Budget(2)——Forecasting

for Activity Cost Control 项目预算(2)——工作成本预测
　　For the purpose of project management and control, it is not sufficient to consider only the past record of costs and revenues incurred in a project. Good managers should focus upon future revenues, future costs and technical problems. For this purpose, traditional financial accounting schemes are not adequate to reflect the dynamic nature of a project. Accounts typically focus on recording routine costs and past expenditures associated with activities. Generally, past expenditures represent sunk costs that cannot be altered in the future and may or may not be relevant in the future. For example, after the completion of some activity, it may be discovered that some quality flaw renders the work useless. Unfortunately, the resources expended on the flawed construction will generally be sunk and cannot be recovered for re-construction (although it may be possible to change the burden of who pays for these resources by financial withholding or charges; owners will typically attempt to have constructors or designers pay for changes due to quality flaws). Since financial accounts are historical in nature, some means of forecasting or projecting the future course of a project is essential for management control. In this section, some methods for cost control and simple forecasts are described.
　　对于项目的管理和控制而言，仅斟酌项目中已经产生了的成本和收益是不够的。好的项目经理还会关注未来成 本、收益和一些技巧问题。传统的财务会计打算无奈反映出项目的动态特点，而只能集中在对日常性成本和已发生 的各项工作开销的记载上。通常把从前已经发生且在未来无法再转变的支出称为“淹没成本”。例如，当某些工作 完成后，有时会发明由于存在质量缺陷而使得产品毫无用途。遗憾的是，消耗在缺陷的建造产品上的各种资源通常 就“淹没了”，并且无法通过重建而得到恢复(尽管可以根据义务的归属来确定由谁承当所造成的丧失，业主也会 要求承包商或设计方来累赘由于质量缺点而发生的用度)。由于财务报告的历史局限性，为了进行有效的管理和控 制，有必要使用一些预测和计划项目未来过程的方法和手腕。下面将先容一些有关成本控制和预测的 方法。
　　An example of forecasting used to assess the project status is shown in Table 5-1. In this example, costs are reported in five categories, representing the sum of all the various cost accounts associated with each category. 一个用来预测和评估项目状况的例子见表 5-1。在这个例子当中，成本按5 个项次进行统计，每个项次再按不同口径进行汇总。
　　Table 5-1 Illustration of a Job Status Report
　　表 5-1 工作状况报告示例（略）
　　Budgeted cost. 预算成本。
　　The budgeted cost is derived from the detailed cost estimate prepared at the start of the project. Examples of project budgets were presented in above section. The factors of cost would be referenced by cost account.
　　预算成本由项目初始阶段的具体成本估算得来。项目预算的例子在上一部分已经介绍过。成本因素可参考成本 报告。
　　z Estimated total cost. 预计总成本。
　　The estimated or forecast total cost in each category is the current best estimate of costs based on progress and any changes since the budget was formed. Estimated total costs are the sum of cost to date, commitments and exposure. Methods for estimating total costs are described below.
　　每一项次的预计总成本是根据预算构成后项目的实际进展和变化对当前成本的最为精确的估算。预计总成本由 完工成本、许诺成本和附加成本累加得到。估算总成本的方法将在下面介绍。
　　z Cost to date. 完工成本。
　　The actual cost incurred to date is recorded in column 6 and can be derived from the financial record keeping accounts.
　　已完工的实际成本记录在表 5-1 的第6 栏里，它可由财务记载报告得到。
　　z Over or Under. 超支或勤俭。
　　A final column in Table 5-1 indicates the amount over or under the budget for each category. This column is an indicator of the extent of variance from the project budget; items with unusually large overruns would represent a particular managerial concern. Note that variance is used in the terminology of project control to indicate a difference between budgeted and actual expenditures. The term is defined and used quite differently in statistics or mathematical analysis.
　　表 5-1 的最后一栏显示了每一项次预算超支或节俭的数值，这一栏也是预算偏差的唆使器。那些超越公道范畴的成本偏差 应当引起治理上的关注。注意，被用在项目掌握中的“偏差”一词指的是预算值和实际值之间的差别。在统计学和 数学分析中，这个术语的定义和使用是完整不同的。
　　In Table 5-1, labor costs are running higher than expected, whereas subcontracts are less than expected. The current status of the project is a forecast budget overrun of $ 5 950, with 23 percent of the budgeted project costs incurred to date.
　　在表5-1 中，人工成本比预期的高，而分包合同成本却比预期的低。项目目前的状况是预计总成原形对于预算 成本超支 5 950 美元，同时完工成本占预算成本的比例为23%。
　　For project control, managers would focus particular attention on items indicating substantial deviation from budgeted amounts. In particular, the cost overruns in the labor and in the other expense category would be worthy of attention by a project manager in Table 5-1. A next step would be to look in greater detail at the various components of these categories. Overruns in cost might be due to lower than expected productivity, higher than expected wage rates, higher than expected material costs, or other factors. Even further, low productivity might be caused by inadequate training, lack of required resources such as equipment or tools, or inordinate amounts of re-work to correct quality problems. Review of a job status report is only the first step in project control.
　　从项目把持的角度而言，项目经理当对那些和估算成本有重大偏差的项次给予特别的关注。具体 地说，在表5-1 中，“人工”和其余两个项次都涌现了超支的景象，应当引起注意。而下一步则要具体剖析这些项次的不同组成局 部的详细情况。例如，成本的超支可能是因为劳动生产率的降低、工资的进步、资料涨价或其他原因等引起的。进 一步讲，劳动生产率的下降又有可能源于新来的工人未经培训、缺少机器和装备等生产所需的资源、改正品质问题 的反复工作不当等原因。分析工作状态讲演只是项目节制的第一步。
　　The job status report illustrated in Table 5-1 employs explicit estimates of ultimate cost in each category of expense. These estimates are used to identify the actual progress and status of an expense category. Estimates might be made from simple linear extrapolations of the productivity or cost of the work to date on each project item. Algebraically, a linear estimation formula is generally one of two forms. Using a linear extrapolation of costs, the forecast total cost, Cf , is:
　　表 5-1 所示的工作状况报告对每一个费用项次都给出了较为精确的终极成本估算。这个估算被用来判断项目的实际进展和 某成本项次的状况。这个估算值可以用每一项次的劳动生产率或完工成本进行简略的线性推演得到。在代数学中， 一个线性估算的方程通常有两种情势。用成本的线性推演可得预测总成本Cf，即 Where Ct is the cost incurred to time t and pt is the proportion of the activity completed at time t. For example, an activity which is 50 percent complete with a cost of $40 000 would be estimated to have a total cost of $40 000/0.5 = $80 000. More elaborate methods of forecasting costs would disaggregate costs into different categories, with the total cost the sum of the forecast costs in each category. 其中，Ct 为某工作在t 时刻所发生的成本，Pt 为t 时刻某工作完工的百分比。例如，某破费40 000 美元且已完工50%的工作其预测总成本为40 000 美元/0.5=80 000 美元。更为精确的方法是将成天职解成不同的项次，再将每一项次的预测成本汇总得到总预测成本。此外，还可以 用单位成本数来得到预测总成本。其公式为
　　Alternatively, the use of measured unit cost amounts can be used for forecasting total cost. The basic formula for forecasting cost from unit costs is:
　　此外，还可以用单位成本数来得到预测总成本。其公式为（公式略）
　　Where Cf is the forecast total cost, W is the total units of work, and ct is the average cost per unit of work experienced up to time t. If the average unit cost is $50 per unit of work on a particular activity and 1 600 units of work exist, then the expected cost is 1 600×50 = $80 000 for completion. The unit cost in Equation (5-2) may be replaced with the hourly productivity and the unit cost per hour (or other appropriate time period), resulting in the equation:
　　其中，Cf 为预测总成本，W 为总劳动单元数，而ct 为已完工劳动单元的平均成本。如果某项具体工作包括1 600 个劳动单元，而每个劳动单元的平均成本为50 美元，则完工时的预测总成本为1 600×50 美元=80 000 美元，方程(5-2)中的单位成本可用每小时劳动生产率和每小时(或其他适合的时间段)单位成本的乘积取代，即
　　where the cost per work unit ct is replaced by the time per unit, ht, multiplied by the cost per unit of time, ut .
　　其中，ht 为每一劳动单元所耗时光，ut 为每一单位时间所耗成本。
　　More elaborate forecasting systems might recognize peculiar problems associated with work on particular items and modify these simple proportional cost estimates. For example, if productivity is improving as workers and managers become more familiar with the project activities, the estimate of total costs for an item might be revised downward. In this case, the estimating equation would become:
　　一些更为准确的方法可以反映出某项具体工作中与劳动有关的特殊问题，并恰当调整成本预测的比例。例如， 如果由于工人和项目经理更加熟习项目工作而使得劳动生产率得以提高，那么项目工作的预测总成本应向下调整。 在这种情况下，预测方程就变为
　　where forecast total cost, fC , is the sum of cost incurred to date, Ct, and the cost resulting from the remaining work ( tW −W ) multiplied by the expected cost per unit time period for the remainder of the activity, As a numerical example, suppose that the average unit cost has been $50 per unit of work, but the most recent figure during a project is $45 per unit of work. If the project manager was assured that the improved productivity could be maintained for the remainder of the project (consisting of 800 units of work out of a total of 1 600 units of work), the cost estimate would be 50×800+45×800= $76 000 for completion of the activity. Note that this forecast uses the actual average productivity achieved on the first 800 units and uses a forecast of productivity for the remaining work.
　　其中，猜测总成本Cf 即是完工成本Ct 加上残余工作(W-Wt)和剩余工作的预测期单位成本ct 的乘积。在前面的例子当中，曾经假设每劳动单元的平均成本为50 美元，但项目近期劳动单元成本为 45 美元。如果项目经理确信项目标剩余工作可能将改良了的生产率坚持下去(在1 600 个劳动单元中，有800 个剩余劳动单元)，那么项目完成的预测成本应为50×800 美元+45×800 美元=76 000 美元。留神，这里面分辨用到了已完工800 个劳动单元的实际平均生产率和剩余劳动单元的预计生产率。
　　In addition to changes in productivities, other components of the estimating formula can be adjusted or substituted. For example, the change in unit prices due to new labor contracts or material supplier’s prices might be reflected in estimating future expenditures. In essence, the same problems encountered in preparing the detailed cost estimate are faced in the process of preparing exposure estimates, although the number and extent of uncertainties in the project environment decline as work progresses. The only exception to this rule is the danger of quality problems in completed work which would require re-construction.
　　除了生产率的变化之外，预测方程中的其他组成部门也可以进行调换或调剂。例如，由于新的劳动合同或材料 价钱所引起的单元上的变更也可以在预测总成本中得以反应。实际上，在计算附加成本时也会碰到同样的问题，只 管跟着项目的一直进展，项目当中不断定性的量和度都呈降落趋势。这个规矩的独一例外是完工产品由于重大质量 问题而需返修重建的情况。
　　Each of the estimating methods described above require current information on the state of work accomplishment for particular activities. There are several possible methods to develop such estimates, including:
　　上面所介绍的每一种预测方法都需要具体工作的劳动量完成状态信息。下面的多少种方法有助于进行成本的预 测。
　　z Units of work completed. 完工劳动单元。
　　For easily measured quantities the actual proportion of completed work amounts can be measured. For example, the linear feet of piping installed can be compared to the required amount of piping to estimate the percentage of piping work completed.
　　对易于丈量的劳动数目，可直接得到实际完工劳动量占总劳动量的比例。例如，将已安装的直线管道和须要安 装的管道数量进行比拟便可测算出已完工管道劳动量的百分比。
　　Incremental milestones. 里程碑累计
　　Particular activities can be sub-divided or “decomposed” into a series of milestones, and the milestones can be used to indicate the percentage of work complete based on historical averages. For example, the work effort involved with installation of standard piping might be divided into four milestones.
　　某项详细工作可被分解成一系列的里程碑，而这些里程碑可用来显示完工劳动量基于历史均匀值的百分比。例 如，某尺度管道装置工作的劳动可被划分为如下4 个里程碑。
　　① Spool in place: 20% of work and 20% of cumulative work.
　　② Ends welded: 40% of work and 60% of cumulative work.
　　③ Hangars and Trim Complete: 30% of work and 90% of cumulative work.
　　④ Hydrotested and Complete: 10% of work and 100% of cumulative work.
　　① 管轴就位：20%的劳动量和20%的累计劳动量。
　　② 管道焊接：40%的劳动量和60%的累计劳动量。
　　③ 支座和清算：30%的劳动量和90%的累计劳动量。
　　④ 热压测试和完工：10%的劳动量和100%的累计劳动量。
　　Thus, a pipe section for which the ends have been welded would be reported as 60% complete.
　　从这里可以看出，管缝焊接完工时，工作总劳动量的 60%已经完成。
　　z Opinion. 判断。
　　Subjective judgments of the percentage complete can be prepared by inspectors,suits armani, supervisors or project managers themselves. Clearly, this estimated technique can be biased by optimism, pessimism or inaccurate observations. Knowledgeable estimaters and adequate field observations are required to obtain sufficient accuracy with this method.
　　对于完工百分比的主观判定可由监视方、监理方或项目经理本人做出。显然，由于乐观、达观或视察不够过细 等主观原因，会使上面所做出的断定有所偏颇。因而，应用这种办法要想保障相称的正确性，就请求预测者岂但存 在丰盛的常识，还应有足够的现场察看。
　　z Cost ratio. 成本率。
　　The cost incurred to date can also be used to estimate the work progress. For example, if an activity was budgeted to cost $20 000 and the cost incurred at a particular date was $10 000, then the estimated percentage complete under the cost ratio method would be 10 000/20 000 = 0.5 or fifty percent. This method provides no independent information on the actual percentage complete or any possible errors in the activity budget: the cost forecast will always be the budgeted amount. Consequently, managers must use the estimated costs to complete an activity derived from the cost ratio method with extreme caution.
　　完工成本也能用来预测工作进度。例如，如果某工作的预算成本为20 000 美元而截止某特定日期已发生的成本为10 000 美元，那么用成本率来表示预测完工百分率就是10 000/20 000=0.5 或50%。然而，用这种方法来精确地反映工作实际完工比例还需依附其他信息，并且会产生工作预算上的一些过 错，因为在这里，预测成本始终等于预算成本。因此，项目经理在用成本率导出的预测成原来完成某工作时必需极 其审慎。
　　Systematic application of these different estimating methods to the various project activities enables calculation of the percentage complete or the productivity estimates used in preparing job status reports.
　　通过对各种项目工作体系地应用不同的预测方式，可以计算出工作状况呈文要用到的完工百分比和生产率的估 算值。
　　In some cases, automated data acquisition for work accomplishments might be instituted. For example, transponders might be moved to the new work limits after each day’s activity and the new locations automatically computed and compared with project plans. These measurements of actual progress should be stored in a central database and then processed for updating the project schedule.
　　在有些情况下，需要构建一个自动读取完工数据的系统。例如，在当天工作完成之后，读取器会主动移向新的 工作表及其地址进行运算并和项目规划进行比较。项目的实际进度会被存储到中心数据库中，经由处置后用以更新 项目方案。
　　Example 5.1 Estimated total cost to complete an activity.
　　例 5.1 完成某项工作的预计总成本。
　　Suppose that we wish to estimate the total cost to complete piping construction activities on a project. The piping construction involves 1 000 linear feet of piping which has been divided into 50 sections for management convenience. At this time, 400 linear feet of piping has been installed at a cost of $40 000 and 500 man-hours of labor. The original budget estimate was $90 000 with a productivity of one foot per man-hour, a unit cost of $60 per man hour and a total material cost of $ 30 000. Firm commitments of material delivery for the $30 000 estimated cost have been received.
　　假定欲估算某项目直线管道铺设工程的总成本。该管道工程是总长为 1 000 英尺(1 英尺=0.304 8 米)的直线管道铺设，为了便利管理被划分成50 段。此时，已有400 英尺的直线管道以40 000 美元的成本和500 人工时的劳能源进行了铺设。初始预算约为90 000 美元，其中生产率为1 英尺/工时，每工时的单位成本为60 美元，且总的材料成本为30 000 美元。材料的运输已得到保证。
　　The first task is to estimate the proportion of work completed. First, 400 linear feet of pipe is in place out of a total of 1 000 linear feet, so the proportion of work completed is 400/1 000 = 0.4 or 40%. This is the “units of work completed” estimation method. Second, the cost ratio method would estimate the work complete as the cost-to-date divided by the cost estimate or $40 000/$ 90 000 = 0.44 or 44%.Third, the “incremental milestones” method would be applied by examining each pipe section and estimating a percentage complete and then aggregating to determine the total percentage complete. For example, suppose the following quantities of piping fell into four categories of completeness:
　　第一项工作是估算完工劳动的比例。首先，已对总长度为 1 000 英尺的直线管道中的400 英尺进行了铺设，所以已完工劳动的百分比为400/1 000=0.4 或40%。这里用到的是完工劳动单元估算法。其次，用成本率法来估算完工劳动率，即用完工成本除以估算成本 ,paul smith spectacles，亦即40 000 美元/90 000 美元=0.44 或44%。最后，用“里程碑累计”法来核查管道的每一分项工程,tory burch reva，估算其完工百分比并进行逐项累计，以肯定总完工百分比。例如，假定把管道工程的完成按4 个种别进行划分。
　　Then using the incremental milestones shown above, the estimate of completed work would be 380 + 20×0.9 + 5×0.6 + 0 = 401 ft and the proportion complete would be 401 ft/1 000 ft =0.401 or 40% after rounding.
　　依据上面的里程碑累计，完工劳动的估算应该为(380+20×0.9+5×0 .6+0)英尺=401 英
　　尺，完工比例为401 英尺/1 000 英尺=0.401，或近似取0.4。
　　Once an estimate of work completed is available, then the estimated cost to complete the activity can be calculated. First, a simple linear extrapolation of cost results in an estimate of $40 000/0.4 = $100 000 for or the piping construction using the 40% estimate of work completed.
　　一旦得到了竣工劳动量的估算值,a&f outlet online，就可以进行工作开工成本的盘算。首先，因为管道工程已实现了约40%，所以用线性推演得到的预计本钱为4 0 000 美元/0.4=100 000 美元。这象征着按当前状况名目将会呈现(100 000-90 000)美元=10 000 美元的成本超支。 This estimate projects a cost overrun of 100 000-90 000 = $10 000.Second, a linear extrapolation of productivity results in an estimate of (1 000 ft)(500 hrs/400 ft)($60/hr) + 30 000 = $105 000 for completion of the piping construction. This estimate suggests a variance of 105 000-90 000 = $15 000 above the activity estimate. The source of the variance can also be identified in this calculation: compared to the original estimate, the labor productivity is 1.25 hours per foot or 25% higher than the original estimate. 其次，假如用生产率进行线性推演，可得管道工程的完工估算成本为1 000 英尺×500小时/400 英尺×60 美元/小时+30 000 美元=105 000 美元。在这种情形下，预计有(105 000-90 000)美元=15 000 美元的成本偏差。偏差的起因也能够懂得为跟初始估算比拟，劳动生产率为1.25 小时/英尺或比初始估算中的劳动出产率在每英尺管道上多用了0.25 小时。
　　Example 5.2 Estimated Total Cost for Completion.
　　例 5.2 完工项目的预计总成本。
　　The forecasting procedures described above assumed linear extrapolations of future costs, based either on the complete experience on the activity or the recent experience. For activities with good historical records, it can be the case that a typically non-linear profile of cost expenditures and completion proportions can be estimated. Figure 5.1 illustrates one possible non-linear relationships derived from experience in some particular activity. For example, point A in Figure 5.1 suggests a higher expenditure than is normal for the completion proportion. This point represents 40% of work completed with an expenditure of 60% of the budget. Since the historical record suggests only 50% of the budget should be expended at time of 40% completion, a 60%-50%=10% overrun in cost is expected. If comparable cost overruns continue to accumulate, then the cost-to-complete will be even higher.
　　上例中的预测程序是在对工作有完全的或近期的教训基本上，用线性方法来推断将来的成本。而对有些历史数 据完全的工作，即便数据之间成非线性关联，仍可预测其成本超支和完工百分比。图5.1 所示为成本和完工百分比呈非线性关系的某工作。例如，图5.1 中的A 点表现在对应的完工百分比上其成本却有所超支，即在该点劳动量完成了40%，但成本支出却占到了预算成本的 60%。而根据历史统计，当劳动量完成40%时，成本支出应占预算成本的50%，因此出现了60%-50%=10%的成本偏差。如果这种可比的成本超支持续累计下去，那么完工成本将变高。