Price, margin and a supplied tax model

A teaching case gives an optical retailer a tax-exclusive frame cost of 40 euros. The desired selling-price-based gross-margin rate, called taux de marque in this exercise, is 60 percent. The case supplies a hypothetical 20 percent tax rate for the arithmetic and does not ask the learner to establish the current legal tax treatment. The store also has annual fixed costs of 150000 euros and a contribution-margin ratio of 0.60 in a separate simplified break-even model. A colleague multiplies cost by 1.60 and calls the result a 60 percent taux de marque. The learner must explain why that denominator is wrong, keep tax-inclusive and tax-exclusive values separate, and avoid confusing the commercial calculation with a guarantee of patient reimbursement.