project costing

Abstract - To solve project cost control problem, the concept of project cost elasticity is introduced and the model of project cost elasticity analysis is proposed. Case study shows that the cost elasticity model is useful and helpful to control project costs. Finally, a road map is provided forstockholders to use cost elasticity model to control projectcosts.Keywords - Elasticity analysis, cost control , projectmanagementI. INTRODUCTIONCost control is a main part of construction projectmanagement, which has the following features: The investment of the project needs to be calculated independently; the evidence determining the investmentis complicated; various levels determining the investments require dynamic tracking control in the process of construction. The investment control has greatdifficulty by virtue of many stockholders involved in theproject. The theories and methods of project investmentcontrol have been the research hotspot in the constructionproject management [1]-[5] .By using elasticity analysis theory, the paper introduces the concept of investment elasticity ofconstruction project, and establishes the model of projectcost elasticity analysis, thus to provide theoreticalsignificance and practical instructiveness for the stockholders of construction project to effectively controland manage the costs in the process of project construction.II. PROJECT COST ELASTICITYElasticity analysis is a classical economic analysismethod, which was first put forward by classical economist Alfred Marshall. In the economic analysis, the basic elasticity is the price elasticity of demand [6] , whose definition is the ratio of percentage of the demand variation to that of the price variation, see the following equation:%%P D E = (1)Where, E is the demand price elasticity; D% is the percentage of demand variation; p% is the percentage of price variation. This equation provides the demand sensitivity measurement when the price varies along with the demand curve and reflects the sensitivity degree of the demand to price variation.The elasticity concept is introduced into the project influenced by various factors, thus to grasp the risk degree of the project. by virtue of their long construction period, construction projects, especially the large and middle-scaled ones, demand hi-technology, involve broad aspects and has greater influence on various markets, so uncertain factors may change in some way are many. Normally speaking, the uncertain factors that affect the project costs are: construction conditions, construction schemes, the costs of equipments and materials, exchange rates, wage level of the workers, different pricingstandards and rates, construction periods and so on. By means of the multi-factor elasticity analysis of the project costs , we can find out the sensitivity factors (keyfactors) and the sensitivity degree (the influence degree on the costs ) , so that we can seize the sensitivity factors to effectively control cost and thus to achieve maximum results with little effort.III. COST ELASTICITY MODEL OF CONSTRUCTION PROJECT Normally we can use the following function to calculate the project costs :),,(21k X X X f I ⋅⋅⋅⋅⋅⋅= (2) Where I denotes Project costs; iX denotes the influence factor; k denotes the sum of the factors that influence the costs . As all the factors vary, 1X ，2X ，……k X respectively change into '1X ，'2X ，……'k X ,therespective variable quantity is 1X Δ，2X Δ，……k X Δ, then,'11'1X X X Δ+=，'22'2XXXΔ+=，……''kkkXXXΔ+=，meanwhile, the constructionproject costs I changes correspondingly from Ito 'I ，the variable quantity is I I I −=Δ'. When ||X Δis not large, i.e. the various influencing factors do not change too much, using multivariate function of Taylor expansion it is obtained that :kkX X fXXf X X fI Δ∂∂++Δ∂∂+Δ∂∂≈Δ (2)211(3)Cost Elasticity Analyzing Model of Construct ProjectDongbing Huang 1, Wen Zhang 11School of Management, Guizhou College of Finance and Economics, Guiyang, ChinaWhere ：iXf ∂∂is the partial derivative toiX toI；i X Δis the variable quantity to i X ；I Δ is the variablequantity of I when all relevant factors change 。

If all the factors do not change except i X ，that is ，ij X X j i ≠=Δ≠Δ,0,0， i I Δ should be taken as thevariable quantity of construction project costs I andiI Δis the influence value of i XΔ to I .From equation (3) we can obtain ：iii X X fI Δ∂∂≈Δ (4)Apparently ：∑=Δ=Δ+Δ+Δ≈Δki kIII II 121 (5)On the basis of the previous discussion, we can make an elasticity analysis on it so as to determine the key factors that influence the project costs. Definition: the ratio of variable quantity of the construction project costs to that of the factors that induce the variation)/()/(i i i X X I I Δis the elasticity of i X to I ，denoted by i E .The meaning of i E is: the change of a percent point of the factor I will induce i E percent point change of theproject costs. When i Eis positive, it means i IΔ and i X Δ change in the same direction, that is, if i X increasesby 1 percent point ，I will be increased byiE percentagepoint correspondingly, vice versa. When i Eis negative,it meansiI Δ andi X Δ change in the opposite directions, in other words, ifiX increases by 1 percent point ，I will be decreased byiE percentage point, viceversa. The larger the value of i E is, the more influenceit will have on the construction project costs and the more sensitive the project costs is to the factor I . Now we can take the factor I as a sensitivity factor, which is the main point we have to control in the process. It can be )()/()/(IXXf X X I I Eiii i i i∂∂=ΔΔ= (6)So as to control the project costs in different phases of the project construction, firstly, we can figure out the elasticity of all the factors, and then arrange them from big to small, thus we can foresee what influence will be exerted by the factors on the project costs. Therefore, we can lay emphasis on the sensitivity factors and control the project costs efficiently in the process of construction.IV. CASE ANALYSISThe following examples tell us how to use parameter to make multi-factor elasticity analysis on the construction project costs.In china, the construction project costs consist of direct costs, indirect costs and profits. 4.1 Direct costs 4.1.1 Main direct cost (GI )4.1.2 Other direct cost (C I )4.2 Indirect cost4.2.1 Construction management cost (E I )4.2.2 Other indirect cost (F I )4.3 profits4.3.1 Planned profit (R I )4.3.2 Tax (S I)Various costs should be calculated as followed ： ∑×=ii G Q P I , （Unit Price i P , Engineering Quantityi Q ）；C G C r I I ×=，C r other direct costs rate ；∑×+×=×+=EC i i E C G E r r Q P r I I I )1)(()(E rConstruction management cost rate ；∑×+×=×+=FC i i F C G F r r Q P r I I I )1)(()(，Fisindirect cost rate ；∑×+++×=×+++=R F E C i i R F E C G R r r r r Q P r I I I I I )1)(1)(()(，R ris profit rate. The taxes includes business taxes, the urban maintenance construction taxes and education surtaxes, the taxes should be calculated on the premise of the integral construction project costs , with the deduction of three items of special fund (other indirect costs ) as the tax base: the temporary facilities expenses, labor insurance expenditure and the transfer costs of the constructionteams. So SF Sr I I I ×−=)(，S r is taxes rate. Combining the previous equations we obtain theconstruction project costs,SF R F E CG S R F E C G r I I I I I I I I I I I I I I ×−+++++=+++++=)()()(；i.e.SSF R F E Ci i S S F R F E C G r r r r r r r Q P r r I I I I I I I −•−++++×=−×−++++=∑1)1)(1()1)((1Taking the price variety of the building materials during the construction period into consideration, we get the construction project cost (suppose we invest evenly during the construction period) is2)1(1)1)(1()1)((N SSF R F E C i i L r r r r r r r Q P I +−•−++++×=∑ (7)every cost should receive its profitWhere L denotes the average annual growth rate of project cost in the predictive construction duration ；N denotes the predictive construction period (unit: year). The elasticity i Eof the variable displacement is the following equation (the detailed calculation is omitted):∑××=×∂∂=ii ii i i Q Q P Q P IQ Q IE i(8)Similarly ，∑××=ii iiP Q P Q P E i From equations (7) and (8) we can see that i Q E and i P E are equal, both of which depend onwhat ratio i iQ P ×is to the main direct cost. The larger the ratio is, the more sensitive it will be, and the moreinfluence the change between unit price i P and project quantity i Q will have on the construction project cost.They are greater than zero, therefore, the constructionproject cost will change in the same direction with i Pi Q .C C C C r r r I r r I E C +=×∂∂=1 (9) Cr E Depends on C r ，the greater C r is, the bigger C r E becomes, the more influence it will be exertedto the costs. S F R F E E R EE r r r r r r r r I r r I E E ×−+×+++=×∂∂=)1()1()1((10)From equation (11) we can see that the value of Er E is not only determined by the construction management cost rate E r ， but also influenced by other indirect cost rate F r 、profit rateR r and tax rate S r .S F R F E F S R FF r r r r r r r r r I r r I E F ×−+×++−+=×∂∂=)1()1()1((11)S F R F E R F E RR r r r r r r r r r I r r I E R×−+×++++=×∂∂=)1()1()1((12)))1()1)((1()12)1)(1((S F R F E S S F R F E S SS r r r r r r r r r r r r r I r r I E S ×−+×++−+−+++=×∂∂=(13))1(2L L N I L L I E L +×=×∂∂= (14) )1ln(L N I N N I E N+×=×∂∂= (15)Supposing the rates are C r =10%，E r =7%，F r =9%，R r =3.24%，the construction period is 4 years, theaverage annual growth rate of prices L =8%，let’s substitute rates and the above integral service fee into the equations respectively, we can obtain the concrete value of sensitivity degree of every factor. Arrange the rates from big to small:N E =0.308，L E =0.148，C r E =0.09，R r E =0.065，E r E =0.06，S r E =0.06，Fr E =0.059.And we can clearly see when N Eis at its maximum, theconstruction period influences the construction costsmost. With other conditions unchanged, to delay theconstruction period by 1%, namely 12 days (supposing the construction period is 300 days) will cause the growthof the construction costs by 0.308%. Similarly, if the construction period is shortened by 1%, that is, 12 days in advance, the total costs will decline by 0.308%. Secondly, the growth rate of prices has more influence on the costs . With other conditions unchanged, so long as the actual annual growth rate of prices is 10% instead of 8% as foreseen, in other words, the change rate of L is ΔL/L=(10%-8%)/8%=25%，then the total costsincreases by 3.7%(=25%*L E =25%*0.148). Similarly, ifthe actual annual growth rate of prices is only 5%, i.e. the change rate ΔL/L = (5%-8%)/8% = −37.5%，then theconstruction costs decreases by 5.55%. Cr has the greatest influence on the construction costs , the next is the profit rate R r .If R r rises from the present7% to 15%, that is, the change rate of R r is ΔR r /R r =(15%-7%)/7%=114.3%. with other conditions unchanged, the construction costs will rise by7.426%(=114.3%*0.065). If Statutory profit rate is 2.5%instead of 7%, the change rate of R ris −64.29%，thenthe construction costs will decrease from the present standards by 4.179%(=64.29%*0.065).with other conditions unchanged, suppose the elasticity of construction management cost rate E r is 0.06, if E rrises from 7% to 8% or declines to 6%, the construction costs will rise or declines by 0.95%(=14.29%*0.06). Due to various member relationships of enterprises or enterprises under different levels, when we make the pretender, pricing standards are also diverse. We can make a pretender on the basis of a certain pricing standard, and use the elasticity analysis to obtain the pretenders of other pricing standards.V. CONCLUSIONIn the construction, the stakeholders involved canapply the method of elasticity analysis to the control ofthe construction project costs. Firstly, in the phrases of designing and contract issuing, because the project hasn’t begun, the majority of the influencing factors are just estimated value, and the costs determined is only a predicted one. In the process of construction, the actual costs will not be completely identical with the predicted one. Especially when the market changes great, there is a deviation from the actual costs of the project to the predicted one. To limit the deviation in the permission scope, the constructers can apply the method of elasticity analysis to the cost control so as to have an in-depth understanding of the influence on the costs caused by the uncertain factors and take corresponding measures in advance to disperse and reduce the costs risk. Moreover, we can be enlightened to re-analyze the key (sensitive) factors to improve the forecasting reliability. Next, in the project bidding, the contractor can take the elasticity analysis on the project costs to accurately estimate the possible risks after undertaking the project, reasonably bid quotation and effectively guarantee their legitimate interests. Finally, relevant departments of the government can also apply this elasticity analysis to supervising and managing the construction costs so that they can precisely estimate the policies concerned, determine what effect will bring out on the whole society and the total construction costs when the project is implemented, and improve the science and correctness of decision. For example, we can apply the elastic analysis on the construction project costs to accurate determining the influence degree of tax rate on the project costs . If adjusting the tax rate, we can take corresponding measures and supporting policies in advance, and make full play to the policy of tax adjustment while decrease the side effect along with it.REFERENCES[1]W. Y. Jin, W. Z. Tong, “Research of the Method on Pre-project Control (periodical style),” Forecasting, no.4, pp.52-55, 2004.[2] A. B. Qi, “The Problem and Solution of Estimate atCompletion Forecasting Method in Earned Value Analysis (periodical style),” Forecasting, no.2, pp.56-60, 2004. [3]X. H. Zhou, "The study of earned value method in projectmanagement. The study of quantitative economics and technical economy (periodical style),” The Journal of Quantitative & Technical Economics, no.4, pp.143-148, 2005.[4]Y. H. Mao, Y. H. Luo, “Problems facing and PolicySuggestion on the construction project investment (periodical style),” Techno economics & Management Research, no.1, pp.91-91, 2006.[5]Pindyck, R. S, “Investments of uncertain cost (periodicalstyle),”Journal of Financial Economics, vol.34, pp.53-76, 1993.[6]Stiglitz, Joseph E, “Economics (Third Edition, Volume1), Beijing, China Renmain University Press, 2006,ch.6, pp.88-89.phases IFB````````````````````。