Convex upper and lower bounds for present value functions

In this paper we present an efficient methodology for approximating the distribution function of the net present value of a series of cash‐flows, when discounting is presented by a stochastic differential equation as in the Vasicek model and in the Ho–Lee model. Upper and lower bounds in convexity order are obtained. The high accuracy of the method is illustrated for cash‐flows for which no analytical results are available. Copyright © 2001 John Wiley & Sons, Ltd.     

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.     

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.     

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.     

ON HYPERBOLIC TIME DISCOUNTING IN EXHAUSTIBLE RESOURCE MODELS: AN APPLICATION TO WORLD OIL RESOURCES

ABSTRACT. Recent research on discounting in long term economic models involves hyperbolic discounting, in which the marginal discount rate shrinks as time passes. To investigate hyperbolic discounting and exhaustible resource allocation, this work develops a discrete‐time world oil model and model solution procedure, then uses the model to examine the consequences of adopting conventional (constant annual) discounting when hyperbolic discounting is appropriate, of adopting one hyperbolic discount rate path when a different hyperbolic path is appropriate, and of adopting hyperbolic discounting when conventional discounting is appropriate. Five conventional and two hyperbolic discount rate paths are considered. One hyperbolic path is that used by Nordhaus and Boyer [2000]; the other is that recommended by Weitzman [2001]. The generality of the findings is also assessed.     

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.     

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.     

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.     

An anticipative hyperbolic discount utility on intertemporal decision making

Discount utility is facilitated to scrutinize human decision behaviors for different points in time under the consideration of time preference. Recent studies are extended from two basic models, which are the exponential and the hyperbolic discount models, and the more popular hyperbolic discount model is well recognized for resolving the effects of preference reversal and is less steeply discounting than the exponential discount model. However, to enhance the capability of explaining intertemporal decision making behavior, an anticipative hyperbolic discount utility model was proposed which revised the conventional hyperbolic discount utility by introducing the anticipative parameters under the consideration of anticipation of future gains or losses. An empirical investigation was employed to validate the effectiveness of the proposed anticipative hyperbolic discounting utility model, which was able to empirically go beyond the traditional hyperbolic discounting utility model. Also, the proposed anticipative hyperbolic model is capable of dealing with the anomalies of preference reverse and framing effects.     

Stock management after catastrophe the economics of hold or destroy

The problem of stock control after a dramatic decrease in demand is considered. This paper presents cash flow models of hold or destroy which are appropriate in such a situation. Certain assumptions are made which enable a simple model to be produced which takes into account the effects of inflation and incorporates cash-flow discounting. The results from this are then compared with some common heuristics and are found to have lower costs in every case.     

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.     

基于营运资金信息匹配平台的供应链金融动态折扣决策研究

当前逐渐受到实业界关注的一种新型供应链金融模式是基于营运资金信息匹配平台的动态折扣。本文针对两级供应链的动态折扣决策问题进行建模,揭示了动态折扣的应用对于改善供应链参与方现金流的影响机理。首先通过考虑供需双方动态折扣的独立决策,得出日折扣率的边界条件、双方效用最大时的日折扣率、买方混合还款方式下营运资金的最优准备方案和最低边界值;其次考虑供需双方动态折扣的最优决策,推导出在不同折扣率和利率关系下的最优还款策略,研究表明动态折扣可以明显提升供需双方的利润情况。     

Handling effects of reinforced preference and counter-veto in credibility of outranking

The aim of this paper is to generalize the way of computing the credibility of outranking in a multiple criteria aggregation procedure, in view of taking into account two new effects called reinforced preference and counter-veto. These effects concern only those criteria for which, as soon as action a is “judged very strongly preferred” to action b, one wishes that the credibility of outranking of a over b is greater than that for the case where (all things equal elsewhere) the preference is not “judged very strong”. To achieve this goal, we propose two complementary ways. The first one involves a reinforced preference threshold which affects the concordance degree, and the second one involves a counter-veto threshold which affects the insertion of discordance degree in the calculation of the credibility of outranking. The introduction of these two new effects remains compatible with the handling of ordinal preference scales. The resulting new index of the credibility of outranking can be used, in particular, in ELECTRE methods.     

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.     

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.     

How to correctly calculate discounted healthcare costs and benefits

A feature of a healthcare policy (such as screening) with interventions at specific ages is that when it is introduced, part of the population is too old to participate in the full programme. This fact changes the formulae to be used for cost and benefit discounting in a non-intuitive way. General formulae are derived for the expected discounted costs and benefits of such health promotion policies, for a stationary population. Correct ways to calculate discounted costs and benefits via simulation are also described. The formulae have some surprising properties, for example the relative cost of two health policies does not depend on the discounting rate. They are also relevant to the ongoing debate over the correct discounting rate for benefits. It is shown that when health benefits follow quickly on treatments, varying the discounting rate for health benefits is merely equivalent to rescaling the cash value of a benefit. It is only when benefit follows long after treatment that the problem of choosing an appropriate discount rate for benefits cannot be simplified.     

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.     

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.     

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.     

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.