Respuesta :
Answer:
Carlita's 2nd restaurant will need to serve 3,644 (with 3,643 still not break-even point) customers per year for the restaurant to break-even.
Step-by-step explanation:
1. Let's review all the information provided for solving this case:
Carlita's 2nd restaurant will open 5 days a week, 50 weeks a year
Rent = US$ 7,200
Insurance = US$ 4,200
Servers full-time (8 hours) = 2
Server part-time (4 hours) = 1
Salary of the servers = US$ 15 per hour
Additional costs to the restaurant : Social Security tax ( 6.2% of gross pay). and Medicare tax ( 1.45% of gross pay).
Average customer consumption = US$ 45.47
Average food cost per consumer = US$ 20.18
Break-even point is when Revenue or Income is equal to the costs and there is no loss nor profitability. In other words, Revenue - Costs = 0.
Customers needed to serve each year for break-even point = x
2. Let's find out how many customers would Carlita need to serve each year for the restaurant to break even?
A. Let's calculate all the costs. The costs are in two categories : fixed and variables. Let's start with the fixed.
Rent = US$ 7,200
Insurance = US$ 4,200
Servers full-time (8 hours) = 2
Server part-time (4 hours) = 1
Salary of the servers = US$ 15 per hour
Additional costs to the restaurant : Social Security tax ( 6.2% of gross pay). and Medicare tax ( 1.45% of gross pay).
Let's calculate how much Carlita pays a year in salaries and salary taxes.
For doing that, we need to know the number of hours the servers work, then:
Total hours per day = 2 * 8 + 1 * 4 (2 servers * 8 hours and 1 server * 4 hours)
Total hours per day = 16 + 4
Total hours per day = 20
Total hours per week = Total hours per day * 5 (The restaurant is open 5 days a week)
Total hours per week = 20 * 5
Total hours per week = 100
Total hours per year = Total hours per week * 50 (The restaurant is open 50 weeks a year)
Total hours per year = 100 * 50
Total hours per year = 5,000
Now we can calculate the total cost of the salaries paid to the servers:
Total cost of salaries = Total hours per year * Cost per hour
Total cost of salaries = 5,000 * 15
Total cost of salaries = 75,000
Now we can calculate the total cost of the taxes, this way:
Social Security Tax = Total cost of salaries or Gross Pay * 6.2%
Social Security Tax = 75,000 * 6.2% = US$ 4,650
Medicare Tax = Total cost of salaries or Gross Pay * 1.45%
Medicare Tax = 75,000 * 1.45% = 1,087.50
Now we can calculate the total fixed costs of Carlita's 2nd restaurant, this way:
Rent = US$ 7,200
Insurance = US$ 4,200
Salaries Gross payments = US$ 75,000
Social Security tax = US$ 4,650
Medicare tax = US$ 1,087.50
Total fixed costs = 7,200 + 4,200 + 75,000 + 4,650 + 1,087.50
Total fixed costs = 92,137.50
The variable costs will depend on the number of customers that will eat at Carlita's restaurant, but we need to add up them to the fixed costs, this way:
Total costs = Total fixed costs + total variable costs
Total costs = 92,137.50 + (x * 20.18) (US$ 20.18 is the average food cost per customer and x is the number of customers needed to serve each year for break-even point)
B. Now, we can express the total income this way:
Total income = x * 45.47 (US$ 45.47 is the average customer consumption)
C. We're ready to write the equation for finding the value of x:
Total Income - Total costs = 0
Replacing with the real values
45.47x - (92,137.50 + 20.18x) = 0
45.47x - 92,137.50 - 20.18x = 0
25.29x = 92,137.50 (Subtracting 92,137.50 at both sides)
x = 92,137.50/25.29 (Dividing by 25.29 at both sides)
x = 3,643.24
Carlita's 2nd restaurant will need to serve 3,644 (with 3,643 still not break-even point) customers per year for the restaurant to break-even.
