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.     

Chance-constrained programming models for capital budgeting with NPV as fuzzy parameters

In an uncertain economic environment, experts’ knowledge about outlays and cash inflows of available projects consists of much vagueness instead of randomness. Investment outlays and annual net cash flows of a project are usually predicted by using experts’ knowledge. Fuzzy variables can overcome the difficulties in predicting these parameters. In this paper, capital budgeting problem with fuzzy investment outlays and fuzzy annual net cash flows is studied based on credibility measure. Net present value (NPV) method is employed, and two fuzzy chance-constrained programming models for capital budgeting problem are provided. A fuzzy simulation-based genetic algorithm is provided for solving the proposed model problems. Two numerical examples are also presented to illustrate the modelling idea and the effectiveness of the proposed algorithm.     

Valuation under technological change

This paper presents a valuation model, which includes the possibility of a future change in technology that affects in the short term the level of net cash flows receivable. The user can consider the effects of such a change on the flows, depending on whether the company is an innovator itself, or a follower of the innovations of others. The model is based upon a number of assumptions. The cash flows before the technological breakthrough follow a geometric Brownian motion. The breakthrough is modelled by a Poisson jump. For the innovator, cash flows are boosted, then decline through competition. By contrast, for the technological follower the breakthrough has an immediate depressing effect on cash flows, but subsequent cash flows rise and are modelled by an upward logistic curve.     

Project Scheduling with Discounted Cash Flows and Progress Payments

In all large scale projects, there correspond cash flows that incur throughout the life of the project. The scheduling of these projects to maximize the present value of the cash flows has been a topic of recent research. The basic assumption of earlier research is that the cash flows are mainly associated with some events of the project and they occur at the event realization times. However, in several real life projects, the cash inflows do not occur at the event realization times, rather they occur at the end of some time periods, like months, as progress payments. In this article, maximizing the present value of the cash flows in such projects is considered and a mixed-integer formulation of the problem is presented. In this formulation, activity profit curves are defined and used. Computational experience on some randomly generated test problems provides promising results especially when the Benders Decomposition technique is employed for solving the problem.     

Order Quantities with Temporary Price Reductions

The temporary price-change problem is studied, in which the objective is to minimize discounted cash flows. As pointed out by Goyal in an earlier paper, only the cash transactions at purchase times (i.e. the payments for the goods and the ordering costs) were considered. The cash flows associated with `inventory maintenance' costs which occur more or less continuously over time were neglected, which changes the structure of the model. Examples of these costs include storage, insurance, record-keeping, deterioration and obsolescence costs. In this paper, these continuously generated cash flows are included in the analysis, thereby making the new model more applicable to practical situations. This model is of interest because order-quantity decisions often must be made under conditions of both temporary price reductions and/or imminent price increases. These changes occur frequently in practice.     

A Decision Analysis Approach to Cash Flow Management

We propose a method of applying the Hespos and Strassmann "stochastic decision tree" framework, originally intended for investment decisions, to cash flow management. Sequences of uncertain events, such as a strike, affecting forecast cash flows are represented by a probability tree. Forecasts of constituent cash flows such as sales and costs are represented by Beta distributions dependent on paths through the tree. Monte Carlo simulations sample these distributions, and equations provided in the model convert the sampled cash flows to cash balances in each period. Frequencies of cash balances weighted by probabilities along paths through the tree yield a combined relative frequency distribution of cash balances for each period. These and related results may be used by management to plan financing arrangements to meet cash requirements in the future.     

A fuzzy approach to R&D project portfolio selection

A major advance in the development of project selection tools came with the application of options reasoning in the field of Research and Development (R&D). The options approach to project evaluation seeks to correct the deficiencies of traditional methods of valuation through the recognition that managerial flexibility can bring significant value to projects. Our main concern is how to deal with non-statistical imprecision we encounter when judging or estimating future cash flows. In this paper, we develop a methodology for valuing options on R&D projects, when future cash flows are estimated by trapezoidal fuzzy numbers. In particular, we present a fuzzy mixed integer programming model for the R&D optimal portfolio selection problem, and discuss how our methodology can be used to build decision support tools for optimal R&D project selection in a corporate environment.     

Simulated annealing and tabu search for multi-mode resource-constrained project scheduling with positive discounted cash flows and different payment models

In this paper the multi-mode resource-constrained project scheduling problem with discounted cash flows is considered. A project is represented by an activity-on-node (AoN) network. A positive cash flow is associated with each activity. Four different payment models are considered: lump-sum payment at the completion of the project, payments at activities' completion times, payments at equal time intervals and progress payments. The objective is to maximize the net present value of all cash flows of the project. Local search metaheuristics: simulated annealing and tabu search are proposed to solve this strongly NP-hard problem. A comprehensive computational experiment is described, performed on a set of instances based on standard test problems constructed by the ProGen project generator, where, additionally, the activities' cash flows are generated randomly with the uniform distribution. The metaheuristics are computationally compared, the results are analyzed and discussed and some conclusions are given.     

Estimation of mean and variance of net present value with certain and uncertain project life: a multiperiod CAPM approach

A multiperiod capital asset pricing model has the ability to consider risk by incorporating correlation between project and market parameters. This paper presents expressions for mean and variance of net present value of a project, in a multiperiod capital asset pricing model context, for the cases of certain and uncertain project lives. Both cases consider two types of cash flows, independent and correlated over time. The effects of (i) uncertainty in project life, (ii) correlation amongst subsequent cash flows, and (iii) the elasticity of expectations on the estimates of mean and variance of net present value have been studied through a numerical example.     

The utility of cash flow forecasts in the management of corporate cash balances

This paper considers the stochastic cash balance problem. A dynamic simple policy (DSP) is proposed to minimise transaction costs, under a general cost structure, when the cash flows are not independently or identically distributed. The validity of the approach is demonstrated using the scenario of double exponentially distributed cash flows considered by Penttinen. A data set from a large multinational is used to demonstrate the practical application of the DSP. To provide conditional expectations of future cash flows, a time series model is developed to provide forecasts.     

Insurance valuation: A computable multi-period cost-of-capital approach

We present an approach to market-consistent multi-period valuation of insurance liability cash flows based on a two-stage valuation procedure. First, a portfolio of traded financial instrument aimed at replicating the liability cash flow is fixed. Then the residual cash flow is managed by repeated one-period replication using only cash funds. The latter part takes capital requirements and costs into account, as well as limited liability and risk averseness of capital providers. The cost-of-capital margin is the value of the residual cash flow. We set up a general framework for the cost-of-capital margin and relate it to dynamic risk measurement. Moreover, we present explicit formulas and properties of the cost-of-capital margin under further assumptions on the model for the liability cash flow and on the conditional risk measures and utility functions. Finally, we highlight computational aspects of the cost-of-capital margin, and related quantities, in terms of an example from life insurance.     

Samsung card lending model

Samsung Card Lending Model (SCLM) analyzes cash flow in individual accounts and measures the level of company-wide risk. Serving as a risk and portfolio management model in the consumer lending business, the main features of SCLM are as follows. Default ratios such as intrinsic balance default probability and annual default ratio are computed using the past, present, and future cash flows of accounts. The provision is shown as the total sum of write-offs. The size of capital required is determined by default probability distribution. The price for new accounts is quoted based on cash flow simulations reflecting future business environments. SCLM has shown good performance in Samsung card consumer lending business since the Korean credit card crisis of 2003.     

Performance of the heuristic procedures for constrained projects with progress payments

All large scale resource constrained projects involve cash flows occurring during their life cycle. Several recent studies consider the problem of scheduling projects to maximise the net present value (NPV) of these cash flows. Their basic common assumption is that cash flows are mainly associated with specific events and they occur at event realisation times. An alternative assumption, which can be more realistic, is that cash inflows occur periodically, for example every month, as progress payments. This article considers the problem of maximising NPV given the alternative assumption. Three different heuristic rules are developed. The performance of these heuristic rules is analysed through a full factorial experiment with 108 scheduling conditions. The results indicate that three rules provide near-optimal schedules with respect to NPV maximisation while producing time schedules that do not delay the project completion time extensively.     

Project network models with discounted cash flows a guided tour through recent developments

The vast majority of the project scheduling methodologies presented in the literature have been developed with the objective of minimizing the project duration subject to precedence and other constraints. In doing so, the financial aspects of project management are largely ignored. Recent efforts have taken into account discounted cash flows and have focused on the maximization of the net present value (npv) of the project as the more appropriate objective. In this paper we offer a guided tour through the important recent developments in the expanding field of research on deterministic and stochastic project network models with discounted cash flows. Subsequent to a close examination of the rationale behind the npv objective, we offer a taxonomy of the problems studied in the literature and critically review the major contributions. Proper attention is given to npv maximization models for the unconstrained scheduling problem with known cash flows, optimal and suboptimal scheduling procedures with various types of resource constraints, and the problem of determining both the timing and amount of payments.     

Discrete-continuous project scheduling with discounted cash inflows and various payment models—a review of recent results

In this work discrete-continuous project scheduling problems with discounted cash flows are considered. These problems are characterized by the fact that activities of a project simultaneously require discrete and continuous resources for their execution. A class of these problems is considered, where the number of discrete resources is arbitrary, and there is one continuous, renewable resource, whose total amount available at a time is limited. Activities are non-preemptable, and the processing rate of an activity is a continuous, increasing function of the amount of the continuous resource allotted to the activity at a time. A positive cash flow (cash inflow) is associated with each activity, and the objective is to maximize the net present value (NPV). The discrete-continuous resource-constrained project scheduling problem with discounted cash flows (DCRCPSPDCF) is defined. Four payment models are considered: lump-sum payment at the completion of the project, payments at activity completion times, payments at equal time intervals, and progress payments. Some properties of optimal schedules are proved for two important classes of processing rate functions: all functions not greater than a linear function (including linear and convex functions), and concave processing rate functions.     

Can properly discounted projects follow geometric Brownian motion?

The geometric Brownian motion is routinely used as a dynamic model of underlying project value in real option analysis, perhaps for reasons of analytic tractability. By characterizing a stochastic state variable of future cash flows, this paper considers how transformations between a state variable and cash flows are related to project volatility and drift, and specifies necessary and sufficient conditions for project volatility and drift to be time-varying, a topic that is important for real option analysis because project value and its fluctuation can only seldom be estimated from data. This study also shows how fixed costs can cause project volatility to be mean-reverting. We conclude that the conditions of geometric Brownian motion can only rarely be met, and therefore real option analysis should be based on models of cash flow factors rather than a direct model of project value.     

Production and payment policies for an imperfect manufacturing system with discount cash flows analysis in fuzzy random environments

ABSTRACT

This paper considers an imperfect manufacturing system with credit policies in fuzzy random environments. The supplier simultaneously offers the retailer either a permissible delay in payments or a cash discount and retailer in turn provides its customer a permissible delay period. We used an alternate approach – discount cash flow analysis to establish an inventory problem. It is assumed that the elapsed time until the machine shifts from ‘in-control’ state to ‘out-of-control’ state is characterized as a fuzzy random variable. As a function of this parameter, the profit function is also a random fuzzy variable. Based on the credibility measure of fuzzy event, the model with fuzzy random elapsed time can be transformed into a crisp model . We establish several theoretical results to obtain the solution that provides the largest present value of all future cash flows. Finally, numerical example is given to illustrate the results and obtain some managerial insights.     

Social Relationship and Transactional Marketing Policies—Maximizing Customer Lifetime Value

We present an analytic approach to address the problem of how sellers can establish and maintain a long-lasting relationship with a buyer and, at the same time, maximize customer lifetime value (CLV). To model the evolution of a relational exchange between a seller and a buyer, we extend a well-known mathematical model of “love dynamics.” The growth of each partner’s commitment to the relationship is a sum of negative and positive terms. The negative term describes each partner’s propensities for opportunism, while the positive terms describe each partner’s trust in the commitment of the other, and the reaction to marketing efforts. The seller controls the evolution of the relationship through social relationships and transactional marketing efforts. The main findings are as follows: (1) Loyal (committed) customers and long-term relationships do not always generate better cash flows, especially when buyers either look for superior current value in each purchase opportunity or are short-term oriented. (2) Without mutual trust between partners, the seller should treat old customers over time as new ones, making the reduction of retention costs impossible. (3) It is only cheaper to retain current customers rather than acquiring new ones if mutual trust between partners overcomes propensities for opportunism and the seller slightly discounts future cash flows.     

Nonlinear reserving and multiple contract modifications in life insurance

Life insurance cash flows become reserve dependent when contract conditions are modified during the contract term on condition that actuarial equivalence is maintained. As a result, insurance cash flows and prospective reserves depend on each other in a circular way, and it is a non-trivial problem to solve that circularity and make cash flows and prospective reserves well-defined. In Markovian models, the (stochastic) Thiele equation and the Cantelli Theorem are the standard tools for solving the circularity issue and for maintaining actuarial equivalence. This paper expands the stochastic Thiele equation and the Cantelli Theorem to non-Markovian frameworks and presents a recursive scheme for the calculation of multiple contract modifications.     

Defensive financial decisions support for retailers in Greek pharmaceutical industry

In this paper, we present a decisions support solution designed for Greek pharmacies comprising a cash flow management system for early warning of financial distress and a financial advisor based on a neural network. The cash flow monitoring system integrates accounting elements with real time transactions and a predictive linear regression model while the decision support module is developed with the help of a neural network. For any given business unit the system associates accounting entries with information about credit times to reflect the precise instants of cash flows and using inflows/outflows equations monthly, eventually build its liquidity curve and cash flow balance over time. Alongside, a linear regression module is introduced to estimate future cash reserves based on past profitability ratios. Lastly, combining the power of artificial neural networks with expertise in this sector of pharmaceutical business, the financial decision support tool focuses on the retailers that face financial difficulties and suggests alternative solutions for escaping from distress and insolvency. The model has an ambitious and useful purpose, to inform and consult the owners of the business units and other members of the pharmaceutical chain, thus reduce financial risk for the chain.