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You run a school in Florida. Fixed monthly cost is $5,376.00 for rent and utilities, $5,680.00 is spent in salaries and $1,512.00 in insurance. Also every student adds up to $98.00 per month in stationary, food etc. You charge $605.00 per month from every student now. You are considering moving the school to another neighborhood where the rent and utilities will increase to $10,137.00, salaries to $6,454.00 and insurance to $2,327.00 per month. Variable cost per student will increase up to $171.00 per month. However you can charge $1,155.00 per student. At what point will you be indifferent between your current mode of operation and the new option? Answer Format: Number: Round to: 0 decimal places.
Expert Answer
Let Indifferent number of students be X which mean X is the indifferent point between Current Option and New Option.
Current Option:
Fixed Monthly Expenses = Rent and Utilities + Salaries + Insurance
Fixed Monthly Expenses = $5,376.00 + $5,680.00 + $1,512.00
Fixed Monthly Expenses = $12,568.00
Variable Expense per student = $98.00
Monthly Fees per student = $605.00
Profit from Operation = Fees Received – Total Variable Expense – Total Fixed Monthly Expense
Profit from Operation = $605.00*X – $98.00*X – $12,568.00
Profit from Operation = $507.00*X – $12,568.00
New Option:
Fixed Monthly Expenses = Rent and Utilities + Salaries + Insurance
Fixed Monthly Expenses = $10,137.00 + $6,454.00 + $2,327.00
Fixed Monthly Expenses = $18,918.00
Variable Expense per student = $171.00
Monthly Fees per student = $1,155.00
Profit from Operation = Fees Received – Total Variable Expense – Total Fixed Monthly Expense
Profit from Operation = $1,155.00*X – $171.00*X – $18,918.00
Profit from Operation = $984.00*X – $18,918.00
Profit from Operation under Current Option = Profit from Operation under New Option
$507.00*X – $12,568.00 = $984.00*X – $18,918.00
$6,350 = $477*X
X = 14 students
So, Current Option and New Option will be indifferent at 14 students
