A group of developers is opening a health club near a new housing development. T
ID: 342666 • Letter: A
Question
A group of developers is opening a health club near a new housing development. The health club-which will have exercise and workout equipment, basketball courts, swimming pools, an indoor walking/running track, and tennis courts-is one of the amenities the developers are building to attract new homebuyers. However, they want the health club to at least break even the first year or two. The annual fixed cost for the building, equipment, utilities, staff, and so on is $850,000, and annual variable costs are $2,000 per member for things like water, towels, laundry, soap, shampoo, and other member services. The membership fee is $350 per month. How many members will the club need to break even? If the clu!b doubles its break-even membership after a year, what will its profit be? Fixed cost - Variable cost - Price = With volume doubled to 700: total revenue = total costs ProfitExplanation / Answer
To be calculated:
Number of members required to break even
Given values:
Annual fixed cost = $850,000
Monthly fixed cost = $70,833.33
Annual variable costs = $2,000 per member
Monthly variable costs = $166.67 per member
Membership fee = $350 per month
Solution:
(a) Let the number of members joining the health club in a year be represented by X. Therefore, break-even is achieved when the Total Costs is equal to the Total Revenue.
At break-even point;
Total Costs = Total Revenue
70833.33 + 166.67 X = 350 X
Solving for X, we get;
183.33 X = 70833.33
X = 386.37
X = 387 members per month or 4,644 members per year
The health club will be able to break-even if it is able to acquire and retain 387 members in a month or 4,644 members in a year.
(b) The club doubles its break-even membership after a year,
Break-even membership = 387 per month
New number of members = 387 x 2 = 774 per month
Profit = Total Revenue - Total Costs
Profit = (350 x 774) - [70833.33 + (166.67 x 774)]
Profit = (270900) - [70833.33 + 129002.58]
Profit = (270900) - (199835.91)
Profit = $71,064 per month or $852,768 per year
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