By the end of this chapter, you will be able to:
Mastering these skills will help you prepare precise cost estimates that are essential for successful project planning and budgeting in the trade.
Building up unit rates is a fundamental skill for quantity surveyors involved in estimating and costing works in Kenya’s construction industry. Accurate unit rates ensure that project budgets reflect realistic costs of labour, materials, plant, and overheads, critical for competitive tendering and cost control. This chapter focuses on the mathematical build-up of unit rates by combining all direct and indirect costs associated with a work item, enabling quantity surveyors to prepare reliable cost estimates.
Building up unit rates involves calculating the cost per unit of work by aggregating costs of materials, labour, plant, and overheads. This process requires a systematic approach to quantify resource requirements and apply current market rates, ensuring the final unit rate is comprehensive and reflects site conditions and procurement factors.
Material cost per unit is the direct cost of all materials required to complete one unit of work. This calculation includes the quantity of each material, wastage allowances, and unit prices obtained from supplier quotations or market rates.
The basic formula to calculate material cost per unit is:
$$\text{Material Cost per Unit} = \sum ( \text{Quantity of Material}_i \times \text{Unit Price}_i \times (1 + \text{Wastage Allowance}_i) )$$
Example 1: Calculate the material cost per square metre for a brick wall where 60 bricks are required per square metre, the cost per brick is Ksh 50, and wastage allowance is 5%.
Given:
Quantity of bricks = 60 bricks/m\(^2\)
Unit price = Ksh 50/brick
Wastage allowance = 5% = 0.05
$$ \text{Material Cost} = 60 \times 50 \times (1 + 0.05) $$$$ = 60 \times 50 \times 1.05 $$$$ = 60 \times 52.5 $$$$ = 3150 \text{ Ksh/m}^2 $$
Answer: Ksh 3,150 per m\(^2\)
Example 2: Calculate the material cost for a concrete slab of 1 m\(^3\) requiring 0.4 m\(^3\) of cement (Ksh 7,000/m\(^3\)), 0.6 m\(^3\) of sand (Ksh 3,000/m\(^3\)), and 1.2 m\(^3\) of aggregate (Ksh 2,500/m\(^3\)) with 3% wastage for all materials.
Given:
Cement = 0.4 m\(^3\), Ksh 7,000/m\(^3\)
Sand = 0.6 m\(^3\), Ksh 3,000/m\(^3\)
Aggregate = 1.2 m\(^3\), Ksh 2,500/m\(^3\)
Wastage = 3% = 0.03
$$ \text{Material Cost} = (0.4 \times 7000 + 0.6 \times 3000 + 1.2 \times 2500) \times (1 + 0.03) $$$$ = (2800 + 1800 + 3000) \times 1.03 $$$$ = 7600 \times 1.03 $$$$ = 7828 \text{ Ksh/m}^3 $$
Answer: Ksh 7,828 per m\(^3\)
Example 3: For plastering 10 m\(^2\) of wall, 0.015 m\(^3\) of cement, 0.03 m\(^3\) of sand are required per m\(^2\). Cement costs Ksh 8,000/m\(^3\), sand costs Ksh 3,500/m\(^3\), and wastage is 2%. Calculate the material cost per m\(^2\).
Given:
Cement = 0.015 m\(^3\)/m\(^2\), Ksh 8,000/m\(^3\)
Sand = 0.03 m\(^3\)/m\(^2\), Ksh 3,500/m\(^3\)
Wastage = 2% = 0.02
$$ \text{Material Cost} = (0.015 \times 8000 + 0.03 \times 3500) \times (1 + 0.02) $$$$ = (120 + 105) \times 1.02 $$$$ = 225 \times 1.02 $$$$ = 229.5 \text{ Ksh/m}^2 $$
Answer: Ksh 229.50 per m\(^2\)
Labour cost per unit accounts for the wages of workers needed to complete one unit of work, including allowances, productivity rates, and working hours. Labour rates are influenced by trade type, skill level, and prevailing wage agreements in Kenya.
The formula to calculate labour cost per unit is:
$$\text{Labour Cost per Unit} = \frac{\text{Labour Time per Unit} \times \text{Labour Rate per Hour}}{\text{Labour Productivity}}$$
Example 1: A mason takes 2 hours to lay 1 m\(^2\) of brickwork. The labour rate is Ksh 500/hour. Calculate the labour cost per m\(^2\).
Given:
Labour time = 2 hours/m\(^2\)
Labour rate = Ksh 500/hour
$$ \text{Labour Cost} = 2 \times 500 $$$$ = 1000 \text{ Ksh/m}^2 $$
Answer: Ksh 1,000 per m\(^2\)
Example 2: A carpenter requires 3 hours to fix 1 door frame. Labour rate is Ksh 600/hour. Productivity adjustment factor is 0.9 (90% efficiency). Calculate the labour cost per door frame.
Given:
Labour time = 3 hours
Labour rate = Ksh 600/hour
Productivity = 0.9
$$ \text{Labour Cost} = \frac{3 \times 600}{0.9} $$$$ = \frac{1800}{0.9} $$$$ = 2000 \text{ Ksh} $$
Answer: Ksh 2,000 per door frame
Example 3: A plasterer takes 1.5 hours to plaster 1 m\(^2\). Labour rate is Ksh 450/hour. On a particular site, due to difficult conditions, productivity drops by 15%. Calculate the adjusted labour cost per m\(^2\).
Given:
Labour time = 1.5 hours/m\(^2\)
Labour rate = Ksh 450/hour
Productivity drop = 15% → productivity factor = 0.85
$$ \text{Labour Cost} = \frac{1.5 \times 450}{0.85} $$$$ = \frac{675}{0.85} $$$$ = 794.12 \text{ Ksh/m}^2 $$
Answer: Ksh 794.12 per m\(^2\)
Plant cost per unit covers the cost of equipment used for a work item, including hire charges, fuel, maintenance, and operator wages. The cost is allocated based on the plant's output capacity and the time used for the particular unit of work.
The formula for plant cost per unit is:
$$\text{Plant Cost per Unit} = \frac{\text{Total Plant Cost per Hour} \times \text{Time to Complete Unit}}{\text{Output per Hour}}$$
Example 1: A concrete mixer costs Ksh 1,200 per hour to hire. It mixes 2 m\(^3\) of concrete per hour. Calculate the plant cost per m\(^3\) of concrete.
Given:
Plant cost = Ksh 1,200/hour
Output = 2 m\(^3\)/hour
$$ \text{Plant Cost} = \frac{1200}{2} $$$$ = 600 \text{ Ksh/m}^3 $$
Answer: Ksh 600 per m\(^3\)
Example 2: An excavator costs Ksh 3,000 per hour including fuel and operator. It can excavate 50 m\(^3\) per hour. Calculate the plant cost per m\(^3\).
Given:
Plant cost = Ksh 3,000/hour
Output = 50 m\(^3\)/hour
$$ \text{Plant Cost} = \frac{3000}{50} $$$$ = 60 \text{ Ksh/m}^3 $$
Answer: Ksh 60 per m\(^3\)
Example 3: A generator costs Ksh 1,500 per day (8 hours). It powers tools for a site where 40 units of work are completed daily. Calculate the plant cost per unit.
Given:
Plant cost = Ksh 1,500/day
Working hours = 8 hours/day
Units per day = 40
$$ \text{Plant cost per hour} = \frac{1500}{8} = 187.5 \text{ Ksh/hour} $$$$ \text{Time per unit} = \frac{8}{40} = 0.2 \text{ hours/unit} $$$$ \text{Plant cost per unit} = 187.5 \times 0.2 = 37.5 \text{ Ksh/unit} $$
Answer: Ksh 37.50 per unit
Overheads and profit are indirect costs added to the direct costs (materials, labour, plant) to arrive at the final unit rate. Overheads cover site establishment, supervision, and administrative expenses, while profit is the contractor’s margin.
The formula for the final unit rate is:
$$\text{Final Unit Rate} = \text{Direct Cost} \times (1 + \text{Overhead Percentage} + \text{Profit Percentage})$$
Example 1: Direct cost for a unit is Ksh 5,000. Overheads are 10%, and profit is 5%. Calculate the final unit rate.
Given:
Direct cost = Ksh 5,000
Overhead = 10% = 0.10
Profit = 5% = 0.05
$$ \text{Final Unit Rate} = 5000 \times (1 + 0.10 + 0.05) $$$$ = 5000 \times 1.15 $$$$ = 5750 \text{ Ksh} $$
Answer: Ksh 5,750
Example 2: For a road paving unit, direct cost is Ksh 12,000. Overhead is 12%, and profit margin is 8%. Calculate the final unit rate.
Given:
Direct cost = Ksh 12,000
Overhead = 12% = 0.12
Profit = 8% = 0.08
$$ \text{Final Unit Rate} = 12000 \times (1 + 0.12 + 0.08) $$$$ = 12000 \times 1.20 $$$$ = 14400 \text{ Ksh} $$
Answer: Ksh 14,400
Example 3: A contractor estimates a direct cost of Ksh 20,000 for a unit. Overheads are 15%, profit is 10%. Calculate the final unit rate.
Given:
Direct cost = Ksh 20,000
Overhead = 15% = 0.15
Profit = 10% = 0.10
$$ \text{Final Unit Rate} = 20000 \times (1 + 0.15 + 0.10) $$$$ = 20000 \times 1.25 $$$$ = 25000 \text{ Ksh} $$
Answer: Ksh 25,000
Calculate the material cost per m\(^2\) for a block wall requiring 10 blocks per m\(^2\) at Ksh 120 per block with 7% wastage. (5 marks)
A carpenter takes 4 hours to build a door at Ksh 550 per hour. With a productivity factor of 0.8, find the labour cost per door. (5 marks)
An excavator costing Ksh 2,400 per hour can dig 40 m\(^3\) per hour. Find the plant cost per m\(^3\). (5 marks)
Direct cost of a unit is Ksh 15,000, overhead is 12%, profit is 8%. Calculate the final unit rate. (5 marks)
For a concrete slab, materials cost Ksh 8,000 per m\(^3\), labour Ksh 2,000 per m\(^3\), and plant Ksh 500 per m\(^3\). Overheads are 10%, profit 12%. Find the total unit rate. (10 marks)
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Create a free accountThis chapter focused on building up unit rates by breaking down the components of work into materials, labor, plant, and overheads to accurately determine the cost per unit. It explained the process of cost estimating as a critical step in preparing budgets and bids, emphasizing the need for precision and thoroughness. Various identified sources of cost information were discussed, including historical data, suppliers’ quotations, and published cost indices, which are essential for reliable estimates. The chapter also explored design variables that significantly affect the cost of a building, such as choice of materials, structural complexity, and site conditions. Understanding these variables allows estimators to anticipate cost variations and make informed decisions. Together, these topics equip students with the skills to prepare detailed and realistic cost assessments for construction projects. The knowledge gained ensures that estimates reflect true project requirements, helping to control budgets and reduce financial risks.
Calculate the unit rate for plastering if the labour cost is Ksh 250 per day, a worker can plaster 8 m² per day, and material cost per m² is Ksh 120. (2 marks)
A wall of dimensions 5 m by 3 m is to be plastered. Using the unit rate calculated in question 1, estimate the total cost of plastering the wall. (3 marks)
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