Note
 20/2/2023: Split from "Estimating and Pricing". Incorporating markup, margin, wastage, bulkage and shrinkage.
Cost and price
 “Cost” and “Price” are often used interchangeably.
 Between the two parties to a transaction, the price quoted by the Seller / Contractor is the cost to the Buyer / Employer / Client.
 For the same party, Cost + Profit = Price.
 Seller's price = buyer's cost.
Values
 Values can be monetary prices or other benefits.
 Cost can also include nonmonetary costs.
Price buildup
 The total price is built up from:
Labour costs (人工費)
+ Material costs (材料費)
+ Plant costs (機械費)
Direct costs (直接費)
+ Site and project overheads (現場及項目管理費)
+ Head office overheads (公司管理費)
Costs (成本)
+ Profit and risks allowance (利潤及風險費)
Allin price before value added tax (稅前綜合價)
+ Value added tax (從價稅）
Allin price (稅後綜合價)
 The value added tax here means a tax chargeable upon the net total price before this tax or the gross total price after this tax. Hong Kong does not implement valued added tax. Hong Kong only charges profit tax on the realisable profit annually.
 Some of the site and project overheads are not directly related to a particular work item but are commonly shared by more than one item. It is normal to price for these site and project overheads as the Preliminaries. The allin rate for the work item will then only include the balance of the site and project overheads not included in the Preliminaries.
 Profit and overheads are usually allowed for as a percentage of the direct costs. The usual norm for variation is 15%, but it will be very different in competitive tenders. The profit and overheads allowed in the prices for different items can be different.
 Some part of the Works may be sublet to subcontractors. They will include their own overheads in their prices to the Contractor. They may also share to provide some of the site overheads otherwise provided by the Contractor. Therefore, the markup on subcontractors' prices for profit and overheads should be less than that on direct labour and materials.
Markup and margin
 100 x (1 + 15%) = 100 + 15 = 115:
 115 has a markup of 15%.
 85 + 15 = 100:
 100 has a margin of 15%.
 15/115 = 13.04%:
 A markup of 15% is equal to a margin of 13.04%.
 15/85 = 17.64%:
 A margin of 15% is equal to a markup of 17.64%.
(revised, 18/2/2023)
Cost, price, profit, markup and margin

Simple approach:

When we face with the above terms, what should be the mathematical formulae to handle them and how can we remember the formulae?
 Instead of using x, y and z to represent the formulae, it would be easier to derive the formulae based on some simple numerical values using 100 as the base.

 cost + profit = price.
 profit markup % = profit / cost x 100%.
 profit margin % = profit / price x 100%.
 Given profit markup and price, how to get the cost?
 A long way:
 Cost + cost * profit markup % = price
 Cost * (1 + profit markup %) = price
 Cost = price / (1 + profit markup %) = price x 100 / (100 + profit based on 100).
 A quicker way:
 If cost = 100 and profit markup = 15%, then profit = 15 and price = 115
 This means, cost = price x 100 / 115
 If cost = 100 and profit markup = 10%, then profit = 10 and price = 110
 This means, cost = price x 100 / 110
 To conclude, if profit markup = P%, then cost = price x 100 / (100 + P).
 If cost = 100 and profit markup = 15%, then profit = 15 and price = 115
% wastage
 If a finished qty of work of 100 requires a material qty of 120. The qty wasted is 20.
 Should the wastage be 20/100 = 20% or 20/120 = 16.67%?
 Both can be correct depending on which is used as the base.
 However, in pricing, when the payment is based on the finished qty, the qty wasted should be borne by the finished qty.
 In the above example, the addition to cover the qty wasted is 20/100 = 20%, so the wastage should be 20%.
 If a 3 x 6 finished board requires a 4 x 8 uncut board, the wastage to be allowed is (4 x 8) / (3 x 6)  1 = 32/18  1 = 77.78%.
 To conclude, the wastage to be allowed
= qty wasted / finished qty
= (qty used  finished qty) / finished qty
= (qty used / finished qty)  1.  The denominator is the payable qty (finished qty).
% bulkage (excavation)
 How to allow for the extra volume to work on if payment is based on the volume before bulking?
 Bulkage or bulking factor = volume after bulking / volume before bulking.
 Volume after bulking = volume before bulking x bulkage.
 The addition to cover the extra volume is volume before bulking x bulkage. This should be simple.
% shrinkage (concrete, mortar, plaster, screed) or % compaction (soil backfilling)
 How to allow for shrinkage if payment is based on the quantity after shrinkage?
 If shrinkage = 20%, for each 100 qty, qty shrunk = 20, qty left = 80.
 The addition to cover the qty shrunk = 20/80 = 25%.
 If shrinkage = 30%, for each 100 qty, qty shrunk = 30, qty left = 70.
 The addition to cover the qty shrunk = 30/70 = 42.86%.
 If shrinkage = S%, then the addition factor = S/(100S).
 The denominator is the payable qty (qty left).
Allin rates and unit of quantity
 Allin rate = allin price / quantity.
 Not all the costs are directly proportional to the quantity of the work, it can be a combination of:
 Variable costs
 Fixed costs.
 Cost = f(weight) + f(volume) + f(area) + f(length) + f(number) + f(quality) + f(quality) + f(time) + f(others).
 When the total price of a work item is required to be broken down into quantity and rate, the unit of the quantity to be used should be one which represents the most cost significant variable.
 If there are more than one cost significant variable, then the work item should be broken down into more than one subitem.
 It is usual and easier to estimate the cost of a bigger sample quantity of a work item first and divide the cost by the quantity to obtain the unit rate so that:
 Those costs not directly related to the quantity of the work item can be shared
 Wastage, laps, etc. which are not measured in the quantity can be allowed for.
(revised, 18/2/2023)
Rate buildup
 Labour costs:
 Daily rates to include for:
 daily basic wage
 travelling and meal allowances
 allowances for hand tools and personal accessories
 allowances for holidays with pay
 mandatory provident fund (MPF) contribution
 year end bonus
 incentive payments
 levies and insurances if not priced separately
 etc.
 Time to consider:
 taking from stores, hoisting, lowering
 placing, fixing
 nonproductive travelling and recess time
 etc.
 Daily rates to include for:
 Material costs:
 Rates to include for:
 exfactory costs, package
 export transportation, transit insurance
 customs clearance and duties
 demurrage, offsite storage
 local delivery
 offloading, returning package
 etc.
 Quantities to consider:
 basic quantities
 breakage, damage, theft
 wastage (cutting, conversion)
 unmeasured laps
 bulkage, consolidation, shrinkage
 etc.
 Rates to include for:
 Plant costs (called "Equipment costs" in civil engineering contracts):
 Rates to include:
 Use of plant (not purchasing of plant)
 Mobilization, relocation and demobilization costs, if not measured separately
 Fuels and consumables
 Maintenance and repair.
 Time to consider:
 Time used
 Unavoidable idling time
 Mobilization, relocation and demobilization time, if not measured separately.
 Rates to include:
 Site and project overheads
 Expenses on site or offsite specifically due to the project, not specifically related to any particular group of work but are commonly shared.
 Head Office Overheads
 Expenses in running the head office, shared between different concurrent projects.
 Profit
 The expected profit with allowance for risks.
 Tax if charged based on total price (not in Hong Kong which implements profits tax on the realisable profit annually, not value added tax on turnover).
 Rates buildup applicable to measured work as well as preliminaries.
Tender pricing
See Tender Pricing for more details.