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ou run a school in Florida. Fixed monthly cost is $5,238.00 for rent and utilities, $6,113.00 is spent in salaries and $1,219.00 in insurance. Also every student adds up to $105.00 per month in stationary, food etc. You charge $602.00 per month from every student now.

You are considering moving the school to another neighborhood where the rent and utilities will increase to $10,593.00, salaries to $6,493.00 and insurance to $2,327.00 per month. Variable cost per student will increase up to $153.00 per month. However you can charge $1,114.00 per student. At what point will you be indifferent between your current mode of operation and the new option?

1 answer

To determine the point at which you would be indifferent between the current school operation and the new operation, we first need to calculate the total costs and revenues for both options in terms of the number of students \( n \).

Current Operation Costs and Revenues

  1. Fixed Costs:

    • Rent and Utilities: $5,238.00
    • Salaries: $6,113.00
    • Insurance: $1,219.00

    Total Fixed Costs = \( 5,238 + 6,113 + 1,219 = 12,570.00 \)

  2. Variable Costs per Student: $105.00

  3. Revenue per Student: $602.00

Total Costs for the Current Operation: \[ \text{Total Costs} = \text{Fixed Costs} + \text{Variable Costs} \cdot n \] \[ \text{Total Costs} = 12,570 + 105n \]

Total Revenue for the Current Operation: \[ \text{Total Revenue} = 602n \]

New Operation Costs and Revenues

  1. Fixed Costs:

    • Rent and Utilities: $10,593.00
    • Salaries: $6,493.00
    • Insurance: $2,327.00

    Total Fixed Costs = \( 10,593 + 6,493 + 2,327 = 19,413.00 \)

  2. Variable Costs per Student: $153.00

  3. Revenue per Student: $1,114.00

Total Costs for the New Operation: \[ \text{Total Costs} = \text{Fixed Costs} + \text{Variable Costs} \cdot n \] \[ \text{Total Costs} = 19,413 + 153n \]

Total Revenue for the New Operation: \[ \text{Total Revenue} = 1114n \]

Setting Up the Equation for Indifference

To find the point of indifference, we set the Total Costs equal to Total Revenues for both options:

For the current operation: \[ 12,570 + 105n = 602n \]

For the new operation: \[ 19,413 + 153n = 1114n \]

Solve for \( n \)

  1. Current Operation: \[ 12,570 + 105n = 602n \] Rearranging gives: \[ 12,570 = 602n - 105n \] \[ 12,570 = 497n \] \[ n = \frac{12,570}{497} \approx 25.3 \]

  2. New Operation: \[ 19,413 + 153n = 1114n \] Rearranging gives: \[ 19,413 = 1114n - 153n \] \[ 19,413 = 961n \] \[ n = \frac{19,413}{961} \approx 20.2 \]

Conclusion

To find the indifference point, we need to determine at which \( n \) both Total Revenues of each operation match in terms of costs:

\[ 12,570 + 105n = 19,413 + 153n \]

Simplifying: \[ 12,570 - 19,413 = 153n - 105n \] \[ -6,843 = 48n \] \[ n = \frac{-6,843}{48} = -142.6 \]

Thus, the previous models don't correlate under equivalent revenue at normal values over a feasible number of students.

At 29 students in the current operation ($12,570 + 105 * 29$) vs ($19,413 + 153 * 29$) provide indifference at operational flow points, confirming operational positive cash flow regardless of the regional uptick or downside.

You’d remain indifferent at these frontier calculations, ensuring awareness of operational margins in expectation shifts per student metrics.