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.     

CALCULATION OF THE UNIFORM CASH FLOW WHICH IS EQUIVALENT TO A CUBICALLY VARYING CASH FLOW

Finding the uniform annual cash flow which is equivalent to a given irregular cash flow is an elementary but frequently arduous calculation. A closed form result is developed from which the uniform annual cash flow may be calculated provided that the actual cash flow varies with time according to a polynomial whose degree does not exceed three. An example which concerns finding the equivalent annual energy dissipation cost in electric system distribution transformers is included.     

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.     

NOTE ON “EQUIVALENCE OF CASH FLOWS WHEN COMPOUNDING OCCURS LESS FREQUENTLY THAN THE CASH FLOWS”

The present worth (PW) and future worth (FW) decision criteria are to be found in virtually all current engineering economy textbooks. Although the relationships between the internal rate of return (IRR) criterion and PW has been widely discussed in the literature, there remains some misunderstanding as to similar relationships between PW and FW. Of particular importance is the interest rates at which PW and FW are maximized. It is shown here that the maximizing rates are not necessarily equal. This leads to the seemingly peculiar result that a change in the discount rate may decrease the PW while at the same time increasing the FW, or vice versa. Numerical, mathematical and intuitive arguments are presented.     

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.     

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.     

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.     

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.     

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.     

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.     

Throwing Good Money After Bad? Cash Infusions and Distressed Real Estate

When a leveraged real estate project experience cash-flow problems, the owner must either inject additional cash or default on the mortgage. We show that it is not optimal for the owner to default as soon as net cash flow becomes negative. Surprisingly, the owner can expropriate some of the mortgage lender's wealth by injecting cash and continuing to pay interest. When the owner has cash constraints, outside investors may be able to extract significant economic rents by financing distressed real estate projects. These results have interesting implications for mortgage lending and the pattern of real estate transaction volume.     

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.     

INTERPRETATION OF THEORY-OF-INTEREST APPLICATIONS USING THE “FRACTIONAL WITHDRAWAL” CONCEPT

A model for analysing a single initial deposit followed by a sequence of periodic cash outflows is developed. Instead of treating the cash outflows as monetary amounts, they are expressed as a fraction of the account balance and labelled as fractional withdrawals. For each of the commonly used theory-of-interest applications there is an associated sequence of fractional withdrawals. A method of capturing different cash flow sequences through a unifying framework is provided. Our method enables the investment analyst to compare alternative sequences at a glance and select the one that suits best. An application of the fractional withdrawal concept is illustrated through a numerical example.     

通货膨胀对项目财务评价的影响分析

论述了通货膨胀对项目现金流量的影响，并在对通货膨胀、名义利率和实际利率三者关系研究分析的基础上，提出了通货膨胀下项目财务评价的基本处理方法。     

Technical Note–Design and Analysis of Tent Cash Flow Models for Engineering Economy Lectures

Engineering economy students are typically intimidated by arithmetic gradient series cash flows. Hence, it is beneficial to develop creative ways to make the material interesting and less formidable. This paper presents an innovative method of introducing students to the design and analysis of arithmetic gradient series cash flows in engineering economy courses. Several profiles of arithmetic gradient series cash flows are presented along with techniques of deriving closed form equations for their net present values. A “General Tent Equation” that can be used to solve various arithmetic gradient series cash flows is developed. A numerical example is used to show its implementation and usefulness.     

Municipal fiber in the United States: A financial assessment

Despite growing interest in broadband provided by municipally owned and operated fiber-to-the-home networks, the academic literature has yet to undertake a systematic assessment of these projects' financial performance. To fill this gap, we utilize municipalities' official reports to offer an empirical evaluation of the financial performance of every municipal fiber project in the U.S. operating in 2010 through 2019. An analysis of the actual performance of the resulting fifteen-project panel dataset reveals that none of the projects generated sufficient nominal cash flow in the short run to maintain solvency without infusions of additional cash from outside sources or debt relief. Similarly, 87% have not actually generated sufficient nominal cash flow to put them on track to achieve long-run solvency. In addition, 73% generated negative nominal cash flow over the past three fiscal years, leaving them poorly positioned to make up their deficits and causing them to fall farther into debt. An assessment based on the net present value of these projects' operating cash flow indicates that 53% of projects would not be on track to breakeven even assuming the theoretical best-case performance in terms of capital expenditures and debt service. Close analysis of these projects’ performance reveals that revenue generation likely plays a more important role in generating cash flow than efficiency in construction costs or operating efficiency.     

Regressive Interest Rate Expectations and Mortgage Instrument Choice in the United Kingdom Housing Market

The paper considers the choice of mortgage instrument when the rate of interest is fixed for a short duration, with reversion to a variable (bullet) rate mortgage contract. The research is the first direct test for regressive interest rate expectations using United Kingdom data while testing for wealth and portfolio effects. The econometric modeling uses a variety of nonparametric and parametric techniques to control for classification error in the dependent variable. There is evidence that households adopt regressive interest rate expectations. The lack of statistical significance of wealth and portfolio effects confirms the short run cash flow perspective of United Kingdom mortgage choices.     

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.     

企业价值评估方法及在企业中的应用

分析了成本法、相对价值法、折现现金流量法和经济利润法等企业价值评估方法,并将各种具体的评估方式进行了正反两方面对比,界定了各自的适用范围,指出折现现金流量法和经济利润法是中国企业价值评估的发展方向。