Optimal Dynamic Investment Policy for Different Tax Depreciation Rates and Economic Depreciation Rates

This paper analyzes the investment policy consequences of incorporating a tax depreciation rate different from the economic depreciation rate. Most often, firms choose their tax depreciation rate in a strategic way. Therefore, it would be a coincidence, should the optimization process lead to a tax depreciation rate that equals the economic depreciation rate. The implications of a difference between tax depreciation rate and economic depreciation rate are investigated in an optimal control model for the determination of the firm investment policy over time.     

Operational asset replacement strategy: A real options approach

This paper analyses the problem of replacement by investigating the optimal moment of investment replacement in a given tax environment with a given depreciation policy. An operation and maintenance cost minimization model, based on the definition of equivalent annual cost, is applied to a real options paradigm. The developed methodology allows for an innovative evaluation of the flexibility of replacement process analysis. A new two-factor evaluation function is introduced to quantify decisions on asset replacement under a unique cycle environment. This study improves upon previous findings in the literature as it accounts for autonomous salvage value processes. Based on partial differential equations, this model achieves a general analytical solution and particular numerical solution. The results differ significantly from those observed in one-factor models by showing evidence of over-evaluation in optimal levels of replacement, and by confirming suspicions that different types of uncertainties produce non-monotonous effects on the optimal replacement level. The scientific contribution of this study lies in new and stronger approaches to equivalent annual cost literature, supplying an algorithm for operation and maintenance cost minimization that is conditioned by autonomous salvage value. This study also contributes to the real options literature by developing a two-factor model with Brownian processes applied to asset replacement.     

Analysis of the asset replacement level with an uncertain salvage value: a two-factor model

The aim of this article is to analyse the asset replacement problem from the perspective of optimal replacement level, given a specific tax environment and depreciation policy. Using a real options approach, our model minimizes current operation and maintenance costs and allows the definition of a new value of the replacement flexibility within a multi-cycle environment. The innovation on the valuation process comes from adding an autonomous salvage value’s factor. The results from partial differential equations reveal relevant differences from those observed in one-factor models, especially with regard to optimal replacement levels and in the non-monotonous effects of salvage value variation. The numerical case study also confirms that the salvage value is indeed a worthwhile element in the replacement process. It was possible to determine that, in terms of the magnitude of the cost replacement level, the key roles are played by changes in the speed of mean reversion, as well in the salvage factor volatility. This paper provides some improvements to the existing literature in equivalent annual cost by drawing up a cost minimization problem conditioned by a different salvage value dynamics, and contributes to real options literature by introducing a salvage value factor in the pricing model.     

The effect of depreciation allowances on the timing of investment and government tax revenue

We develop a model of the behavior of a potential investor (under uncertainty and in a fiscal environment) who wishes to invest into a project in the real sector of an economy and faces a timing problem. We find an optimal solution within this model and examine the dependence of the tax revenue from the newly created firm on the depreciation policy. It is shown that there exists a domain in the space of the parameters of the investment project where both the tax revenue and the incentives can be increased by using the depreciation policy.     

A learning curve model with knowledge depreciation

Empirical studies in several industries have verified that unit costs decline as organizations gain experience or knowledge in production, which is referred to as the learning curve effect. In the past two decades, there has also been analytical work on the relationship between a firm's learning curve effects and its pricing and output decisions. Learning rates differ significantly across firms in the same industry and recent empirical evidence has shown that knowledge depreciation may be an important reason for these differences. We propose and analyze a learning curve model with knowledge depreciation and provide several new insights. First, we show that there exists a steady state where knowledge level and unit cost remain constant over time and there exists an optimal path to this steady state. Many empirical researchers have observed this ‘plateau’ phenomenon, whereby unit costs decline but reach saturation after some time. While this has been traditionally modeled exogenously in the learning curve literature by assuming that cost reduction stops at some level of knowledge through a convex, decreasing unit cost function, we provide an alternative endogenous explanation. We are also able to show that, unlike in the model without knowledge depreciation, the production rate along the optimal path to the steady state may decrease over time. Also, the knowledge level along the optimal path may actually decline over time. Finally, we show that the optimal production rate decreases at higher interest rates and increases at higher knowledge depreciation rates. In turn, this implies that a high interest rate environment discourages firms from achieving high knowledge levels and results in higher prices. On the other hand, higher knowledge depreciation rates result in higher production rates and lower prices.     

环境税费政策下快递包装材料回收利用的最优决策及社会福利分析

本文在一个两阶段的决策模型中研究了政府环境税收政策下快递包装材料的回收利用问题,通过比较快递服务商在不同经营策略下的总利润和碳排放总量,刻画出不同环境税费水平下的最优经营策略选择。研究结果表明,当快递包装材料回收再利用的固定投资成本过高时,随着环境税费水平的不断升高,快递服务商并不一定总是选择绿色经营策略。此外,在这种情况下快递服务商即使选择了绿色经营策略也并不能总是带来碳排放的减少和环境的改善。而如果政府能够进行适当的固定投资补贴,则可有效地促进快递服务商选择并保持绿色经营策略,并且能够实现经济发展与环境保护的双赢。在引入单位碳排放的外部性成本后,本文分析了社会福利最大化下的最优环境税费水平。算例分析显示,政府的政策干预有可能同时实现社会福利最大化、快递服务商总利润的增加和碳排放总量的减少。     

Optimal repair–replacement policies for a system with two types of failures

In this paper, the optimal replacement problem is investigated for a system with two types of failures. One type of failure is repairable, which is conducted by a repairman when it occurs, and the other is unrepairable, which leads to a replacement of the system at once. The repair of the system is not “as good as new”. The consecutive operating times of the system after repair form a decreasing geometric process, while the repair times after failure are assumed to be independent and identically distributed. Replacement policy N is adopted, where N is the number of repairable failures. The system will be replaced at the Nth repairable failure or at the unrepairable failure, whichever occurs first. Two replacement models are considered, one is based on the limiting availability and the other based on the long-run average cost rate of the system. We give the explicit expressions for the limiting availability and the long-run average cost rate of the system under policy N, respectively. By maximizing the limiting availability A(N) and minimizing the long-run average cost rate C(N), we theoretically obtain the optimal replacement policies N^∗ in both cases. Finally, some numerical simulations are presented to verify the theoretical results.     

Optimal tax depreciation with uncertain future cash-flows

Since taxable income consists of cash-flows reduced with depreciation charges, the choice of the depreciation method affects taxable income in future periods. A manager can therefore try to minimize the present value of future tax payments by choosing a particular depreciation method among those that are accepted by the tax authorities. We focus here on the choice between the two most commonly used methods in practice, i.e. the straight line depreciation method (SDM) and an accelerated depreciation method (ADM), such as the double declining balance (DDB) method and the sum of the years–digits (SYD) method. We show how the optimal choice depends on the discount factor, the degree of uncertainty in future cash-flows, and the structure of the tax system.     

Revenue recycling of a CO2 tax: Results from a general equilibrium model for Switzerland

This paper combines a recent proposal by the Swiss government for a CO₂ tax with a policy that uses the tax revenues to lower the pre-existing marginal labor income tax rates, and examines the efficiency and distribution effects of such a revenue recycling policy. The investigation, based on a large-scale general equilibrium model, contrary to other studies, indicates that an environmental tax reform involves negative gross cost, that is, increases welfare even when environmental benefits are not accounted for. The simulation results further show that the adverse distributional effects of a pure CO₂ tax are neutralized or even reversed when tax revenues finance cuts of existing taxes.We thank Tom Rutherford, Reto Schleiniger and two anonymous referees for helpful comments on an earlier draft of this paper. Financial support by the Federal Agency for Energy under the SOEFF program is gratefully acknowledged. The views expressed here are those of the authors and do not represent the opinions of the granting agency.     

An optimal replacement policy for a multistate degenerative simple system

In this paper, a degenerative simple system (i.e. a degenerative one-component system with one repairman) with k + 1 states, including k failure states and one working state, is studied. Assume that the system after repair is not “as good as new”, and the degeneration of the system is stochastic. Under these assumptions, we consider a new replacement policy T based on the system age. Our problem is to determine an optimal replacement policy T^∗ such that the average cost rate (i.e. the long-run average cost per unit time) of the system is minimized. The explicit expression of the average cost rate is derived, the corresponding optimal replacement policy can be determined, the explicit expression of the minimum of the average cost rate can be found and under some mild conditions the existence and uniqueness of the optimal policy T^∗ can be proved, too. Further, we can show that the repair model for the multistate system in this paper forms a general monotone process repair model which includes the geometric process repair model as a special case. We can also show that the repair model in the paper is equivalent to a geometric process repair model for a two-state degenerative simple system in the sense that they have the same average cost rate and the same optimal policy. Finally, a numerical example is given to illustrate the theoretical results of this model.     

A stocking policy for spare part provisioning under age based preventive replacement

A new policy, called stocking policy for ease of reference, has been advanced for joint optimization of age replacement and spare provisioning. It combines age replacement policy with continuous review (s, S) type inventory policy, where s is the stock reorder level and S is the maximum stock level. The policy is generally applicable to any operating situation having either a single item or a number of identical items. A simulation model has been developed to determine the optimal values of the decision variables by minimizing the total cost of replacement and inventory. The behaviour of the stocking policy has been studied for a number of case problems specifically constructed by 5-factor second order rotatory design and the effects of different cost elements and item failure characteristics have been highlighted. For all case problems, optimal (s, S) policies to-support the Barlow-Proschan age policy have also been determined. Simulation results clearly indicate that the optimal stocking policy is, in general, more cost-effective than the Barlow-Proschan policy.     

An optimal repair–replacement policy for a cold standby system with use priority

In this paper, the maintenance problem for a cold standby system consisting of two dissimilar components and one repairman is studied. Assume that both component 1 and component 2 after repair follow geometric process repair and component 1 is given priority in use when both components are workable. Under these assumptions, using geometric process repair model, we consider a replacement policy N under which the system is replaced when the number of failures of component 1 reaches N. Our purpose is to determine an optimal replacement policy N1 such that the average cost rate (i.e. the long-run average cost per unit time) of the system is minimized. The explicit expression for the average cost rate of the system is derived and the corresponding optimal replacement policy N1 can be determined analytically or numerically. Finally, a numerical example is given to illustrate some theoretical results and the model applicability.     

Optimal replacement policies with minimal repair and age-dependent costs

In this paper, we study a modified minimal repair/replacement problem that is formulated as a Markov decision process. The operating cost is assumed to be a nondecreasing function of the system's age. The specific maintenance actions for a manufacturing system to be considered are whether to have replacement, minimal repair or keep it operating. It is shown that a control limit policy, or in particular a (t, T) policy, is optimal over the space of all possible policies under the discounted cost criterion. A computational algorithm for the optimal (t, T) policy is suggested based on the total expected discounted cost.     

碳税政策下生产和销售的选址问题

本文考虑碳税政策下一个生产型企业生产和销售的选址问题。消费者分布在一条直线上,运输成本是线性的,企业除承担自身产品的运输费用外还承担消费者的运输成本。本文建立了利润最大化模型,分析了利润函数的性质,给出了求解方法。通过数值实验证明了求解方法的有效性,同时得出,即使消费者分布是中心对称的,最优的选址也不一定中心对称,这纠正了人们的错觉。增加碳税可使销售点靠近自己的消费者,增加企业的费用,但不一定起到减排的作用,只有通过灵活的碳税政策才有可能达到减排的目的。     

Optimization problems of replacement first or last in reliability theory

This paper takes up age and periodic replacement last models with working cycles, where the unit is replaced before failure at a total operating time T or at a random working cycle Y, whichever occurs last, which is called replacement last. Expected cost rates are formulated, and optimal replacement policies which minimize them are discussed analytically. Comparisons between such a replacement last and the conventional replacement first are made in detail. It is determined theoretically and numerically which policy is better than the other according to the ratios of replacement costs and how the mean time of working cycles affects the comparison results. It is also shown that the unit can be operating for a longer time and avoid unnecessary replacements when replacement last is done. For further studies, expected cost rates of modified models and their applications in a standard cumulative damage model with working cycles are obtained and computed numerically. Finally, case studies on replacement last and first in maintaining electronic systems of naval ships under battle and non-battle statuses are given.     

A note on replacement policy for a system subject to non-homogeneous pure birth shocks

A system is subject to shocks that arrive according to a non-homogeneous pure birth process. As shocks occur, the system has two types of failures. Type-I failure (minor failure) is removed by a general repair, whereas type-II failure (catastrophic failure) is removed by an unplanned replacement. The occurrence of the failure type is based on some random mechanism which depends on the number of shocks occurred since the last replacement. Under an age replacement policy, a planned (or scheduled) replacement happens whenever an operating system reaches age T. The aim of this note is to derive the expected cost functions and characterize the structure of the optimal replacement policy for such a general setting. We show that many previous models are special cases of our general model. A numerical example is presented to show the application of the algorithm and several useful insights.     

Hybrid block replacement and inspection policies for a multi-component system with heterogeneous component lives

Novel replacement policies that are hybrids of inspection maintenance and block replacement are developed for an n identical component series system in which the component parts used at successive replacements arise from a heterogeneous population. The heterogeneous nature of components implies a mixed distribution for time to failure. In these circumstances, a hybrid policy comprising two phases, an early inspection phase and a later wear-out replacement phase, may be appropriate. The policy has some similarity to burn-in maintenance. The simplest policy described is such a hybrid and comprises a block-type or periodic replacement policy with an embedded block or periodic inspection policy. We use a three state failure model, in which a component may be good, defective or failed, in order to consider inspection maintenance. Hybrid block replacement and age-based inspection, and opportunistic hybrid policies will also arise naturally in these circumstances and these are briefly investigated. For the simplest policy, an approximation is used to determine the long-run cost and the system reliability. The policies have the interesting property that the system reliability may be a maximum when the long-run cost is close to its minimum. The failure model implies that the effect of maintenance is heterogeneous. The policies themselves imply that maintenance is carried out more prudently to newer than to older systems. The maintenance of traction motor bearings on underground trains is used to illustrate the ideas in the paper.     

Optimal tax depreciation with loss carry-forward and backward options

The choice of depreciation method from among straight-line and accelerated methods can have a significant impact on the present value of expected tax payments. This is a problem that has been studied for decades, with most results indicating the optimality of accelerated methods. Recent research questions this claim by relaxing the assumption of positive taxable income. The situation where net-operating losses may be carried-forward and backward in time is the subject of this paper. We model this situation and establish conditions that allow straight-line depreciation to be preferred over accelerated methods. The results are focused around a threshold number of periods of consecutive losses, which are determined by the allowable periods to carry a loss forward. For consecutive losses beyond this threshold, straight-line will always be optimal. When the cumulative depreciation charges up to and including the window are guaranteed to be applied on or before the threshold period, then straight-line will never be optimal.     

油价波动和资源环境补偿视角下石油资源税率研究——基于山东省数据

油价、资源与环境统筹管理政策缺失导致石油资源外部性问题日益严重,从油价波动和资源环境补偿视角出发研究石油资源税率是解决石油资源外部性,实现对油价、资源与环境统筹管理的关键。基于山东省2000~2013年石油资源开采行业数据,根据使用者成本法测算山东省石油开采行业的资源耗减成本,发现当前资源税费比率应提高14%;根据生态补偿标准模型测算生态环境成本,结合大量实地调研,指出生态环境补偿水平应从目前补偿水平的22%逐步提高至完全补偿生态环境成本。然后,根据价值对等原则构建资源生态环境补偿方程,探索性地计算了基于油价波动的石油资源税率,发现当油价处于(23~52)、(52~78)、(78~115)美元/桶的油价区间时,在7%折现率下分别对应17.51%、18.84%、19.04%的补偿税率,得出结论:当前条件下将资源税费与环境补偿费用合并征收,需要将补偿税率逐步提高至15%~20%。最后,从税率确定、计征方式以及监管体系三方面提出了执行对策。     

服务贸易出口退税政策优化及国际竞争力评价

服务贸易出口退税政策事关服务贸易逆差的缩小及国际竞争力的提升。为探索我国服务贸易出口退税政策的优化方式及其对服务贸易国际竞争力的影响程度,文章构建中国服务贸易出口退税动态可计算一般均衡模型(ET-DCGE),对建筑服务业、旅游业、金融业、咨询业和其他服务业设计包括零税率、免税向零税率过渡和增加退税率档次等方式的出口退税政策优化模拟方案。结果显示,在全部实行零税率政策下,服务业贸易逆差降低程度和国际竞争力提升程度最大。