Question

2. 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. The annual fixed cost for the building, equipment, utilities, staff, and so on is $600,000 and annual variable costs are $145 per member for thing like water, towels, laundry, soap, shampoo, and other member services.

(a) The developers want the health club to break even at the end of the first year from the opening (12 months in total) by attracting 400 customers (assuming all the customers keep their memberships from the opening for the whole year, and no customer is added during the period). What is the minimal monthly fee to achieve their plan?

(b) When they decide the membership fee as $250 per month, under the same assumption in (a), how many members will the club need at the opening in order to break even?

Answer 1

Annual fixed cost = $ 600,000

Annual variable cost = $ 145

(a)

Number of customers = 400

Minimum annual fee required to break-even = Annual fixed cost / number of customers + Annual variable cost

= 600000/400+145

= $ 1,645

Minimum monthly fee = 1645/12

= $ 137.83

(b)

Given monthly membership fee = $ 250

Annual membership fee = 250*12 = $ 3000

Number of members needed to break even = Annual fixed cost / (annual membership fee - annual variable cost )

= 600000/(3000-145)

= 210.2 customers