Step 1: Calculate profit (250 * 250 * 0.27 = 16875) Step 2: Calculate discount price (250 * 0.9 = 225) Step 3: Calculate price of chair (250 * 0.73 = 182.5) Step 4: Calculate profit margin ( (225 - 182.5)/225 = .19) Step 5: Calculate new conversion rate (225 * 0.19 * x = 16875) x = 395 395/50000 = 0.79% the new conversion rate

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%

Scenario 1 Number of sales=50,000*.5/100 = 250. Revenue=250*250 = 62,500. Profit is 27%. Therefore 62,500 = 1.27*cost Therefore cost = 49,212.598. Profit = 62,500-49212.598 = 13,287.40. Cost of chair = 250/1.27 = 196.85 Scenario 2 Number of sales = 50,000*r/100 = 500*r (r is new converion rate) Revenue = 500*r*.9*250 Total cost = 500*r*196.85 Profit = 500*r(250*.9-196.85) = 13,287.40 500*r*(28.1496) = 13,287.40. Therefore r = 0.944. The first answer considers profit as margin (percentage of sales) which seems incorrect or needs to be clarified

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?

July 9th Answer is the correct answer. It is not hard: Initial profit is = 50000 * 0.005 * 250 * 0.27 (No need for the calculator yet) After sale profit = 50000 * x * 250 * 0.01 * 0.27 (Still don't need the calc) The question asks for the conversion rate such that profit are the same before and after the sale, so... Initial profit = After Sale profit 50000 * 0.005 * 250 * 0.27 = 50000 * x * (250 - (250 * 0.01)) * 0.27 (divide through & cancel) 0.005 * 250 = x * 225 x = (0.005 * 250) / 225 x = 0.0056 or 0.56%

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%.

July 9 is correct. Nov 21 is incorrect.

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

$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.

No of chairs sold = 50000*0.005 = 250 Selling price of chairs sold = 250 Cost price of chairs = 250*(1-0.27) = 182.5 Scenario 1 Total profit = no of chairs sold * selling price - no of chairs sold * cost price = 250*250 - 250*182.5 = 62500 - 45625 = 16875 Total profit = 16875 Scenario 2 No. of chairs sold = x Selling price = 250*(1-0.1) = 225 Cost price = 182.5 Total profit = no of chairs sold * selling price - no of chairs sold * cost price 16875 = x*225 - x*182.5 x = 16875/42.5 x = 397.06 397.06 or 398 chairs should be sold to make the same amount of profit No of chairs sold = 50000*conversion rate 398 = 50000* conversion rate conversion rate = 398/50000 = 0.00796 Required conversion rate would be 0.8%

- Number of customers that purchase chair: 50,000 * .5% = 2500 Customers - Revenue: 250 Customers * $250 = $62,500 - Profit: $62,500 * 27% = $16,875 - Discount Price: $250 * 90% = $225 - Revenue with Discount: ($225*X customers) * 27% = $16,875 - X = 278 Customers - Conversion Rate: .556%

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.

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