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Statistical applications to construction Chapter  12 265


                  1.20
                  1.00
                 Probability  0.60
                  0.80
                  0.40
                  0.20
                  0.00
                  $25,800.00  $25,900.00  $26,000.00  $26,100.00  $26,200.00  $26,300.00  $26,400.00  $26,500.00  $26,600.00
                                         Project range ($)
             FIG. 12.9.1 Risk graph of contingency for exhaust stack silencer.




                Observe Fig. 12.9.1; the probability the expected value exceeds the expected
             cost is 50%.
                Therefore, the values less than $26,200 are greater than 50%.
                From the analysis, the estimator can estimate the contingency from the
             risk graph.

             12.10 Bid assurance

             The contractor needs to bid high enough to make profit but low enough to get
             the job.
                The “optimum bid” or the “best bid” will result in a successful bid. When the
             bid leads to winning a job, then there is an opportunity to verify the estimate’s
             accuracy, reliability, and quality. The purpose of this section is to provide
             methods for optimizing the bid and regulate cost. This defines bid assurance.


             12.10.1 Expected profit

             It is important the contractor understand the bidding process. For example, the
             contractor will bid high and win no jobs or bid low and get many jobs with no
             profit. The higher the bid, the lower the chance of success. The lower bid has
             better chances of success but more chance of loss. The difference between the
             bid price and the cost depends on the contractor’s need for work, minimum
             acceptable markup, and the maximum contractor markup. Markup is defined
             as the difference between the bid price and the estimated cost. Expected profit
             is defined as
                Profit: P ¼ Bp   Ec
                Expected profit: Ep ¼ Pr*(B   Ec)
             where
                Bp ¼ bid price
                Ec ¼ estimated cost
                Pr ¼ probability of event (Bp   Ec), 0   Pr   1
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