Eric wants to start a car detailing business but is unsure h

Eric wants to start a car detailing business but is unsure how many cars he will need to detail before making a profit. His cousin has offered to let him use a small section of his shop for only $400 per month. Eric is going to pay his friend $10/hour to help him. He has estimated his additional expenses to be the following:

Insurance $150/month

His share of monthly utilities $110

Wax (will yield 10 cars) $16.00

Towels, soap, and other supplies $2.75/vehicle

Leasing of equipment $100/month

Marketing $125/month budgeted

He estimates that it will take him 4 hours to detail a vehicle if he has help from his friend.

He plans to charge $90 per vehicle.

Eric is now considering leaving his full-time job to grow his car detailing business but does not want to lose his salary. If he decides to pay himself $2000 per month how many cars does he have to detail in a month now to breakeven?                                        

Solution

Given Information :

Eric wants to start a car detailing business

but is unsure how many cars he will need to detail before making a profit.

His cousin has offered to let him use a small section of his shop

Rent = $400 per month.

Eric is going to pay his friend $10/hour to help him.

He has estimated his additional expenses to be the following:

Insurance = $150/month

share of monthly utilities = $110

Wax (will yield 10 cars)= $16.00

Towels, soap, and other supplies = $2.75/vehicle

Leasing of equipment = $100/month

Marketing = $125/month budgeted

Time required for servicing :

He estimates that it will take him 4 hours to detail a vehicle if he has help from his friend.

He plans to charge = $90 per vehicle.

Eric is now considering leaving his full-time job to grow his car detailing business but does not want to lose his salary.

If he decides to pay himself $2000 per month how many cars does he have to detail in a month now to break even?

Solution

Let X be the no of cars .

Formula for BEP :

px = vx + FC + Profit   

Where,
p is the price per unit,
x is the number of units,
v is variable cost per unit and
FC is total fixed cost.

Price = P =$ 90 / vehicle

Profit = $ 2000

Variable cost = V = Friend cost +Wax + Towels, soap, and other supplies

= ($10/hour * 4 ) + ($ 16/10) +$2.75

=$ 44.35

Fixed cost =FC= Rent + Insurance + share of monthly utilities + Leasing of equipment +Marketing

= $400 + $150 + $110 +$100 + $125

=$885

Now add these values in formula

px = vx + FC + Profit   

90X= 44.35 X + 885 + 2000

90X - 44.35X = 885 + 2000

45.65X = 2885

X = 2885 / 45.65

=63.19

= 64 (Approximately)

64 no of cars needs to maintain the BEP.