Margin and markup are different numbers and confusing them is expensive: a 50 per cent markup is a 33 per cent margin. This calculates both from any two inputs, prices backwards from a target, and works out how many units cover your fixed costs.
Margin is profit as a share of the selling price; markup is profit as a share of the cost. Buy at 100 and sell at 150 and you have a 50% markup but a 33.3% margin. Pricing as if they were the same is a common way to under-price systematically.
Divide the cost by one minus the margin, not multiply by one plus it. For a 40% margin on a cost of 100: 100 / 0.6 = 166.67. Multiplying by 1.4 gives 140, which is only a 28.6% margin.
How many units you must sell before fixed costs are covered and further sales become profit. It falls out of the contribution per unit - price minus variable cost - so raising the price or cutting variable cost moves it far more than trimming fixed costs does.