## Note

21 Mar 2020: Created.

## 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, price, profit, margin, markup

- 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).

## % 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/(100-S).
- The denominator is the payable qty (qty left).