CVP Analysis with Semifixed Costs: Discovery Day Care Center³: Beverly Miller, director and owner of the Discovery Day Care Center, has a master's degree in elementary education. In the seven years she has been running the Discovery Center, her salary has ranged from nothing to $10,000 per year. "The secondyear," she says, "I made 62 cents an hour." Her salary is what's left over after all other expenses are met.

Could she run a more profitable center? She thinks perhaps she could if she increased the student-teacher ratio, which is currently five students to one teacher. (Government standards for a center like this set a maximum of 10 students per teacher.) However, she refuses to increase the ratio to more than six to one. "If you increase the ratio to more than 6:1, the children don't get enough attention. In addition, the demands on the teacher are far too great." She does not hire part-time teachers.

Beverly rents the space for her center in the basement of a church for $450 per month, including utilities. She estimates that supplies, snacks, and other nonpersonnel costs are $40 per student per month. She charges $190 per month per student. Teachers are paid $600 per month, including fringe benefits. There are no other operating costs. At present, there are 30 students and 6 teachers in addition to Ms. Miller, who is not considered a teacher for this analysis.

Required:

a. What is the present operating profit per month of the Discovery Day Care Center before Ms. Miller's salary?

b. What is (are) the break-even point(s) assuming a student-teacher ratio of 6:1?

c. What would be the break-even point(s) if the student-teacher ratio was allowed to increase to 10:1?

d. Ms. Miller has an opportunity to increase the student body by six students. She must take all six or none. Should she accept the six students if she wants to maintain a maximum student-teacher ratio of 6:1?

e. [Continuation of part (d).] Suppose Ms. Miller accepts the six children. Now she has the opportunity to accept one more. What would happen to profit if she did. assuming she has to hire one more teacher?