A unit-price/measure-and-value example

Our second example of a cost estimate is for the construction of an embankment and roadway. Once again, the example is oversimplified but still includes the basic concepts. In this example, the result of our effort will be a series of unit prices for each of the specified bid items, as required by the tender instructions. These unit prices, multiplied by their respective quantities, will determine the total tender price, which will be compared with those from other tenderers. Our approach will be to calculate the total tender price using methods similar to those employed for the previous example, to allocate that total to each of the various bid items and to divide by the respective estimated quantities to determine the unit prices.

The tender documents would include a schedule of quantities such as those shown in Table 4.2. It is important to understand that the items listed here are the only items for which the owner will pay. Thus all project expenses not included under the listed items must somehow be channelled into the unit prices for the listed items. If the contractors proposal is accepted by the owner, its payments will be based on the actual quantities installed multiplied by their respective unit prices, as explained in Chapter 2. The estimated quantities are used only to determine a total tender price and thus compare the tender prices from each tenderer.

Table 4.3 shows the cost estimate for the project whose quantities are listed in Table 4.2. First, we develop the direct costs for each of the 11 pay items. Note that the contractor intends to perform clearing and grubbing, earthwork, culvert piping and geotextile installation with its own forces and subcontract the paving, signage and traffic marking.

For each element of direct cost, we compile a cost estimate. The contractors cost records may contain sufficient unit cost information to allow simply multiplying that unit cost by the estimated quantity. Clearing and grubbing might be an example of this approach. In other cases, the items cost may be developed as a combination of several different components, each with its unit costs. For example, the material cost for corrugated steel pipe might be a combination of the costs of pipe, connectors, bedding material and hardware, even though the pay item is based solely on length of pipe. Another approach is to conduct an analysis of the works details, setting forth, in the case of labour, the estimated time required, based on crew size and productivity and the cost per hour or day. The labour involved in base course installation might include studies of loading, hauling, dumping, spreading, watering, compacting and final grading. Whatever method is used, we arrive at a direct cost for each element of each item. In the case of aggregate base course, for example, the estimated direct costs are US$ 201 662, based on US$ 40 364 for labour and US$ 161 298 for material. In this example, we have elected to show equipment costs as a single item, rather than as an element of each item. We noted this approach in our previous discussion of equipment costs. The rationale in this case might be that we expect our equipment fleet to be assigned to the project for its duration or specified periods within its duration and the project will be responsible for the fleets costs continuously during the time the equipment is on the job. We thus calculate these costs based on their cost per time (say, per month) and the duration each is expected to be assigned to the project. In our example, the total of the direct costs (excluding equipment) for all pay items is US$ 903 968. However, there are other costs that relate directly to construction operations. Whether they are classified as direct or overhead costs may be arguable, but in any case, they must be included in our cost estimate! For this project, we expect to have mobilisation, surveying and layout, traffic control and demobilisation expenses in the amounts shown. Because no pay items include these expenses, we will allocate them to the items in a process to be explained shortly. The subtotal for all direct costs is US$ 1 291 132. To this subtotal we add costs for site overhead, general overhead, profit and contingency, bonds and sales tax, in a manner similar (though not in the same order) to that explained for our lump-sum estimate. The bottom line total tender price is US$ 1 711 743. If this were a lump-sum tender, we would submit this single number as our proposed price. However, in the case of a unit-price (measure-and-value) tender, we also furnish unit prices for each item listed in the schedule of quantities. The final steps in our calculations result in unit prices for each of the 11 items which, when multiplied by their respective estimated quantities, give a sum equal, or nearly equal, to US$ 1 711 743. One way to approach the task is to allocate the sum of all the amounts below the US$ 903 968 of direct costs in Table 4.3 to each of the 11 items in proportion to that items listed direct cost. The amount to be added is the difference between the total tender price of US$ 1 711 743 and the US$ 903 968 of direct costs, or US$ 807 775. To accomplish this calculation, we find the ratio of US$ 1 711 743 to US$ 903 968, or 1.893588 and multiply that ratio by the direct cost for each item to arrive at the tender total for the item. In the case of unclassified excavation, the calculation is (US$ 77 406)(1.893588) = US$ 146 575. As shown in Table 4.3, the total of these 11 tender totals is our total tender price of US$ 1 711 743, as expected. Finally, we divide each tender total by its respective estimated quantity to find its unit price. Because the unit price has been derived in this fashion, the total price in our tender, which shows unit prices multiplied by their estimated quantities, will give the desired total tender price. Table 4.4 summarises the results of the various calculations in Table 4.3; the pricing section of the contractors tender would consist essentially of the information in Table 4.4. Note that rounding of the unit prices to the nearest US$ 0.01, as would be required in a tender offer, results in some minor differences between the 11 tender total numbers in Table 4.3 and the estimated amounts in Table 4.4, although the final tender price, at US$ 1 711 741.50, is remarkably close to our target of US$ 1 711 743. The calculations explained above are an example of balanced unit-price tendering, in which the allocations of the various overheads and other non-direct charges are allocated proportionately to each tender items direct cost. There are a variety of other ways we could split the total tender price of US$ 1 711 743 among the 11 items and still arrive at the desired total. For example, we could reduce the amount for asphalt concrete by US$ 10 000 and add an equal amount to the clearing and grubbing item. The resulting unit prices would be US$ 23 434 per hectare and US$ 126.22 per tonne. This practice of unbalanced tendering might be used by a contractor interested in increasing its cash flow early in the project by receiving higher revenue on clearing and grubbing; note that the total revenue is unchanged, assuming the actual quantities are the same as the estimated quantities. A contractor might also employ unbalanced tendering if it believed the actual quantities for some items were going to be different than estimated. (This is a good reason to perform independent calculations to check the quantities furnished in the schedule of quantities.) Items whose quantities were expected to be higher than estimated would be assigned higher than proportional unit prices, while those anticipated to be lower than estimated would have their unit prices reduced. An exercise at the end of this chapter demonstrates this effect. Caution is advised in using unbalanced tendering for this latter purpose; if the actual quantities are not as anticipated, the results may be unfavourable.


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