Question

You run a school in Florida. Fixed monthly cost is $5,396.00 for rent and utilities, $6,006.00 is spent in salaries and $1,475.00 in insurance. Also every student adds up to $97.00 per month in stationary, food etc. You charge $699.00 per month from every student now.

You are considering moving the school to another neighborhood where the rent and utilities will increase to $11,585.00, salaries to $6,315.00 and insurance to $2,371.00 per month. Variable cost per student will increase up to $195.00 per month. However you can charge $1,199.00 per student. At what point will you be indifferent between your current mode of operation and the new option?

Answer 1

• The indifference point between current mode and new option is that ‘no. of students’ where the total Net Income under both alternative becomes equal.
• Let the indifferent point be ‘x’ no. of student, then:

--Net Income under current mode:

Total revenues	699x
Rent	$               5,396.00
Utilities	$               6,006.00
Insurance	$               1,475.00
Total Fixed Cost	$            12,877.00
Stationery (Variable cost)	97x
Total Cost	12877 + 97x
Net Income	[699x - [12877 + 97x]
	= 699x – 97x - 12877
	= 602x - 12877

---Net Income under New Option:

Total revenues	1199x
Rent	$         11,585.00
Salaries	$            6,315.00
Insurance	$            2,371.00
Total Fixed Cost	$         20,271.00
Variable cost	195x
Total Cost	20271 + 195x
Net Income	[1199x - (20271 + 195x)]
	= 1199x-195x-20271
	= 1004x - 20271

• At Indifference point: Net Income under Current Method = Net Income under new option.

Hence, Equation: 602x – 12877 = 1004x – 20271

>602x – 12877 = 1004x – 20271
>20271 – 12877 = 1004x – 602x
>7394 = 402x
>x = 18.39 students or 18 students. = Answer