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You run a nail salon
You run a nail salon. Fixed monthly cost is $5,836.00 for rent and utilities, $6,043.00 is spent in salaries and $1,673.00 in insurance. Also every customer requires approximately $3.00 in supplies. You charge $121.00 on average for each service.
You are considering moving the salon to an upscale neighborhood where the rent and utilities will increase to $11,660.00, salaries to $6,614.00 and insurance to $2,332.00 per month. Cost of supplies will increase to $7.00 per service. However you can now charge $147.00 per service. At what point will you be indifferent between your current location and the new loaction?
Expert Solution
Point of indifference is the point of sale at which the profit under both the alternatives will be same.
Let X be the point of indifference
Now, Profit at old place is
X* (121 - 3) - 5836 - 6043 - 1673
Now profit at new locality will be
X * (147 -7) - 11,660 - 6614 - 2332
Now , we will equate both the equations and get X
X*118 - 13552 = X*140 - 20,606
22X = 7,054
X = 320.63
Hence at 321(Approximate) services for month cost under both the alternatives will be same.
Note - Amount of supplies is variable cost and other expenses like rent , salaries insurance is fixed cost.
This can be better tabulated as below at 320 units profit under both the alternatives is approximately equal.
| Old Place | New Place | ||||||||
| Units | Service cost | Variable Cost | Fixed Cost | Profit | Units | Service cost | Variable Cost | Fixed Cost | Profit |
| 250 | 121 | 3 | 13552 | 15948 | 250 | 147 | 7 | 20606 | 14394 |
| 260 | 121 | 3 | 13552 | 17128 | 260 | 147 | 7 | 20606 | 15794 |
| 270 | 121 | 3 | 13552 | 18308 | 270 | 147 | 7 | 20606 | 17194 |
| 280 | 121 | 3 | 13552 | 19488 | 280 | 147 | 7 | 20606 | 18594 |
| 290 | 121 | 3 | 13552 | 20668 | 290 | 147 | 7 | 20606 | 19994 |
| 300 | 121 | 3 | 13552 | 21848 | 300 | 147 | 7 | 20606 | 21394 |
| 310 | 121 | 3 | 13552 | 23028 | 310 | 147 | 7 | 20606 | 22794 |
| 320 | 121 | 3 | 13552 | 24208 | 320 | 147 | 7 | 20606 | 24194 |
| 330 | 121 | 3 | 13552 | 25388 | 330 | 147 | 7 | 20606 | 25594 |
| 340 | 121 | 3 | 13552 | 26568 | 340 | 147 | 7 | 20606 | 26994 |
| 350 | 121 | 3 | 13552 | 27748 | 350 | 147 | 7 | 20606 | 28394 |
| 360 | 121 | 3 | 13552 | 28928 | 360 | 147 | 7 | 20606 | 29794 |
| 370 | 121 | 3 | 13552 | 30108 | 370 | 147 | 7 | 20606 | 31194 |
| 380 | 121 | 3 | 13552 | 31288 | 380 | 147 | 7 | 20606 | 32594 |
| 390 | 121 | 3 | 13552 | 32468 | 390 | 147 | 7 | 20606 | 33994 |
| 400 | 121 | 3 | 13552 | 33648 | 400 | 147 | 7 | 20606 | 35394 |
| 410 | 121 | 3 | 13552 | 34828 | 410 | 147 | 7 | 20606 | 36794 |
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