Calculating percentage commission without losing desire markup

Question

Suppose I am selling an item with the following conditions:

cost = $100
markup = 10%
commission = 15%

If the item sells at $110, there is a $16.50 commission paid. This obviously takes me below the cost after paying commission.

If I add the commission on top of the $110 as a buffer I get $126.50, at which point a 15% commission of $18.98 comes off that. Subtracting $18.98 from $126.50 gives me $107.52, which is below my desired 10% markup.

What formula would I use to consistently calculate how much commission must be accounted for to ensure the profit markup is always met no matter how the variables change?

Answer 1

The sale price must be greater than

(Cost + Cost * markup) / (1 - commission)

or in your example

(100 + 100 * .10) / (1 - .15)
110 / .85
129.42 (round UP)

Giving a commission of 19.41 and a net of 110.01, less your cost gives you your 10% markup

Answer 2

Or equivalently, cost × (1+markup)/(1-commission)