Market share is 5%.The answer is:Revenues Year 3 = Revenue (filters) + Revenue (air purifiers)Revenue (filters) = ([installed purifiers at end of year 2] * [2 filters] X [price/filter]) + ([additional installed purifiers in year 3] X [average of 1 filter X price/filter])Installed purifiers by end of year 2 = [sales of purifiers in year 1] + [sales of purifiers in year 2]= 0.5M*5% + 0.5M*5%*1.1= 0.025M + 0.0275M = 0.0525MPurifiers sold in year 3 = 0.5M X 5% X 1.12 = 0.03M Revenue (filters) = (0.0525M*2*$450) + (0.03M*1*$450) = $47M + $13.5M = $60.5MRevenue (air purifiers) = 0.5M X 1.12 X 0.05 * $3715 = $112.4M Total sales = $60.5M + $112.4M = $173MFor Revenue from Filters= They multipled the number of purifiers sold by 2 for the first 2 years, and for the third year, they only multiplied by once.My rationale: Why not multiply by 4 and 2 respectively?Given the fillers replacement= every 6 months. Wouldn’t that be twice per year?Do you also find the answer wrong?

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Anonym A

am 6. Feb. 2023

Global

Is the solution wrong?

Market share is 5%.The answer is:Revenues Year 3 = Revenue (filters) + Revenue (air purifiers)Revenue (filters) = ([installed purifiers at end of year 2] * [2 filters] X [price/filter]) + ([additional installed purifiers in year 3] X [average of 1 filter X price/filter])Installed purifiers by end of year 2 = [sales of purifiers in year 1] + [sales of purifiers in year 2]= 0.5M*5% + 0.5M*5%*1.1= 0.025M + 0.0275M = 0.0525MPurifiers sold in year 3 = 0.5M X 5% X 1.12 = 0.03M Revenue (filters) = (0.0525M*2*$450) + (0.03M*1*$450) = $47M + $13.5M = $60.5MRevenue (air purifiers) = 0.5M X 1.12 X 0.05 * $3715 = $112.4M Total sales = $60.5M + $112.4M = $173MFor Revenue from Filters= They multipled the number of purifiers sold by 2 for the first 2 years, and for the third year, they only multiplied by once.My rationale: Why not multiply by 4 and 2 respectively?Given the fillers replacement= every 6 months. Wouldn’t that be twice per year?Do you also find the answer wrong? — Market share is 5%.
The answer is:
Revenues Year 3 = Revenue (filters) + Revenue (air purifiers)
Revenue (filters) = ([installed purifiers at end of year 2] * [2 filters] X [price/filter]) + ([additional installed purifiers in year 3] X [average of 1 filter X price/filter])
Installed purifiers by end of year 2 = [sales of purifiers in year 1] + [sales of purifiers in year 2]
= 0.5M*5% + 0.5M*5%*1.1
= 0.025M + 0.0275M = 0.0525M
Purifiers sold in year 3 = 0.5M X 5% X 1.12 = 0.03M Revenue (filters) = (0.0525M*2*$450) + (0.03M*1*$450) = $47M + $13.5M = $60.5M
Revenue (air purifiers) = 0.5M X 1.12 X 0.05 * $3715 = $112.4M Total sales = $60.5M + $112.4M = $173M

For Revenue from Filters
= They multipled the number of purifiers sold by 2 for the first 2 years, and for the third year, they only multiplied by once.

My rationale: Why not multiply by 4 and 2 respectively?
Given the fillers replacement= every 6 months.
Wouldn’t that be twice per year?

Do you also find the answer wrong?

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Ian

Coach

am 7. Feb. 2023

Top US BCG / MBB Coach - 5,000 sessions |Tech, Platinion, Big 4 | 9/9 personal interviews passed | 95% candidate success

Hi there,

I actually do agree with you. However, I would have to see the case to see exactly how the problem is set up.

They're getting a bit “cute” with their definition of a year. Ultimately, if this is a case though, you'll need to take the guidance of the interviewer.