02 // Visual Math & Finance SolversNet Price = List × (1 − d%) × (1 + tax%), Margin = (P − C) / P
Visual Retail Discount, Gross Margin & Markup Analyzer
Retail pricing distinguishes Gross Margin $\text{Margin} = \frac{\text{Price} - \text{Cost}}{\text{Price}}$ (share of revenue retained) from Markup $\text{Markup} = \frac{\text{Price} - \text{Cost}}{\text{Cost}}$ (multiple added onto cost).
Net Price = List × (1 − d%) × (1 + tax%), Margin = (P − C) / PInputs & Parameters (3)
$
10$±52000$
%
0%±190%
%
0%±0.530%
30% of $200
$60.00
Remainder = $140 (70%)
Increased (+30%)
$260
Multiplier = 1.300×
Discounted (−30%) + 8.5%
$152
Net factor = 75.95% of base
Recovery Gain Needed
+42.86%
To recover from a −30% drawdown
20-Row Comparison Table
Compare across:
| # | List / Unit Price ($) | Primary Share (P₁% of V) | V × (1 − 30%) | With +8.5% Tax |
|---|---|---|---|---|
| 01 | 10 $ | $3.00 | $7.00 | $7.60 |
| 02 | 115 $ | $34.50 | $80.50 | $87.34 |
| 03 | 220 $ | $66.00 | $154 | $167 |
| 04 | 325 $ | $97.50 | $228 | $247 |
| 05 | 430 $ | $129 | $301 | $327 |
| 06 | 535 $ | $161 | $375 | $406 |
| 07 | 640 $ | $192 | $448 | $486 |
| 08 | 745 $ | $224 | $522 | $566 |
| 09 | 850 $ | $255 | $595 | $646 |
| 10 | 955 $ | $287 | $669 | $725 |
| 11 | 1,055 $ | $317 | $739 | $801 |
| 12 | 1,160 $ | $348 | $812 | $881 |
| 13 | 1,265 $ | $380 | $886 | $961 |
| 14 | 1,370 $ | $411 | $959 | $1,041 |
| 15 | 1,475 $ | $443 | $1,033 | $1,120 |
| 16 | 1,580 $ | $474 | $1,106 | $1,200 |
| 17 | 1,685 $ | $506 | $1,180 | $1,280 |
| 18 | 1,790 $ | $537 | $1,253 | $1,360 |
| 19 | 1,895 $ | $569 | $1,327 | $1,439 |
| 20 | 2,000 $ | $600 | $1,400 | $1,519 |
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Key Analytical Takeaways
- 01Whether sales tax is applied before or after a percentage discount, the final checkout price is identical because $(P \times 0.70) \times 1.085 = (P \times 1.085) \times 0.70$.
- 02A $50\%$ markup on cost corresponds to a $33.3\%$ gross profit margin on selling price ($\text{Margin} = \text{Markup} / (1 + \text{Markup})$).
- 03Stacking a $20\%$ discount plus an extra $10\%$ off yields $1 - (0.80 \times 0.90) = 28\%$ off, not $30\%$ off.
Frequently Asked Questions
What is the difference between markup and gross margin?+
Markup divides profit by Cost ((Price - Cost) / Cost), while Gross Margin divides profit by Selling Price ((Price - Cost) / Price). Margin is always a smaller percentage than markup.
How do stacked promotional discounts work?+
Sequential discounts multiply their retention factors: a 30% discount followed by an extra 20% coupon leaves 0.70 × 0.80 = 56% of list price (a 44% effective discount).
How do you convert gross margin directly into markup percentage?+
Markup % = Margin / (1 − Margin). For example, achieving a 40% gross margin requires a 0.40 / 0.60 = 66.67% markup above unit cost.