Question

Answer the following questions. Show all work.

3.   If the fixed costs for keeping the pool open all summer is $20,000 (of which $10,000 is allocated to open swim time as opposed to swim lessons or the swim team) and the variable costs of open swim is $.50 per person, how many people will it take to show a profit for the summer if you charge $1.50 per person for open swimming? How about $2.00 per person for open swimming?

4.   Within your nonprofit organization, all children’s swimming lessons are subsidized at $5.00 per participant. The fixed costs for the children’s learn-to-swim program are $8,000 and the variable costs are $5,000. You expect an enrollment of 600 children—what should the cost per child be? Explain your thoughts and calculations.

Answer 1

Answer to Question No. 3

It is given that $ 20,000 is incurred for keeping the pool open for all summer out of which $ 10,000 pertains to open swim time alone. Therefore, we can infer that the balance $10,000 belongs to fixed costs incurred with respect to providing facilities for swim lessons or swim teams.

The question is to find out the required number of people who should use open swimming facility at a rate of $ 1.50 per person so that we can break even with the costs incurred. For this purpose, we should take $10,000 as fixed costs since we are focusing on finding out break-even point for open swimming.

Calculation of break-even point where the profit earned equals the cost incurred when fee is $1.50

Open Swim fee per person	$ 1.50
Less: Variable Costs per person	$ 0.50
Contribution per person	$ 1.00
Fixed Costs pertaining to open swimming	$ 10,000
Break-even point = Fixed costs/Contribution per person ie, $ 10,000 / $ 1	10,000 persons

It means that when the open swimming fee per person is $ 1.50, after 10,000 people attend for open swimming the pool will start to earn profits.

Calculation of break-even point where the profit earned equals the cost incurred when fee is $2.00

Open Swim fee per person	$ 2.00
Less: Variable Costs per person	$ 0.50
Contribution per person	$ 1.50
Fixed Costs pertaining to open swimming	$ 10,000
Break-even point = Fixed costs/Contribution per person ie, $ 10,000 / $ 1.50	6,667 persons

It means that when the open swimming fee per person is $ 2.00, after 6,667 people attend for open swimming the pool will start to earn profits.

Answer to Question No. 4

The question is to find out the cost incurred for each child who is enrolled to the learn-to-swim program. Assuming that all 600 children as expected will enrol in this program, we need to calculate the cost per child.

Calculation of cost per child

Total Variable Costs for 600 children (given in question)	$ 5,000
Total Fixed Costs (given in question)	$ 8,000
Total Costs (add both of the above costs)	$ 13,000
Less: Subsidy received for 600 children ie, $ 5.00 multiplied by 600	$ 3,000
Costs after deducting subsidy	$ 10,000
Cost per child ie, $10,000 / 600 children	$ 16.67