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

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Business Intelligence Analyst Interview Boston, MA (US)

Wayfair## 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?

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17 Answers

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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

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

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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%

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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%.

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July 9 is correct. Nov 21 is incorrect.

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

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

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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.

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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.

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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.

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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

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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!!!

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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%