Project options valuation with net present value and decision tree analysis

Real options analysis (ROA) has been developed to correctly value projects with inherent flexibility, including the possibility to abandon, defer, expand, contract or switch to a different project. ROA allows computing the correct discount rate using the replicating portfolio technique or risk-neutral probability method. We propose an alternative approach for valuing Real Options based on the certainty-equivalent version of the net present value formula, which eliminates the need to identify market-priced twin securities. In addition, our approach can be extended to the case of multinomial trees, a useful tool for modeling uncertainty in projects. We introduce within decision tree analysis (DTA) a method to derive the different discount rates that prevail at different chance nodes. We illustrate the valuation method with an application presented in “A Scenario Approach to Capacity Planning” [Eppen, G.D., Martin, R.K., Schrage, L.E., 1989. A scenario approach to capacity planning. Operations Research, 37 (4)], in which the authors state that for the capacity configuration investment decision studied at General Motors, “… there is no scientific way to determine the appropriate discount rate based on estimated demand.” Our method allows deriving the scientifically correct discount rates. A major result of the analysis is that the discount rates are endogenously derived from the project structure and its behavior in light of prevailing market conditions, instead of being exogenously imposed.     

Scheduling non-critical activities using multicriteria approach

In many projects the problem of selecting the start time of a non-critical activity arises. Usually it is possible to use the “as soon as possible” or “as late as possible” rules. In some situations, however, the result of such a decision depends on external factors such as exchange rate. This leads to an approach in which the problem of scheduling non-critical activities is solved using an expanded Cox–Ross–Rubinstein (CRR) binomial tree method. In the paper a bi-criteria problem of determining the start time of a non-critical activity is considered. We assume that the early start and the late start of the activity have been identified using Critical Path Method, but the project manager is free to select the time when the activity will actually be started. This decision cannot, however, be changed later, as it is associated with the allocation of key resources. Two main criteria are considered: cost and risk. While cost depends on exchange rate, risk increases with the delay of the start of the activity. The problem can be described as a dynamic process. We propose a new interactive technique for solving such a bi-criteria decision making problem under risk. The procedure uses trade-offs to identify a candidate solution. The CRR binomial method is applied to evaluate the cost of the activity.

     

Capital budgeting and optimal timing of investments in flexible manufacturing systems

This paper investigates the financial-economic decision process for investments in flexible manufacturing systems (FMS). Contrary to popular belief, we show that conventional capital budgeting techniques can be used to make such investment decisions. First, we identify theoverall impact of installing an FMS and present guidelines for a cash flow forecasting model. We then present ways in which to incorporate uncertainty in these cash flows within a risk-adjusted discount rate. These expected cash flows and the discount rate are used in calculating the net present value (NPV). Once the capital budgeting analysis is completed, a critical issue facing the firm is the optimal timing of the installation. We reinterpret the general results on optimal timing of investments within the special context of an FMS project. Finally, we illustrate the above technique via a stylized example.     

Network companies and competitiveness: A framework for analysis

Business networking for the purpose of becoming globally more competitive seems to form the very basis of strategic decisions in many companies today. The concept of “network company” has recently been the subject of many studies in the literature, perhaps mostly due to its world wide practice among more successful companies. Yet, there is no model-based formal treatment of the concept per se leading to the development of frameworks that are instrumental in formulating networking strategies. This paper addresses itself to formalizing the concept of “network company” within the context of global competition. For this purpose, “network company” is positioned in the value chain of pertinent product–market chain systems and then its functioning is decomposed into a set of minimal and basic components, which are termed “elementary resources, methods, products, and activities”. The set thus defined at that detail level is used to analyze and evaluate “network companies” at any desired condensed level reflecting the needs of a project or a function for the purpose of competitive strategy formulation. The formal analytical framework developed is then discussed in association with three basic approaches to competitive strategy formulation: resource-based strategy, activity-based strategy, and strategy based on the economic theory of the firm. The usefulness of the proposed framework in connection with these approaches is expressed in terms of formal propositions.     

Strong solutions for stochastic partial differential equations of gradient type

Unique existence of analytically strong solutions to stochastic partial differential equations (SPDE) with drift given by the subdifferential of a quasi-convex function and with general multiplicative noise is proven. The proof applies a genuinely new method of weighted Galerkin approximations based on the “distance” defined by the quasi-convex function. Spatial regularization of the initial condition analogous to the deterministic case is obtained. The results yield a unified framework which is applied to stochastic generalized porous media equations, stochastic generalized reaction–diffusion equations and stochastic generalized degenerated p-Laplace equations. In particular, higher regularity for solutions of such SPDE is obtained.     

The effects of sensitization and habituation in durable goods markets

We develop a model to study the impact of changes in price sensitivity on the firm as it introduces multiple generations of a durable product where unit costs are a convex function of quality. We incorporate the psychological processes of sensitization and habituation into a model of discretionary purchasing of replacement products motivated by past experience. When price sensitivity decreases with each purchase (sensitization), the myopic firm offers a higher quality product at a much higher price with each generation. When price sensitivity increases with each purchase (habituation), the myopic firm engages in price skimming. When sensitization is followed by habituation, the myopic firm eventually provides higher quality than the market is willing to pay for, leading to a steep drop-off in sales and profits. The actions of the forward-looking firm depend on the discount rate. A firm with a low discount rate builds its customer base before offering a higher quality and higher priced product. In contrast, a firm with a high discount rate quickly increases price and quality following the same path to falling profits of the myopic firm. These results provide insight into the firm and consumer behaviors underlying the phenomenon of “performance oversupply” identified in the innovation literature.     

A Bridge Between Bilevel Programs and Nash Games

We study connections between optimistic bilevel programming problems and generalized Nash equilibrium problems. We remark that, with respect to bilevel problems, we consider the general case in which the lower level program is not assumed to have a unique solution. Inspired by the optimal value approach, we propose a Nash game that, transforming the so-called implicit value function constraint into an explicitly defined constraint function, incorporates some taste of hierarchy and turns out to be related to the bilevel programming problem. We provide a complete theoretical analysis of the relationship between the vertical bilevel problem and our “uneven” horizontal model: in particular, we define classes of problems for which solutions of the bilevel program can be computed by finding equilibria of our game. Furthermore, by referring to some applications in economics, we show that our “uneven” horizontal model, in some sense, lies between the vertical bilevel model and a “pure” horizontal game.     

Zygmund-type estimates for fractional integration and differentiation operators of variable order

We consider non-standard generalized Hölder spaces of functions defined on a segment of the real axis, whose local continuity modulus has a majorant varying from point to point. We establish some properties of fractional integration operators of variable order acting from variable generalized Hölder spaces to those with a “better” majorant, as well as properties of fractional differentiation operators of variable order acting from the same spaces to those with a “worse” majorant.     

DYNAMICS OF OPTIMAL STOCKING IN PLANT/HERBIVORE SYSTEMS

This paper explores stocking patterns in an optimally-managed plant/herbivore system where periodic economic rents result from stocking animals on plant-bearing range/pasture to gain a desired weight for eventual sale. Optimization of the present value of economic rents in a predator-prey framework results in a two differential equation model of animals (predators) and forage (prey). The characteristics of this model are analyzed with phase diagrams under various assumptions about both biological and economic parameters. The results show when it pays to stock close to the “Golden-Rule” forage level (where the marginal productivity of the forage stock equals the discount rate), and when the solution is economically “buffered” away from the Golden-Rule stock.     

Corporate taxes, changing risk, and wealth transfers between shareholders, lenders, and the taxman

This paper examines how risk and corporate taxes jointly affectthe value of the debt and equity of a firm. We view thetotalpretax value of the firm as being divided between the taxman,lenders, and shareholders, and examine how increasing the riskof a leveraged firm, with no change in its pretax value, affectsthese claimants. We show that shareholders may gain while thetaxman loses, or vice versa, or that both gain at the expenseof lenders. The outcome depends on several factors includingthe ranking of the claims of the taxman and lenders. The analysisis extended to investments which expand the firm; here our conclusionsare at variance with some frequently expressed views on possibletax advantages of merging. We obtain different conclusions becausewe make allowance for the diversification effects of mergingon the value of the debt claims. A careful examination of thisrequires a precise mathematical formulation of the values ofthe tax, debt, and equity claims using option-pricing techniques.     

An investment model with switching costs and the option to abandon

We develop a complete analysis of a general entry–exit–scrapping model. In particular, we consider an investment project that operates within a random environment and yields a payoff rate that is a function of a stochastic economic indicator such as the price of or the demand for the project’s output commodity. We assume that the investment project can operate in two modes, an “open” one and a “closed” one. The transitions from one operating mode to the other one are costly and immediate, and form a sequence of decisions made by the project’s management. We also assume that the project can be permanently abandoned at a discretionary time and at a constant sunk cost. The objective of the project’s management is to maximise the expected discounted payoff resulting from the project’s management over all switching and abandonment strategies. We derive the explicit solution to this stochastic control problem that involves impulse control as well as discretionary stopping. It turns out that this has a rather rich structure and the optimal strategy can take eight qualitatively different forms, depending on the problems data.     

广义对偶犹豫模糊软集及其在决策中的应用

犹豫模糊软集作为一种处理不确定问题的工具受到了广泛关注。本文将广义模糊软集与对偶犹豫模糊集相结合,提出了广义对偶犹豫模糊软集的概念,给出了广义对偶犹豫模糊软集的交、并、补、“且”、“或”运算的概念,并基于这些概念研究其若干相关性质。此外,定义了广义对偶犹豫模糊软集的信息能量、相关性和相关系数的概念并讨论了它的性质。最后,给出了基于广义对偶犹豫模糊软集的多属性决策方法,并通过实例说明了该方法的的可行性和有效性。     

广义多值直觉模糊软集及其在多属性决策中的应用

软集理论作为一种处理不确定问题的数学新工具弥补了传统模糊理论在参数工具上的不足。本文将广义模糊软集与多值直觉模糊集相结合,提出了广义多值直觉模糊软集的概念,给出了广义多值直觉模糊软集的交、并、补、“且”、“或”运算的概念,并基于这些概念研究其若干相关性质。此外,还将广义多值直觉模糊软集应用到多属性决策问题中去,给出相应的算法。并进行实例分析说明该决策方法的可行性和有效性。     

委托代理冲突下的企业投融资决策

采用实物期权与均衡定价理论,研究委托-代理冲突下的企业投融资决策问题.考虑管理者拥有企业投融资决策权时,其如何同时选择投资时机、投资规模及资本结构.分析了管理者持股与项目风险(不确定性)对企业非效率投融资的影响.数值分析表明:给定资本结构下,杠杆企业管理者决策的投资时机与投资规模变化呈现出负相关;对比于纯股权融资企业,杠杆企业管理者加速了投资期权的执行并增大了投资规模;财务杠杆率是管理者持股比例的U形函数,且管理者持股比例的增大,会加速投资期权的执行、增大投资规模与债务融资规模,并降低代理成本;项目风险的增大会导致企业投资时机、投资规模、债务融资规模和代理成本增大及财务杠杆率降低.     

Combination of numerical and structured approaches to the construction of a second-order incomplete triangular factorization in parallel preconditioning methods

Parallel versions of the stabilized second-order incomplete triangular factorization conjugate gradient method in which the reordering of the coefficient matrix corresponding to the ordering based on splitting into subdomains with separators are considered. The incomplete triangular factorization is organized using the truncation of fill-in “by value” at internal nodes of subdomains, and “by value” and ‘by positions” on the separators. This approach is generalized for the case of constructing a parallel version of preconditioning the second-order incomplete LU factorization for nonsymmetric diagonally dominant matrices with. The reliability and convergence rate of the proposed parallel methods is analyzed. The proposed algorithms are implemented using MPI, results of solving benchmark problems with matrices from the collection of the University of Florida are presented.     

The effect of human agent in project management

The article deals with the effect of a human agent on the activity realization in a project. It does so from the perspective of the Theory of Constraints where the weakest point is the deadline of partial activity. Every existing activity in any project is, to a higher or lower extent, determined by the effect of the human agent. The inefficiency of a number of projects in practice is largely caused by an unsuccessful realization of partial activities. The effect of the human agent is in this respect fundamental. The human agent, as an allocated resource in the activity, is liable to a number of non-specified impacts and stimuli, and as such s/he is rather versatile in his/her behaviour. The versatility of the human agent in projects can be described by the “Student Syndrome” phenomenon and by the first “Parkinson’s law”. Both these qualitative phenomena create a starting point for the introduced theoretical and quantitative research. The findings in this article are based on the set of real data of work effort of the students of daily study programme on one university in the Czech Republic. The article presents, as the authors’ own theoretical contribution, a mathematical model for the “Student Syndrome” phenomenon with a practical use in quantitative methods of project management. This model was derived analytically from a performed data analysis and we can assume that it will be useful for further theoretical development of quantitative methods in project management. In the article we deduce the theoretical differentiation of the “Student Syndrome” phenomenon in work effort into three terminable phases during three different types of resource work allocation. We can regard this original viewpoint as suggestive for the area of human resources management in projects. Its contribution lies in delimitation of time-targeted resource stimulation, which may lead to lower project costs, besides higher work efficiency and compliance with time-targeted deadlines of activity termination. The article brings the quantification of qualitative features of the human agent in project management.     

Term structure of discount rates for firms in the insurance industry

There is strong evidence in the literature for the hypothesis that interest rates and the market risk premium are not constant during the business cycle. The beta risk of firms in the insurance industry is also time-varying. The major implication of these results is that discount rates for risky cash flows are time varying and must obey a term structure similar to the term structure of interest rates. The purpose of this paper is to estimate discount rates for cash flows with different time horizons for the U.S. insurance industry and for different insurance sectors. We find that the term structure cost of capital takes on different shapes depending on the business cycle. It is therefore meaningful for insurers to evaluate risky projects by selecting a discount rate most appropriate for the nature and the time horizon of each project.     

高阶Lagrange中值定理“中值点”的渐近性

借助Stirling数研究了高阶Lagrange微分中值定理在f(n+1)(a)=0或f(n+1)(a)不存在时的“中值点”的渐近性,并给出了渐近性估计式.     

Decision-making in Government

The economic assessment of a research and development project is an important factor in planning and carrying out a project but its value depends on the forecasts on which it is based. The reasons why probabilistic methods are considered inappropriate when forecasting for novel projects are discussed and an alternative technique using credibility forecasts is described. Credibility forecasts for stages of a project are transformed into pairs of standardized “focus” forecasts from which are obtained two focus cash flow curves for the complete project. Two derived focus values of any suitable economic criterion are compared with a neutral value of the criterion to evaluate the attractiveness of the project and the degree of risk involved. The use of this technique for the initial assessment of a project and for reassessment at later stages is discussed and the procedure is illustrated by an example.