I would like to know the formula to calculate margin percentage after a discount. I can figure this out in excel manually but would be great to know the formula to figure it out quickly as a back-of-the-envelope calculation?
Just to clarify that the question is about the margin %, not the markup %
Margin % = 1 - (Cost per unit/Selling Price)
Mark up % = (Selling price/Cost per unit) - 1
First of all we have $1-\frac{c}s=0.6=m^{bd}\Rightarrow \frac{c}s=0.4 \qquad (*)$
After a 10% discount the equation is $100-\frac{c}{0.9s}\cdot 100=m^{ad}$
$m^{bd}$ is the margin before discount in percentage
$m^{ad}$ is the margin after discount in percentage
Then $\frac1{0.9}=\frac{10}9$.
$\frac99-\frac{10}{9}\frac{c}s=x$
Inserting the value of $\frac{c}s$ from $(*)$
$m^{ad}=\frac99-\frac{10}{9}\cdot \frac4{10}=\frac59\approx 0.56$
Therefore the formula is $$\boxed{m^{ad}=100\left(1-\frac{100}{100-d}\cdot \left(1-{\frac{m^{bd}}{100}} \right)\right)}$$
$d:$= discount in percentage