Mark up

Mark up is defined as the rate of gross profit to cost of sales:

Mark up = Gross Profit

              Cost of sales

Margin is defined as the rate of gross profit to sales:

Margin = Gross profit
                     Sales

Calculations of markup and margin are necessary to compute the profit loading on:

• Closing stock at the branch
• Returns from branch to head office

Examination questions may provide information on either the markup or the margin. If one is provided, it may be necessary to compute the other.

Let us assume:   X    =    Gross Profit
                         Y    =    Sales

Therefore:  Margin = Gross Profit    = X
                                  Sales            Y

However:  Sales – Costs = Gross Profit

Or: Costs = Sales – Gross Profit

Which is stated as: Costs = Y – X

And since: Mark up = Gross Profit
                                 Costs

This is stated as: Mark up =  X
                                       Y – X

In summary, if: Margin = P/Q

Then the related Markup shall be P/(Q – P)   

Using similar arguments, it can be established tat if the Markup is give by P/Q,

Then the related margin shall be P/(Q+P)