I think a better approach would be to display an initially high price, and mention automatically applied coupons at checkout - or require the user to use their smartphone's app to apply the coupon.
That makes calculating the final price far too hard. If the customer has to use a smartphone app to shop anyways, why not just have the app display the personalized price?
This is how Amazon Books stores work. Prices aren't displayed on the shelf, but using an app. The price is different for Prime members vs. non-Prime members.
I think a better approach would be to display an initially high price, and mention automatically applied coupons at checkout - or require the user to use their smartphone's app to apply the coupon.