Question 4 of 6: Estimating and Bidding — Unit-Price Estimate with Local Labour Rates

Question 4: Estimating and Bidding — Unit-Price Estimate with Local Labour Rates (20 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Given. A quantity of 1,500 m² of a single work item, priced from a published unit-cost line for crew CR-7, together with local bare wage rates that differ from the ones behind the published line.

Find. The duration of the activity in working days and the construction cost of the 1,500 m², both at the published rates and re-priced with the local labour rates, on a bare-cost basis and on a basis including overhead and profit.

Approach. Confirm that the published line is internally consistent so the crew size and the working day are known, obtain the duration from the daily output and the labour content from the labour-hour figure, then re-price only the labour component at the local rates while carrying the material component and the overhead-and-profit markups across unchanged.

1. Check the published line for internal consistency. Multiplying the daily output by the labour-hours per unit must return the crew’s labour-hours in one day:$$\begin{aligned}\text{LH per day} &= 13.94\ \frac{\text{m}^2}{\text{day}}\times 1.148\ \frac{\text{h}}{\text{m}^2}\\ &= 16.00\ \frac{\text{h}}{\text{day}}\end{aligned}$$Sixteen labour-hours a day is two people on an eight-hour shift, which matches the stated crew of one worker plus one helper. The published bare labour cost also checks: $1.148 \times 23.55 = 27.04$ dollars per square metre against the 27 shown in the line.
2. Compute the duration from the daily output. With production fixed at the published rate,$$t = \frac{Q}{\text{daily output}} = \frac{1{,}500}{13.94} = 107.6\ \text{working days}$$so the activity is scheduled as $\boxed{108\ \text{working days}}$, about 21.5 five-day weeks or five calendar months, before any allowance for weather or holidays.
3. Compute the total labour content. The labour-hour figure applies directly to the quantity:$$H = Q \times 1.148 = 1{,}500 \times 1.148 = 1{,}722\ \text{labour-hours}$$shared between two people, so 861 hours each — which divided by an eight-hour day returns 107.6 days and confirms the duration independently of step 2.
4. Price the work at the published rates as a baseline. Applying the line item unchanged,$$\begin{aligned}C_{\text{bare,book}} &= 1{,}500\times 75.50 = 113{,}250\\ C_{\text{O\&P,book}} &= 1{,}500\times 93.50 = 140{,}250\end{aligned}$$in Canadian dollars. These are the figures an estimator would read straight out of the manual, and they are the ones the local wage rates now displace.
5. Convert the local wage rates to a crew cost per labour-hour. The crew is one worker and one helper, so the crew average is the arithmetic mean of the two bare rates:$$r_{\text{local}} = \frac{30.00+25.00}{2} = 27.50\ \text{per labour-hour}$$against the 23.55 dollars per labour-hour behind the published line — local labour is 16.8 per cent more expensive.
6. Re-price the bare labour component. Labour cost per unit is the labour-hour content times the crew rate:$$c_{\text{lab,local}} = 1.148 \times 27.50 = 31.57\ \text{per m}^2$$The material component is a purchase price and is untouched by the wage change, so the adjusted bare unit cost and total are$$c_{\text{bare,local}} = 48.50 + 31.57 + 0 = 80.07\ \text{per m}^2$$$$C_{\text{bare,local}} = 1{,}500\times 80.07 = \boxed{120{,}105}$$Canadian dollars, an increase of 6,855 dollars on the published bare estimate.
7. Carry the overhead-and-profit markups across to the local rates. The published line prices labour at 34.83 dollars per labour-hour including overhead and profit against 23.55 bare, a markup factor of$$f_{\text{lab}} = \frac{34.83}{23.55} = 1.4790$$and the material markup follows by subtraction from the published total, $93.50 - 1.148\times 34.83 = 53.5152$ dollars per square metre against 48.50 bare, which is the usual ten per cent on purchased material. Applying the labour factor to the local crew rate gives $27.50\times 1.4790 = 40.6720$ dollars per labour-hour, hence$$c_{\text{lab,O\&P}} = 1.148\times 40.6720 = 46.6914\ \text{per m}^2$$
8. Assemble the priced estimate. Adding the marked-up material and labour,$$c_{\text{O\&P,local}} = 53.5152 + 46.6914 = 100.2066\ \text{per m}^2$$$$C_{\text{O\&P,local}} = 1{,}500\times 100.2066 = \boxed{150{,}310}$$Canadian dollars. This is the figure that would be carried into the bid for this work item, the 120,105 dollar bare cost being the internal budget against which the site will be measured.