing. Integrating the expertise and industry knowledge of management, this approach makes possible a more rigorous estimation of model inputs for real option pricing.     

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.     

Adjustments within discount rates to cater for uncertainty—Guidelines

Deterministic discounted cash flow (DCF) analysis is a well-accepted technique in engineering appraisals. Common practice is to incorporate all uncertainty influences within a single variable—namely, the discount rate—which also represents the time value of money. Commentary already exists in the literature that such a practice is expedient but not rational and has shortcomings. This article examines the error involved in this practice and provides guidelines and precautions for using blanket or constant discount rates in dealing with uncertainties. It shows the adjustments necessary for any given investment scenario. This is done through establishing equivalence of the expected utility of deterministic and probabilistic present worth, allowing a rate adjustment to be calculated. Numerical studies look at the relationship or trends of this rate adjustment to the key analysis variables. Generally, it is found that the rate adjustment should be decreased as the timing of a cash flow's occurrence increases, increased as the variance of the cash flow increases, kept almost as an additive constant as the base rate increases, and increased as the investor's level of risk aversion increases. The article provides practitioner-friendly usable guidelines for adjusting rates, something that is unavailable elsewhere in the literature.     

A Review of: “REAPPRAISAL OF A ROAD PROJECT IN IRAN” By Herman G. Van Der Tak and Jan de Weille World Bank Staff Occasional Papers - No. 7 The Johns Hopkins University Press 1969 127pp. $3.00

This paper presents time-dependent deterministic and stochastic variations of common discounted cash flow formulae with explicit consideration given to inflation. The cash flows, the rates of discount or of compounding, and the rate of inflation are allowed to vary with time in a deterministic as well as random fashion in equations for the Compound Amount of a Single Payment, Present Worth of a Single Payment, Amount of an Annuity, Periodic Deposits to Accumulate a Future Amount, Present Worth of an Annuity, Capital Recovery, and the Present Worth of a Deferred Annuity.     

A BETTER UNDERSTANDING OF WHY NPV UNDERVALUES MANAGERIAL FLEXIBILITY

The Real Options paradigm addresses the valuation of managerial flexibility in capital budgeting. Despite the great strides achieved by researchers in this field, many financial analysts have chosen not to adopt this new paradigm due to a lack of comfort with the approach and the mathematical complexity of the valuation models. This article shows how some projects with real options can be valued using simple and familiar tools-discounting expected cash flows after adjusting the discount rate. Unless the discount rate is adjusted to account for the impact of real options on risk, a traditional net present value (NPV) analysis misses the value of flexibility. By narrowing the gulf between Real Options analysis and more familiar tools, the weighted average discount rate (WADR) approach introduced in this paper may help novices better understand die Real Options paradigm, which subsequently may gain the wider acceptance it deserves. Though the WADR approach is practical only for simple real options, comfort with the approach may encourage analysts to pursue more advanced and robust real option valuation techniques for more complex applications.     

Risk Allowance in Original Capital Investments*

In engineering economy studies, the total risk capital is often not the original capital investment. If a firm remains profitable in the future, a portion of a completely unsuccessful investment can be recovered (1) through income-tax saving as a result of the depreciation cash flows, and (2) through possible reuse of the idle depreciating facilities.

To allow for income-tax savings, the authors propose that the present worth of the guaranteed depreciation cash flow be discounted at the cost of capital and subtracted from the total initial investment to give a better measure of the risk capital. The operating profit, depreciation-free net income, can then be treated in an appropriate fashion using probabilities or a higher discount rate to account for future uncertainties in forecasting market volume, price, manufacturing costs, etc. The application of this principle has been illustrated through a number of ex amples. The results indicate the value of distinguishing between the depreciation and operational cash flow in evaluating high-risk projects in which the yield criterion is used and in mutually exclusive evaluations in which capital investment and depreciation life vary.

A further reduction in original risk capital investment may be justified if the investment still has alternate use value should the project fail; that is, in addition to the depreciation tax credit from an idle piece of equipment. The application of this principle to a mutually exclusive decision involving a grass roots plant versus a plant located as a part of an integrated facility is illustrated. Interestingly, while most decision-makers tend to be conservative with regard to reducing risk capital, ignoring the reuse potential is inconsistent in this situation as it will tend to favor the investment with the greater risk, i.e., the grass roots location.     

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: “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 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).     

DETERMINATION OF ECONOMIC VALUE ADDED FOR A PROPOSED INVESTMENT IN NEW MANUFACTURING

This paper discusses a measure for estimating the wealth creation potential of capital investments in manufacturing. The measure, called “Economic Value Added,” has recently become popular in the United States and can be derived from an after-tax analysis of cash flows generated by a capital investment. A proposed investment in manufacturing capacity is analyzed to illustrate the after-tax cash flow calculations required to determine its EVA potential.     

A Model of the Asset Disposition Decision of the RTC

The purpose of this paper is to develop a model of the asset disposition decision for the Resolution Trust Corporation (RTC). In this paper, we focus on the primary goal of the RTC—to maximize the net present value of the cash flows generated through holding and selling the assets it acquires. A major decision it faces is whether to hold or sell assets. This decision ultimately depends on the RTC's discount rate versus that of the marginal buyer. A second question relates to the decision of which assets to sell first and which ones to delay sale. The model developed in this paper characterizes the asset disposition decision process of the RTC for different types of assets. We develop a set of optimal disposition rules based on the simple premise of a multi-period cash flow maximization. In addition, we test some of these rules by analyzing RTC disposition performance. Through this exercise, we hope to provide some guidance to the RTC in implementing its enormous task as well as to policy makers in charting the progress of the RTC. The main results of this analysis indicate that liquid assets and retail deposit franchises should be sold as quickly as possible. Illiquid assets that are performing and do not have high servicing costs are good candidates to finance through senior/subordinated securities or sale with seller financing by the RTC. Illiquid non-performing assets are good candidates for equity participation financing by the RTC. The sales proceeds obtained by the RTC will be increased if buyers have greater certainty with respect to expected cash flows and RTC sales policies.     

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.     

风险贴现率法在工程项目风险决策分析中的运用

风险贴现率法是风险决策分析中常用的方法。章根据工程项目的特点，论述了在工程项目决策中引入风险贴现率法的可能性，以及针对实际情况调整风险贴现率的几种方法，同时也指出了风险贴现率法的局限性。