Curtis Institute of Music (CIM) provides instrumental music education to children of all ages. Payment for services

Question:

Curtis Institute of Music (CIM) provides instrumental music education to children of all ages. Payment for services comes from two sources: (1) a contract with Imagine That School to provide private music lessons for up to 140 band students a year (where a year is 9 months of education) for a fixed fee of $150,000, and (2) payment from individuals at a rate of $120 per month for 9 months of education each year. In the 2012–2013 school year, CIM made a profit of $1,000 on revenues of $270,000:

CIM conducted an activity analysis and found that teaching staff wages and supplies costs are variable with respect to student-months. (A student-month is one student educated for 1 month.) Administrative staff and facilities costs are fixed within the range of 1,800–2,300 student-months. At volumes between 2,300 and 2,800 student-months, an additional facilities charge of $2,800 would be incurred. During the last year, a total of 2,200 student-months of education were provided, 1,000 of which were for private students and 1,200 of which were offered under the contract with Imagine That School.

1. Compute the following using cost information from year 2012–2013 operations:

Fixed cost per year

Variable cost per student-month

2. Suppose that in 2013–2014 Imagine That School decreased its use of CIM to 90 students (that is, 810 student-months). The fixed contract price of $150,000 was still paid. If everything else stayed as it was in 2012–2013, what profit or loss would be made in 2013–2014?

3. Suppose that at the beginning of 2013–2014 Imagine That School decided not to renew its contract with CIM, and the management of CIM decided to try to maintain business as usual with only private students. How many students (each signing up for 9 months) would CIM require to continue to make a profit of $1,000 per year?