Question

You run a school in Florida. Fixed monthly cost is $5,130.00 for rent and utilities, $6,403.00 is spent in salaries and $1,689.00 in insurance. Also every student adds up to $97.00 per month in stationary, food etc. You charge $612.00 per month from every student now.

You are considering moving the school to another neighborhood where the rent and utilities will increase to $10,467.00, salaries to $6,335.00 and insurance to $2,027.00 per month. Variable cost per student will increase up to $175.00 per month. However you can charge $1,035.00 per student. At what point will you be indifferent between your current mode of operation and the new option?

Answer 1

Say point of indifference between current mode of operation and the new option is x

At x, profit earned through current mode of operation = revenue-(fixed+variable cost) = 612x-(5130+6403+1689+97x) = 515x-13222

At x, profit earned through new mode of operation = revenue-(fixed+variable cost) = 1035x-(10467+6335+2027+175x) = 860x-18829

So, at x,

515x-13222 = 860x-18829

or, (18829-13222)/(860-515) = x

or, x = 16.25217391 (Answer is 16 if rounding is required) = Point of indifference between your current mode of operation and the new option