Firm behavioral response to multiple sources of risky cash flow

We extend previous research to demonstrate that risk-averse firms can appear to be risk-seeking when facing multiple sources of risky cash flow. While our model requires that cash flows from operations are independently, uniformly distributed, we are able to demonstrate that three previous derived results hold with multiple sources of risk. Using chance constrained programming, we demonstrate that binding probability constraints can cause (1) a higher degree of aversion to illiquidity to induce increased risk taking; (2) apparent risk-seeking behavior; and (3) an increase in endowment to lead to lower expected profit.     

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.     

Valuation of cash flows under random rates of interest: A linear algebraic approach

This paper reformulates the classical problem of cash flow valuation under stochastic discount factors into a system of linear equations with random perturbations. Using convergence results, a sequence of uniform approximations is developed. The new formulation leads to a general framework for deriving approximate statistics of cash flows for a broad class of models of stochastic interest rate process. We show applications of the proposed method by pricing default-free and defaultable cash flows. The methodology developed in this paper is applicable to a variety of uncertain cash flow analysis problems.     

Optimal cash management using impulse control

We consider the impulse control of Lévy processes under the infinite horizon, discounted cost criterion. Our motivating example is the cash management problem in which a controller is charged a fixed plus proportional cost for adding to or withdrawing from his/her reserve, plus an opportunity cost for keeping any cash on hand. Our main result is to provide a verification theorem for the optimality of control band policies in this scenario. We also analyze the transient and steady-state behavior of the controlled process under control band policies and explicitly solve for an optimal policy in the case in which the Lévy process to be controlled is the sum of a Brownian motion with drift and a compound Poisson process with exponentially distributed jump sizes.     

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.     

A stochastic integral arising in discounting continuous cash flows and certain transformed characteristic functions

Transformed characteristic functions are universally recognized as the most powerful tools for investigating distribution functions of complicated stochastic models. The paper is mainly devoted to the establishment of properties and applications of a particular convolution model. More precisely, the paper derives the characteristic function of a convolution model based on a stochastic integral and provides applications of this model in discounting continuous cash flows.     

Complete discounted cash flow valuation

This paper concerns discounted cash flow valuation of a company. When the company is in trouble, the owners have an option to provide it with a new capital; otherwise it is liquidated. In the absence of capital outflows and inflows, the company’s own funds are modelled by a spectrally negative Lévy process. Within this framework, we look for a strategy of dividend payments and capital injections which maximizes the firm’s value. We provide an optimal strategy as well as the corresponding valuation formula. Illustrative examples are given.     

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.     

Optimal cash management under uncertainty

We solve an agent’s optimization problem of meeting demands for cash over time with cash deposited in bank or invested in stock. The stock pays dividends and uncertain capital gains, and a commission is incurred in buying and selling of stock. We use a stochastic maximum principle to obtain explicitly the optimal transaction policy.     

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.     

A fuzzy stochastic single-period model for cash management

The major purpose of this paper is to apply a stochastic single-period inventory management approach to analyze optimal cash management policies with fuzzy cash demand based on fuzzy integral method so that total cost is minimized. We will find that, after defuzzification, the cash-raising amounts and the total costs between the fuzzy case and the crisp case are slightly different when the variation of cash demand is small. As a result, we point out that the fuzzy stochastic single-period model is one extension of the crisp models. In any case, one may conclude that a conscientious analysis in fuzzy mathematics like that presented in this paper provides a financial decision maker with a deeper insight into the more real cash management problem.     

Analysis of the stochastic cash balance problem using a level crossing technique

The simple cash management problem includes the following considerations: the opportunity cost of holding too much cash versus the penalty cost of not having enough cash to meet current needs; the cost incurred (or profit generated) when making changes to cash levels by increasing or decreasing them when necessary; the uncertainty in timing and magnitude of cash receipts and cash disbursements; and the type of control policy that should be used to minimize the required level of cash balances and related costs. In this paper, we study a version of this problem in which cash receipts and cash disbursements occur according to two independent compound Poisson processes. The cash balance is monitored continuously and an order-point, order-up-to-level, and keep-level \( \left( {s, S, M} \right) \) policy is used to monitor the content, where \( s \le S \le M \). That is, (a) if, at any time, the cash level is below s, an order is immediately placed to raise the level to S; (b) if the cash level is between s and M, no action is taken; (c) if the cash level is greater than M, the amount in excess of M is placed into an earning asset. We seek to minimize the expected total costs per unit time of running the cash balance. We use a level-crossing approach to develop a solution procedure for finding the optimal policy parameters and costs. Several numerical examples are given to illustrate the tradeoffs.     

Evaluating the interest aspect of cash management

An important aspect of cash management is how to deal with temporary liquidity positions. Clearly a treasurer wants to maximise interest gain in case of a liquidity surplus and to minimise interest cost whenever there is a shortage of liquidity. This is done by means of transactions in the money market, deposits and loans. A model is presented that yields a strategy which optimises the interest cost for a certain period in the past, taking into account the dynamic character of interest expectations.     

Continuing value in firm valuation by the discounted cash flow model

The discounted cash flow model, like other firm valuation models, proceeds in two periods. For each year in the explicit forecast period, there is an individual forecast of free cash flow. On the other hand, all of the years in the post-horizon period are represented through one single continuing value formula, being the steady-state value of the firm’s productive assets at the horizon. Continuing value is typically derived by applying the Gordon formula to a simple extrapolation of free cash flow at the end of the explicit forecast period. This paper examines the components of continuing value, in particular capital expenditures and tax savings due to depreciation of property, plant and equipment (PPE). The estimation of two somewhat elusive parameters related to capital expenditures, equipment economic life and capital intensity, is discussed. A further analysis indicates that a substantial part of continuing value derives from cash flow associated with already acquired equipment. Also, the error resulting from assuming steady-state rather than lumpy capital expenditures is identified. Implementation issues relating to the explicit forecast period are also commented on.     

Comparison of Random Cash Flows

In this paper we provide stochastic-dominance conditions forrandom cumulated cash flows, when various criteria of choiceare assumed. Three (progressively finer) criteria are considered.The first one assumes only the expected utility principle. Thesecond one involves discounting and preference scaling. Thethird one involves discounting and preference scaling, too,but in reverse order. Our results are finally compared withother known results for the case of nonrandom cash flows.     

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.     

Pre-commitment vs. time-consistent strategies for the generalized multi-period portfolio optimization with stochastic cash flows

In this paper, we propose a multi-period portfolio optimization model with stochastic cash flows. Under the mean–variance preference, we derive the pre-commitment and time-consistent investment strategies by applying the embedding scheme and backward induction approach, respectively. We show that the time-consistent strategy is identical to the optimal open-loop strategy. Also, under the exponential utility preference, we develop the optimal strategy for multi-period investment, which is time-consistent. We show that the above two time-consistent strategies are equivalent in some cases. We compare the pre-commitment and time-consistent strategies under different situations with some numerical simulations. The results indicate that the time-consistent strategy is more stable and secure than pre-commitment strategy under the generalized mean–variance criterion.     

A stochastic programming approach to cash management in banking

The treasurer of a bank is responsible for the cash management of several banking activities. In this work, we focus on two of them: cash management in automatic teller machines (ATMs), and in the compensation of credit card transactions. In both cases a decision must be taken according to a future customers demand, which is uncertain. From historical data we can obtain a discrete probability distribution of this demand, which allows the application of stochastic programming techniques. We present stochastic programming models for each problem. Two short-term and one mid-term models are presented for ATMs. The short-term model with fixed costs results in an integer problem which is solved by a fast (i.e. linear running time) algorithm. The short-term model with fixed and staircase costs is solved through its MILP equivalent deterministic formulation. The mid-term model with fixed and staircase costs gives rise to a multi-stage stochastic problem, which is also solved by its MILP deterministic equivalent. The model for compensation of credit card transactions results in a closed form solution. The optimal solutions of those models are the best decisions to be taken by the bank, and provide the basis for a decision support system.     

两货栈及延期支付和现金折扣情形下变质产品的最优订货策略

已有的两货栈库存模型通常不考虑将延期支付和现金折扣相结合的情形,但实际上,供应商在给予销售商延期支付政策的同时,也会实施现金折扣策略以激励销售商尽快付款,加快资金周转,减少坏账损失。为此,本文建立了延期支付和现金折扣情形下变质产品的两货栈库存模型,并对模型的最优解进行理论分析,给出了最优解的求解步骤。最后通过数值算例对模型的可行性进行了验证,并分析了模型参数变化对最优订货策略和最优付款时间的影响。     

两货栈及延期支付和现金折扣情形下变质产品的最优订货策略

已有的两货栈库存模型通常不考虑将延期支付和现金折扣相结合的情形,但实际上,供应商在给予销售商延期支付政策的同时,也会实施现金折扣策略以激励销售商尽快付款,加快资金周转,减少坏账损失。为此,本文建立了延期支付和现金折扣情形下变质产品的两货栈库存模型,并对模型的最优解进行理论分析,给出了最优解的求解步骤。最后通过数值算例对模型的可行性进行了验证,并分析了模型参数变化对最优订货策略和最优付款时间的影响。