Building construction project has become an everyday issue, and this involves the spending of hard earned money by the project owner called the client. The expectation of the owner of any building project is justification of good project delivery. This is enabled by the objectives of the project which definitely includes project cost that envelopes the cost and quality of delivery at the expected time. The major issue, is the project cost which dictates its success. Project cost variance has been affecting the speedy and successful delivery of building construction projects. The key fact in this study method was to collect and analyse public building project cost estimates containing building components, which includes preliminaries, substructure, superstructure, mechanical/electrical, external works and contingency in the bill of quantity (BOQ) from projects handled by Education Trust Fund(ETF) in the tertiary institutions located in Kaduna, Kwara, Kogi and Abuja from 2009 to 2010. The study adopted mean component cost method modeled by Skitmore and Ng (2002) to determine the projected cost variance of the Lecture Theatres and Lecture Rooms handled by the organization in various tertiary institutions in Nigeria. The analysis of the data collected was made by using standard method of analysis which employs SPSS for the project costs.Skitmore and Ng (2002) model was employed to test the variability of the project cost data. The result shows that; the building component cost data 4782.50 had closer link to the mean 4773.92(mean) for preliminaries component column in project ID 4 of Lecture Theatreandanother component data 2797.62 is also close to 2312.91(mean) for Ext.Wkscolumn in project ID 7 for the Lecture Theatre building projects butfor the Lecture Classrooms building the preliminaries column had 1531.41 and 1416.33(mean) in project ID 2 and 1611.22 and 1673..58(mean) for M/E column for project ID 5. This project therefore concludes in addition to the results of the cost variances, that the lecture theatre and classrooms projects are underestimated.Interview was also conducted on the professional estimators in building industry. Moreover significant differences exist among the components in those public buildings.The analytical calculation shows that the correct variance for an average lecture theatre project from this research was found to be 34.73%. The sample analyzed had shown that the correct variance of the class room was found to be 38. 50%. Therefore lecture theatre is observed to be a better building project than the class room building. The study recommends the need to minimize the occurrence of the overrun by thoroughly crosschecking the initial estimate and addressing other technical issues before the contract is awarded. It also recommends the employment of the mean component cost method of analysis and setting of a committee to properly scrutinize the estimate.

In the building construction industry, it is a formal procedure to determine the initial cost of a building project before awarding the contract. This is in order to ascertain the financial level of the client whether the project is worth undertaking. The underlyingfact is because of the instability of the market prices of material, labour and equipment which are the major tools involved in the construction.

The wave of project production cost variability in the recent time calls for a concern in the building industry. If a building project cost estimate is presented for tender and the contractor gives his quotations, with all necessary adjustment made and contract is awarded, it is not likely that the agreed contract price will still be the final project cost at completion. The final project cost is often found to be higher at completion.

There are many factors leading to the changes in the final cost. Giwa (1998) had stated that the effect of change between the initial and the final cost incurred constitute a major problem in the building industry, especially between the client and estimator. This cost differential is called cost variance in the building construction industry. Cost variance is significant for general cost planning, and can be a big problem to solve by the managers in the building industry.