What this lesson covers
Procurement and Contracting Requirements is the largest subject area on the NASCLA Commercial General Building exam: 31 of the 115 scored questions. A good share of it is business arithmetic, and the single most common trap is confusing markup with margin. This free lesson teaches the difference, the four formulas that convert between them, and how to price a bid in layers. If you can do these, you can answer these questions faster than any lookup.
The book to tab for business arithmetic is the NASCLA Contractors Guide to Business, Law and Project Management. But you should not need to open it for these questions: learn the formulas.
The idea in one line
Markup is measured against cost. Margin is measured against price. The dollars of profit are the same; only the base changes. Because price is bigger than cost, the margin percentage is always smaller than the markup percentage for the same dollars.
The four formulas
| You know | You want | Formula |
|---|---|---|
| Cost and markup | Price | Price = cost x (1 + markup) |
| Cost and margin | Price | Price = cost / (1 - margin) |
| Markup | Margin | Margin = markup / (1 + markup) |
| Margin | Markup | Markup = margin / (1 - margin) |
Write percentages as decimals: 20% is 0.20.
Step 1: price from a markup
A contractor's estimated cost for a tenant build-out is $250,000 and the company marks up cost by 20%.
- Price = 250,000 x 1.20 = $300,000.
- Profit = 300,000 - 250,000 = $50,000.
- Margin = 50,000 / 300,000 = 16.67%.
Check with the conversion formula: 0.20 / 1.20 = 0.1667. Same answer.
Step 2: price from a margin
The same contractor wants a 20% margin instead.
- Price = 250,000 / (1 - 0.20) = 250,000 / 0.80 = $312,500.
- Profit = 312,500 - 250,000 = $62,500.
- Check: 62,500 / 312,500 = 0.20, a 20% margin. And as a markup, 62,500 / 250,000 = 25%, which matches 0.20 / 0.80 = 0.25.
The gap: marking up by 20% when you need a 20% margin leaves the bid at $300,000 instead of $312,500, short by $12,500.
Step 3: convert between the two
Two quick conversions to practice until they are automatic:
- A 25% markup is a margin of 0.25 / 1.25 = 20%.
- A 10% margin is a markup of 0.10 / 0.90 = 11.11%.
Check the first in dollars: cost 100, price 125, profit 25; 25 / 125 = 20%. Check the second: price 100, profit 10, cost 90; 10 / 90 = 11.11%.
Step 4: layered overhead and profit
Many bids add overhead first, then profit on cost plus overhead. Apply each percentage to the base the question names.
Example. Direct cost $180,000. Overhead 12% of direct cost. Profit 10% of cost plus overhead.
- Overhead = 180,000 x 0.12 = 21,600. Subtotal = 201,600.
- Profit = 201,600 x 0.10 = 20,160. Bid = $221,760.
Check in one line: 180,000 x 1.12 x 1.10 = 180,000 x 1.232 = 221,760.
What it is not: adding 12% and 10% to get 22% and multiplying 180,000 x 1.22 = 219,600. That is $2,160 lower, because the profit was meant to apply to the overhead too.
Step 5: read the question's base
Exam wording tells you which base to use. Look for these phrases:
- "Markup on cost", "percentage of cost", "marked up by": the base is cost.
- "Margin", "gross profit as a percentage of sales", "percentage of the selling price" or "of the contract amount": the base is price.
- "Profit on cost plus overhead": apply after overhead is added.
Common traps
- Treating markup and margin as the same. They are equal only at zero.
- Subtracting a margin from price to get cost the wrong way. If price is $312,500 at a 20% margin, cost is 312,500 x 0.80 = $250,000, not 312,500 / 1.20.
- Adding layered percentages instead of multiplying them.
- Forgetting to check. Divide profit by the base the question names. If it matches, you are done.
Try it
The ten free practice questions that go with this lesson use the same formulas with different numbers. Work each one twice: once with the formula, once in dollars.
Not affiliated with or endorsed by NASCLA or PSI.