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5 million of operating profit on 20 million of capital employed is a 25 % return. Against a cost of capital of 8 % that is a spread of 17 points; at 6 % it would be a spread of −2, and every extra euro invested would destroy value.
Camille Laurent · 4 min read
50,000 of net income on 200,000 of revenue is 25 %. Two identical businesses can show 22.5 % and 15 % on the same operations, with the entire gap coming from how they are financed.
Camille Laurent · 3 min read
60,000 of operating income on 200,000 of revenue is 30 %. It sits between a gross margin that depends on accounting policy and a net margin that depends on debt and tax.
Camille Laurent · 3 min read
200,000 of revenue less 120,000 of cost of sales is 80,000 of gross profit and a 40 % margin. Everything the business spends after that comes out of the 80,000 — and out of nowhere else.
Camille Laurent · 3 min read
Sunrise, sunset and the moment the sun is highest all hang off your longitude, not off the clock on the wall. In the same legal time zone, solar noon can be an hour and three quarters apart — and that gap explains most surprises about when the sun comes up.
Lena Hoffmann · 7 min read
8 grams obtained where 10 were possible is an 80 % yield. Chain five such steps and 32.8 % of the starting material reaches the end — which is why a long synthesis is judged step by step.
Lena Hoffmann · 3 min read
One mole per kilogram of a salt that splits in two lowers water's freezing point by 3.72 °C. The same amount of something that stays whole manages 1.86 °C — exactly half.
Marco Bianchi · 3 min read
Mass percent divides by the solution, not by the solvent. Twenty-five grams into a hundred gives 125 grams of solution and 20 %, a quarter less than the number most people expect.
Lena Hoffmann · 3 min read
50 mg in a litre is 50 ppm, because a litre of water weighs a million milligrams. Change the liquid, or move to air, and the two units stop agreeing.
Sofia Nunes · 3 min read
0.5 mol in 2 litres is 0.25 mol/L. The two litres have to be the finished solution — adding solute to two litres of water gives something else, and the label will be wrong.
Lena Hoffmann · 3 min read
Buying at 100 and selling at 130 is a profit of 30 %, measured on the cost. Measured on the sale it is 23.08 % — the same trade, and a gap of nearly a quarter of the figure.
Camille Laurent · 3 min read
2 is to 5 as 8 is to 20. Map scales, unit prices, percentages, recipe scaling and drawing enlargements are the same equation wearing five different names.
Lena Hoffmann · 3 min read