3.2 Preparation of Schedule of Rates

Preparation of the schedule of rates is a crucial step in civil engineering cost estimation in Kenya. It involves determining the unit cost for each item of work based on abstracted quantities and cost data. These rates form the basis for preparing the bill of quantities and help ensure accurate budgeting and tendering. This section addresses the calculation of rates, applying standard costing guidelines, ensuring accuracy, and adjusting rates according to project-specific conditions.

3.2.1 Calculating Rates Based on Abstracted Quantities

Calculating rates based on abstracted quantities involves deriving unit costs for each work item by analyzing detailed quantities from drawings and specifications. The quantities abstracted must be precise and representative of the actual work scope to produce reliable rates. The formula for the rate per unit typically combines direct costs, overheads, and profit margins.

The general formula for rate per unit is:

$$ \text{Rate per unit} = \frac{\text{Total cost for work item}}{\text{Quantity of work item}} $$

Worked Examples

Example 1: Calculate the unit rate for concrete work when 5 m³ of concrete costs Ksh 75,000.

Given:
Quantity \(Q = 5\) m³, Total cost \(C = 75,000\) Ksh

$$ \text{Rate} = \frac{C}{Q} $$

$$ = \frac{75,000}{5} $$

$$ = 15,000 \text{ Ksh/m}^3 $$

Answer: 15,000 Ksh per m³

Example 2: A wall plastering work has an abstracted quantity of 120 m² with a total cost of Ksh 36,000. Calculate the rate per m².

Given:
Quantity \(Q = 120\) m², Total cost \(C = 36,000\) Ksh

$$ \text{Rate} = \frac{C}{Q} $$

$$ = \frac{36,000}{120} $$

$$ = 300 \text{ Ksh/m}^2 $$

Answer: 300 Ksh per m²

Example 3: For excavation work, 25 m³ costs Ksh 50,000 including labour and equipment hire. Find the unit rate.

Given:
Quantity \(Q = 25\) m³, Total cost \(C = 50,000\) Ksh

$$ \text{Rate} = \frac{C}{Q} $$

$$ = \frac{50,000}{25} $$

$$ = 2,000 \text{ Ksh/m}^3 $$

Answer: 2,000 Ksh per m³

Example 4: A road surfacing item has 80 m² abstracted quantity with a total cost of Ksh 112,000. Calculate the rate per m².

Given:
Quantity \(Q = 80\) m², Total cost \(C = 112,000\) Ksh

$$ \text{Rate} = \frac{C}{Q} $$

$$ = \frac{112,000}{80} $$

$$ = 1,400 \text{ Ksh/m}^2 $$

Answer: 1,400 Ksh per m²

Example 5: A steel reinforcement item has 1,000 kg abstracted quantity costing Ksh 250,000. Calculate the rate per kg.

Given:
Quantity \(Q = 1,000\) kg, Total cost \(C = 250,000\) Ksh

$$ \text{Rate} = \frac{C}{Q} $$

$$ = \frac{250,000}{1,000} $$

$$ = 250 \text{ Ksh/kg} $$

Answer: 250 Ksh per kg

3.2.2 Applying Standard Costing Guidelines

Applying standard costing guidelines ensures consistency and comparability of rates across projects. These guidelines include using approved cost data, standard labour productivity rates, material prices, and equipment hire charges. The Kenya Building and Road Research Institute (KBRRI) and other recognized bodies provide such standardized data.

The formula to calculate rates using standard costing is:

$$ \text{Rate} = \text{Labour cost} + \text{Material cost} + \text{Plant cost} + \text{Overheads} + \text{Profit} $$

Worked Examples

Example 1: Calculate the rate per m³ for concrete using the following standard data: Labour cost Ksh 3,000, Material cost Ksh 8,000, Plant cost Ksh 1,000, Overheads 10% of direct costs, Profit 5% of total cost.

Given:
Labour = 3,000 Ksh
Material = 8,000 Ksh
Plant = 1,000 Ksh
Overheads = 10% of (3,000 + 8,000 + 1,000)
Profit = 5% of total cost

Step 1: Calculate direct costs

$$ \text{Direct costs} = 3,000 + 8,000 + 1,000 = 12,000 $$

Step 2: Calculate overheads

$$ \text{Overheads} = 0.10 \times 12,000 = 1,200 $$

Step 3: Calculate subtotal before profit

$$ \text{Subtotal} = 12,000 + 1,200 = 13,200 $$

Step 4: Calculate profit

$$ \text{Profit} = 0.05 \times 13,200 = 660 $$

Step 5: Calculate total rate

$$ \text{Rate} = 13,200 + 660 = 13,860 \text{ Ksh/m}^3 $$

Answer: 13,860 Ksh per m³

Example 2: For brickwork, labour cost is Ksh 1,500, material cost Ksh 4,000, plant cost Ksh 500, overheads 12%, profit 8%. Calculate the unit rate.

Given:
Labour = 1,500 Ksh
Material = 4,000 Ksh
Plant = 500 Ksh
Overheads = 12%
Profit = 8%

Step 1: Direct costs

$$ 1,500 + 4,000 + 500 = 6,000 $$

Step 2: Overheads

$$ 0.12 \times 6,000 = 720 $$

Step 3: Subtotal

$$ 6,000 + 720 = 6,720 $$

Step 4: Profit

$$ 0.08 \times 6,720 = 537.60 $$

Step 5: Total rate

$$ 6,720 + 537.60 = 7,257.60 \text{ Ksh/m}^3 $$

Answer: 7,257.60 Ksh per m³

Example 3: Excavation labour Ksh 2,000, materials Ksh 3,000, plant Ksh 1,200, overheads 15%, profit 10%. Calculate rate per m³.

Given:
Labour = 2,000 Ksh
Material = 3,000 Ksh
Plant = 1,200 Ksh
Overheads = 15%
Profit = 10%

Step 1: Direct costs

$$ 2,000 + 3,000 + 1,200 = 6,200 $$

Step 2: Overheads

$$ 0.15 \times 6,200 = 930 $$

Step 3: Subtotal

$$ 6,200 + 930 = 7,130 $$

Step 4: Profit

$$ 0.10 \times 7,130 = 713 $$

Step 5: Total rate

$$ 7,130 + 713 = 7,843 \text{ Ksh/m}^3 $$

Answer: 7,843 Ksh per m³

Example 4: For plastering, labour Ksh 1,200, materials Ksh 2,800, plant Ksh 600, overheads 8%, profit 7%. Calculate rate per m².

Given:
Labour = 1,200 Ksh
Material = 2,800 Ksh
Plant = 600 Ksh
Overheads = 8%
Profit = 7%

Step 1: Direct costs

$$ 1,200 + 2,800 + 600 = 4,600 $$

Step 2: Overheads

$$ 0.08 \times 4,600 = 368 $$

Step 3: Subtotal

$$ 4,600 + 368 = 4,968 $$

Step 4: Profit

$$ 0.07 \times 4,968 = 347.76 $$

Step 5: Total rate

$$ 4,968 + 347.76 = 5,315.76 \text{ Ksh/m}^2 $$

Answer: 5,315.76 Ksh per m²

Example 5: Steel reinforcement labour Ksh 4,000, materials Ksh 12,000, plant Ksh 2,000, overheads 10%, profit 12%. Calculate rate per kg.

Given:
Labour = 4,000 Ksh
Material = 12,000 Ksh
Plant = 2,000 Ksh
Overheads = 10%
Profit = 12%

Step 1: Direct costs

$$ 4,000 + 12,000 + 2,000 = 18,000 $$

Step 2: Overheads

$$ 0.10 \times 18,000 = 1,800 $$

Step 3: Subtotal

$$ 18,000 + 1,800 = 19,800 $$

Step 4: Profit

$$ 0.12 \times 19,800 = 2,376 $$

Step 5: Total rate

$$ 19,800 + 2,376 = 22,176 \text{ Ksh/kg} $$

Answer: 22,176 Ksh per kg

Kenyan Context Notes

In practice, standard costing guidelines in Kenya are often based on data published by organizations such as the Kenya Building and Road Research Institute (KBRRI), the National Construction Authority (NCA), and the Institution of Quantity Surveyors of Kenya (IQSK). For example, rates for labour and materials may be referenced from NCA's annual construction cost reports, while equipment hire charges can be obtained from rental firms such as Mantrac Kenya or Quipbank Trust Limited. When preparing rates for public projects, compliance with the Public Procurement and Asset Disposal Act is mandatory.

3.2.3 Ensuring Accuracy in Costing

Accuracy in costing requires precise measurement, proper data collection, and verification of all inputs. Small errors in quantities or rates can lead to significant budget deviations. Accuracy is achieved by cross-checking quantities, validating unit prices with suppliers and contractors, and updating data regularly.

The error margin can be calculated as:

$$ \text{Error \%} = \frac{|\text{Estimated cost} - \text{Actual cost}|}{\text{Actual cost}} \times 100 $$

Worked Examples

Example 1: Estimated cost Ksh 1,200,000, actual cost Ksh 1,150,000. Calculate error percentage.

Given:
Estimated \(E = 1,200,000\) Ksh
Actual \(A = 1,150,000\) Ksh

$$ \text{Error \%} = \frac{|1,200,000 - 1,150,000|}{1,150,000} \times 100 $$

$$ = \frac{50,000}{1,150,000} \times 100 $$

$$ = 4.35\% $$

Answer: 4.35% error

Example 2: Estimated cost Ksh 850,000, actual cost Ksh 900,000. Calculate error percentage.

Given:
Estimated \(E = 850,000\) Ksh
Actual \(A = 900,000\) Ksh

$$ \text{Error \%} = \frac{|850,000 - 900,000|}{900,000} \times 100 $$

$$ = \frac{50,000}{900,000} \times 100 $$

$$ = 5.56\% $$

Answer: 5.56% error

Example 3: Estimated cost Ksh 2,500,000, actual cost Ksh 2,600,000. Calculate error percentage.

Given:
Estimated \(E = 2,500,000\) Ksh
Actual \(A = 2,600,000\) Ksh

$$ \text{Error \%} = \frac{|2,500,000 - 2,600,000|}{2,600,000} \times 100 $$

$$ = \frac{100,000}{2,600,000} \times 100 $$

$$ = 3.85\% $$

Answer: 3.85% error

Example 4: Estimated cost Ksh 4,000,000, actual cost Ksh 3,900,000. Calculate error percentage.

Given:
Estimated \(E = 4,000,000\) Ksh
Actual \(A = 3,900,000\) Ksh

$$ \text{Error \%} = \frac{|4,000,000 - 3,900,000|}{3,900,000} \times 100 $$

$$ = \frac{100,000}{3,900,000} \times 100 $$

$$ = 2.56\% $$

Answer: 2.56% error

Example 5: Estimated cost Ksh 1,000,000, actual cost Ksh 1,050,000. Calculate error percentage.

Given:
Estimated \(E = 1,000,000\) Ksh
Actual \(A = 1,050,000\) Ksh

$$ \text{Error \%} = \frac{|1,000,000 - 1,050,000|}{1,050,000} \times 100 $$

$$ = \frac{50,000}{1,050,000} \times 100 $$

$$ = 4.76\% $$

Answer: 4.76% error

3.2.4 Adjusting Rates Based on Project Constraints

Adjusting rates considers unique project conditions such as site location, accessibility, labour availability, and climatic factors. These constraints affect productivity, material handling, and equipment usage, requiring rate adjustments to reflect increased costs or savings.

The adjustment factor can be applied as:

$$ \text{Adjusted rate} = \text{Base rate} \times (1 + \text{Adjustment percentage}) $$

Worked Examples

Example 1: Base rate for excavation is Ksh 3,000 per m³. Due to difficult site access, a 12% adjustment is necessary. Calculate the adjusted rate.

Given:
Base rate \(R = 3,000\) Ksh/m³
Adjustment \(A = 12\%\)

$$ \text{Adjusted rate} = R \times (1 + \frac{A}{100}) $$

$$ = 3,000 \times (1 + 0.12) $$

$$ = 3,000 \times 1.12 = 3,360 \text{ Ksh/m}^3 $$

Answer: 3,360 Ksh per m³

Example 2: Concrete work base rate is Ksh 15,000 per m³. A 7% reduction applies due to proximity to supplier. Calculate new rate.

Given:
Base rate \(R = 15,000\) Ksh/m³
Adjustment \(A = -7\%\)

$$ \text{Adjusted rate} = 15,000 \times (1 - 0.07) $$

$$ = 15,000 \times 0.93 = 13,950 \text{ Ksh/m}^3 $$

Answer: 13,950 Ksh per m³

Example 3: Labour-intensive finishing has a base rate of Ksh 800 per m². Due to scarcity of skilled labour, a 20% increase is applied. Calculate adjusted rate.

Given:
Base rate \(R = 800\) Ksh/m²
Adjustment \(A = 20\%\)

$$ \text{Adjusted rate} = 800 \times (1 + 0.20) $$

$$ = 800 \times 1.20 = 960 \text{ Ksh/m}^2 $$

Answer: 960 Ksh per m²

Example 4: Road surfacing base rate is Ksh 1,200 per m². Wet season reduces productivity, requiring a 15% increase. Find adjusted rate.

Given:
Base rate \(R = 1,200\) Ksh/m²
Adjustment \(A = 15\%\)

$$ \text{Adjusted rate} = 1,200 \times (1 + 0.15) $$

$$ = 1,200 \times 1.15 = 1,380 \text{ Ksh/m}^2 $$

Answer: 1,380 Ksh per m²

Example 5: Steel reinforcement base rate is Ksh 220 per kg. Due to difficult handling conditions, a 10% increase is needed. Calculate adjusted rate.

Given:
Base rate \(R = 220\) Ksh/kg
Adjustment \(A = 10\%\)

$$ \text{Adjusted rate} = 220 \times (1 + 0.10) $$

$$ = 220 \times 1.10 = 242 \text{ Ksh/kg} $$

Answer: 242 Ksh per kg

Chapter Summary

This chapter focused on the preparation of the bill of quantities, starting with the development of clear and detailed specifications that cover both materials and workmanship, ensuring alignment with SMM and CESMM standards. It emphasized the importance of cross-referencing specifications with drawings and designs to maintain accuracy and consistency. The chapter then addressed the preparation of the schedule of rates, detailing how to calculate rates from abstracted quantities while applying standard costing guidelines. Attention was given to maintaining accuracy in costing and making necessary adjustments to rates based on specific project constraints. Finally, the chapter covered the compilation of the bill of quantities itself, highlighting the need for it to be comprehensive, accurate, and formatted according to standard practices. The process concludes with a thorough review of the bill of quantities to ensure consistency with the prepared specifications.