CVP analysis with semifixed costs. Melissa Mooring, director and owner of the Kids Education Center, has a master's degree in elementary education. In the seven years she has been running the Kids Education Center, her salary has ranged from nothing to $20,000 per year. ‘‘The second year,'' she says, ‘‘I made 62 cents an hour.'' (Her salary is what's left over after meeting all other expenses.)
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 such as this set a maximum of 10 students per teacher.) She refuses to increase the ratio to more than six-to-one. ‘‘If you increase the ratio to more than six-to-one, 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.
Mooring rents the space for her center in the basement of a church for $900 per month, including utilities. She estimates that supplies, snacks, and other nonpersonnel costs are $80 per student per month. She charges $380 per month per student. Teachers receive $1,200 per month, including fringe benefits. She has no other operating costs. At present, she cares for 30 students and employs six teachers.
a. What is the present operating profit per month of the Kids Education Center before Ms. Mooring's salary?
b. What is (are) the break-even point(s), before Ms. Mooring's salary, assuming a student- teacher ratio of 6:1?
c. What would be the break-even point(s), before Ms. Mooring's salary, if the student- teacher ratio increased to 10:1?
d. Ms. Mooring 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 that Ms. Mooring accepts the six children. Now she has the opportunity to accept one more, which requires hiring one more teacher. What would happen to profit, before her salary, if she accepts one more student?