62 lines
1.5 KiB
Markdown
62 lines
1.5 KiB
Markdown
---
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title: Markup vs. Margin
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tags:
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- status/complete
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- type/encyclopedia-entry
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---
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# Markup vs. Margin
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**Markup** and **margin** describe the profit of a sold good or service in terms of its cost.
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$$
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\text{Profit} = \text{Sell Price} - \text{Cost}
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$$
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**Markup** describes an item's profit as a fraction of its cost to the merchant.
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$$
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\text{Markup} = \frac{\text{Profit}}{\text{Cost}}
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$$
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**Margin** describes an item's profit as a fraction of its **sell price**,
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its cost to the customer.
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$$
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\text{Margin} = \frac{\text{Profit}}{\text{Sell Price}}
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$$
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$$
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\begin{align}
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\rm Margin &= \rm \frac{(Sell\ Price - Cost)}{Sell\ Price} \\
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\rm Margin \times Sell\ Price &= \rm Sell\ Price - Cost \\
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\rm Cost &= \rm -1 \times (Margin \times Sell\ Price - Sell\ Price) \\
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\rm &= \rm -1 \times Margin \times Sell\ Price + Sell\ Price \\
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\rm &= \rm Sell\ Price \times (1 - Margin)
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\end{align}
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$$
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## Example
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Suppose a product that
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* costs $80 to produce
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* is sold for $100
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$$
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\text{Profit} = \$100 - \$80 = \$20, \quad
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\text{Markup} = \frac{(\$20)}{\$80} = 25\%, \quad
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\text{Margin} = \frac{(\$20)}{\$100} = 20\%
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$$
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## Converting Between Markup and Margin
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$$
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\text{Margin} = \frac{\text{Markup}}{1 + \text{Markup}}, \quad
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\text{Markup} = \frac{\text{Margin}}{1 - \text{Margin}}
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$$
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> [!warning]
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> Contractors (and sellers of products and services in general)
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> almost exclusively talk about profit in terms of margin.
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> **Even if someone says "15% _markup_"**
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> **they may still be talking about margin.**
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