Question

You run a nail salon. Fixed monthly cost is $5,025.00 for rent and utilities, $6,341.00 is spent in salaries and $1,232.00 in insurance. Also every customer requires approximately $4.00 in supplies. You charge $94.00 on average for each service. You are considering moving the salon to an upscale neighborhood where the rent and utilities will increase to $10,907.00, salaries to $6,203.00 and insurance to $2,378.00 per month. Cost of supplies will increase to $8.00 per service. However you can now charge $164.00 per service. At what point will you be indifferent between your current location and the new loaction?

Answer 1

Let the point at which we will be indifferent between the two locations be x customers

At x customers, the net profit for each location will be same

Net Profit = Revenue - Cost

For old location,

Net Profit = 94x - (5025 + 6341 + 1232 + 4x)

For new location,

Net Profit = 164x - (10907 + 6203 + 2378 + 8x)

Hence, 94x - (5025 + 6341 + 1232 + 4x) = 164x - (10907 + 6203 + 2378 + 8x)

=> 164x - 8x - 94x + 4x = 10907 + 6203 + 2378 - 5025 - 6341 - 1232

=> x = (10907 + 6203 + 2378 - 5025 - 6341 - 1232) / (164 - 8 - 94 + 4)

=> x = 104.39

Hence, we would be indifferent if the number of customers is 105