Question

You run a nail salon. Fixed monthly cost is $5,403.00 for rent and utilities, $5,679.00 is spent in salaries and $1,112.00 in insurance. Also every customer requires approximately $5.00 in supplies. You charge $61.00 on average for each service.
You are considering moving the salon to an upscale neighborhood where the rent and utilities will increase to $11,923.00, salaries to $6,037.00 and insurance to $2,359.00 per month. Cost of supplies will increase to $7.00 per service. However you can now charge $172.00 per service. At what id the profit or loss at the crossover point? If a loss includes the -. indifferent between your current location and the new location? Round the quantity to 3 digits when using to calulate the profit.

Answer 1

First compute fixed costs and contribution margins.

Current location
- Fixed costs = 5,403 + 5,679 + 1,112 = $12,194
- Contribution margin per service = $61 − $5 = $56

New location
- Fixed costs = 11,923 + 6,037 + 2,359 = $20,319
- Contribution margin per service = $172 − $7 = $165

Crossover quantity x where profits are equal:
(FC_new − FC_current) / (CM_new − CM_current) = (20,319 − 12,194) / (165 − 56) = 8,125 / 109 ≈ 74.541 (rounded to 3 decimals as requested).

Profit (loss) at that quantity (use x = 74.541):
Profit = 56×74.541 − 12,194 ≈ 4,174.296 − 12,194 = −$8,019.70

So you are indifferent between the two locations at about 74.541 services per month, but at that point both locations would be operating at a loss of approximately −$8,019.70.