6-5. Nonlinear Cost and Revenue Analysis (Joanne Collins) Edith Wharton, a gradu
ID: 2585702 • Letter: 6
Question
6-5. Nonlinear Cost and Revenue Analysis (Joanne Collins) Edith Wharton, a graduate of an Eastern business school has decided to establish a business school to compete with Alma Mater. She is planning for an institution that will handle from 1.000 to 5.000 students Based on a survey conducted by one of her associates, she believes the fol- lowing demand curve is relevant for her enterprise: Demand (Students) Tuition/Student/Year S10.000 9.000 8.000 7.000 6.000 1000 2000 3000 4000 5000 Her fixed costs (for facilities and administrative expenses) are expected to be 58.000.000 per year up to an enrollment of 3.000 students. Above 3,000 students additional facilities must be provided and fixed costs will double Her variable costs per student include the cost of instructors and instructional supplies. Assume she wishes a student/faculty ratio of 10:1 for an enrollment of 3,000 students and that instructors are paid an average of S30.000 per year. Supply costs per student are S1000. Finally, assume variable costs will decline by $1.00 per student for each additional student enrolled (beyond 3,000 students) and conversely will increase $1.00 per student for each reduction in the number of students below 3.000 students Required At what tuition does the school break-even? What tuition maximizes operating income?Explanation / Answer
SOLUTION:
CALCULATION OF TOTAL INCOME:
CALCULATION OF TOTAL COST:
WORKING NOTES:
RATIO (STUDENTS:FACULTY) = 10:1
TOTAL NO. OF INSTRUCTORS(FACULTY) = 3000/10 = 300
TOTAL COST OF INSTRUCTORS = 300*30000 = $9,000,000
TOTAL COST OF SUPPLIES = 3000*1000 = $3,000,000
VARIABLE COST (3000) = 9000000+3000000 = $12,000,000
VARIABLE COST (1000) = 12000000 + (1*2000) = $12,002,000
VARIABLE COST (2000) = 12000000 + (1*1000) = $12,001,000
VARIABLE COST (4000) = 12000000 - (1*1000) = $11,999,000
VARIABLE COST (5000) = 12000000 - (1*2000) = $11,998,000
CALCULATION OF OPERATING INCOME:
BREAK-EVEN POINT IS THE POINT AT WHICH REVENUES EQUAL EXPENSES. IT IS A "NO PROFIT NO LOSS" SITUATION.
(A) The Tuition ($7,000/student/year) having 4000 students demand is the break-even point for the school.
(B) The Tuition ($8,000/student/year) having 3000 students demand maximizes the operating income.
DEMAND(STUDENTS) (a) TUITION/STUDENT/YEAR ($) (b) TOTAL INCOME ($) (a*b) 1000 10000 10,000,000 2000 9000 18,000,000 3000 8000 24,000,000 4000 7000 28,000,000 5000 6000 30,000,000Related Questions
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