You run a nail salon. Fixed monthly cost is $5,800.00 for rent and utilities, $5,909.00 is spent in salaries and $1,619.00 in insurance. Also every customer requires approximately $5.00 in supplies. You charge $63.00 on average for each service.

Question

You are considering moving the salon to an upscale neighborhood where the rent and utilities will increase to $10,864.00, salaries to $6,428.00 and insurance to $2,383.00 per month. Cost of supplies will increase to $6.00 per service. However you can now charge $156.00 per service. At what point will you be indifferent between your current location and the new location?

Answer 1

To determine the point at which you will be indifferent between your current location and the new upscale location, we need to analyze both scenarios in terms of profit.

Current Location:

• Fixed Costs:
  • Rent and utilities: $5,800.00
  • Salaries: $5,909.00
  • Insurance: $1,619.00
• Variable Costs:
  • Supplies per service: $5.00
• Revenue per service: $63.00

Total Fixed Costs (Current Location) = Rent + Salaries + Insurance \[ \text{Total Fixed Costs} = 5,800 + 5,909 + 1,619 = 13,328 \]

Total Cost per Service (Current Location): \[ \text{Total Cost per Service} = \text{Supply Cost} = 5.00 \]

Profit per Service (Current Location): \[ \text{Profit per Service} = \text{Revenue} - \text{Total Cost per Service} = 63 - 5 = 58 \]

• To find the total profit for a given number of customers \(N\): \[ \text{Total Profit (Current Location)} = (58 \cdot N) - 13,328 \]

New Location:

• Fixed Costs:
  • Rent and utilities: $10,864.00
  • Salaries: $6,428.00
  • Insurance: $2,383.00
• Variable Costs:
  • Supplies per service: $6.00
• Revenue per service: $156.00

Total Fixed Costs (New Location) = Rent + Salaries + Insurance \[ \text{Total Fixed Costs} = 10,864 + 6,428 + 2,383 = 19,675 \]

Total Cost per Service (New Location): \[ \text{Total Cost per Service} = \text{Supply Cost} = 6.00 \]

Profit per Service (New Location): \[ \text{Profit per Service} = \text{Revenue} - \text{Total Cost per Service} = 156 - 6 = 150 \]

• To find the total profit for a given number of customers \(N\): \[ \text{Total Profit (New Location)} = (150 \cdot N) - 19,675 \]

Finding the Indifference Point:

To find the indifference point, we need to set the total profits of both locations equal to each other:

\[ (58 \cdot N) - 13,328 = (150 \cdot N) - 19,675 \]

Now, solve for \(N\):

1. Rearranging the equation: \[ 58N - 150N = -19,675 + 13,328 \] \[ -92N = -6,347 \]

2. Dividing by -92: \[ N = \frac{6,347}{92} \approx 69 \]

Conclusion:

You will be indifferent between your current location and the new upscale location at approximately 69 customers per month. If you expect to serve more than this amount, the new location becomes more profitable; if fewer, the current location is preferable.