50,000 shoppers with a 0.5% conversion rate for a chair that costs $250. Wayfair makes a 27% profit. Next, 50,000 shoppers will get a 10% discount. What is the conversion rate they must achieve to achieve the same profits as before?

This is incorrect Old revenue = 50000*250*.005=250*250 New revenue with conversion rate r% = 50000*r*250*.9 = old revenue = 250*250 r = .55%

July 9 is wrong because the profit margin changes(As sale price changes, but the cost doesn't change)

The new conversion rate is 0.944, Profit from case 2 = $16,875 and the third part, if this scenario actually occurred I would give a 10% discount (with the new conversion rate .944%) because the overall profit margin would remain same i.e. $16,875

The correct answer is 0.79%. If the selling price is reduced by 10%, the profit margin will not remain 27%. It actually becomes 18.9%. People who calculated 0.56% assumed the margin was static at 27% despite the price reduction.

$250 is the actual cost of the chair (profit not included) or the price listed？？

Answer from Nov 21 is correct while July 9 is incorrect. The latter one is just making the revenues equal before and after the sale. It is ignoring the fact that profit % i.e. cost price is also changing after the sale. Before the sale cost price is 182.5*250. After sale cost price would be 182.5*(no >250), as with new conversion rate more customers will be buying. So even if the revenues are equal, profits won't be equal.

Total Shoppers 50000 Conversion Rate 0.5 Total Customers 250 Selling Price 250 Profit % 27 Cost price 196.8503937 Profit in $ 53.1496063 Total Sales 12500000 Total Profit 13287.40157 Scenario 2: Selling price 225 Profit 28.1496063 Customers required 472.027972 Conversion Rate in % 0.944055944 Please note that the $250 selling price is (Cost price + 27% profit) on it. So Nov 21, 2014, assumption of doing .27*250 to get the profit is wrong.

Number 2 is wrong, number 1 is right. Just because revenues equal doesnt mean profits will equal - they sacrifice profits when they decide to give the sale

Do they expect you to do this in your head, or will they give you pen/paper and a minute?

Wow!!! All I can say is if these are the types of questions asked, it is no longer a mystery to me as to why corporate people are COMPLETELY out of touch with reality of the field experiences!!!

July 9 is correct. Nov 21 is incorrect.

You don't actually need to calculate anything other than the new conversion rate. Why? Look at the equation below: (customer sent = 50000) * (customer bought / customer sent = 0.005 conversion rate) * (revenue / customer bought = 250) * 0.27 (profit / revenue) gives (profit / customer sent). this should be equal to the one after discount. only (revenue / customer bought) changed -> it decreased 10%. therefore, conversion rate needs to increase by (1/0.9), which gives 5.56%.