# Profit, margin, markup, wastage, bulkage and shrinkage

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## Note

21 Mar 2020: Created.

## Simple approach

1. When we face with the above terms, what should be the mathematical formulae to handle them and how can we remember the formulae?
2. 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

1. cost + profit = price.
2. profit markup % = profit / cost x 100%.
3. profit margin % = profit / price x 100%.
4. Given profit markup and price, how to get the cost?
5. 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)
6. 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

1. If a finished qty of work of 100 requires a material qty of 120. The qty wasted is 20.
2. Should the wastage be 20/100 = 20% or 20/120 = 16.67%?
3. Both can be correct depending on which is used as the base.
4. However, in pricing, when the payment is based on the finished qty, the qty wasted should be borne by the finished qty.
5. In the above example, the addition to cover the qty wasted is 20/100 = 20%, so the wastage should be 20%.
6. 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%.
7. To conclude, the wastage to be allowed
= qty wasted / finished qty
= (qty used - finished qty) / finished qty
= (qty used / finished qty) - 1.
8. The denominator is the payable qty (finished qty).

## % bulkage (excavation)

1. How to allow for the extra volume to work on if payment is based on the volume before bulking?
2. Bulkage or bulking factor = volume after bulking / volume before bulking.
3. Volume after bulking = volume before bulking x bulkage.
4. 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)

1. How to allow for shrinkage if payment is based on the quantity after shrinkage?
2. If shrinkage = 20%, for each 100 qty, qty shrunk = 20, qty left = 80.
3. The addition to cover the qty shrunk = 20/80 = 25%.
4. If shrinkage = 30%, for each 100 qty, qty shrunk = 30, qty left = 70.
5. The addition to cover the qty shrunk = 30/70 = 42.86%.
6. If shrinkage = S%, then the addition factor = S/(100-S).
7. The denominator is the payable qty (qty left).

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