Andre has a hair styling business and he has five barbers who each make $9.90 per hour then work 40-hours a week and 50-weeks a year, the rent and other fixed expenses are $1,750 per month. shampoo is used on all client is .40 per client, the unit price of the haircut is $12. Andre has asked you to find the following:
1. Determine the annual break-even point, in number of haircuts.
2. What will the operating income if 20,000 haircuts are performed?
3. What if Andre revises the compensation method. The barbers will receive $4 per hour plus $6 for each haircut. What is the new contribution margin per haircut? What is the annual break-even point (in numbers of haircuts)?
I believe earlier this week I posted a method for solving this very problem.
Use basic algebra to solve. Let HC be hair cuts. Break even occurs when total costs equal total revenue. Annual wage expenses (W) are 9.9*40*50*5=99000., (9.90 per hour times 40 hrs per week times 50 weeks times 5 barbers).
So, total costs are 1750 + 99000 + 0.4*HC. Total revenue is 12*HC. Break even is therfore 12*HC - 1750 - 99000 - .4*HC = 0.
Solve for HC.
2) Instead of solving for HC, simply plug 20000 for HC in the above equation.
3) adjust the equation, what is the new fixed cost of labor, what is the variable cost of each hair cut.
To solve for the annual break-even point, we need to set the total costs equal to total revenue and solve for HC (haircuts):
Total costs = Rent and fixed expenses + Annual wage expenses + Shampoo cost
Total costs = $1,750 + $99,000 + $0.40 * HC
Total revenue = Unit price of the haircut * HC
Total revenue = $12 * HC
Setting the two equal, we have:
$12 * HC - $1,750 - $99,000 - $0.40 * HC = 0
Simplifying the equation:
$11.60 * HC - $100,750 = 0
Now solve for HC by isolating it:
$11.60 * HC = $100,750
HC = $100,750 / $11.60
HC ≈ 8,673.28
So, the annual break-even point, in number of haircuts, is approximately 8,673 haircuts.
To find the operating income when 20,000 haircuts are performed, plug the value of HC into the total revenue equation:
Total revenue = $12 * 20,000
Total revenue = $240,000
Operating income = Total revenue - Total costs
Operating income = $240,000 - ($1,750 + $99,000 + $0.40 * 20,000)
Operating income = $240,000 - ($101,750 + $8,000)
Operating income = $240,000 - $109,750
Operating income = $130,250
Therefore, the operating income if 20,000 haircuts are performed is $130,250.
For the revised compensation method, the new contribution margin per haircut can be calculated as follows:
Fixed cost of labor = $4 per hour * 40 hours * 50 weeks * 5 barbers
Fixed cost of labor = $40,000
Variable cost per haircut = $6
The new contribution margin per haircut is the unit price of the haircut minus the variable cost per haircut:
New contribution margin per haircut = $12 - $6
New contribution margin per haircut = $6
To find the new annual break-even point, we modify the equation by replacing the wage expenses with the new fixed cost of labor and the shampoo cost with the variable cost per haircut:
Total costs = Rent and fixed expenses + New fixed cost of labor + Variable cost per haircut * HC
Total costs = $1,750 + $40,000 + $6 * HC
Total revenue = Unit price of the haircut * HC
Total revenue = $12 * HC
Setting the two equal, we have:
$12 * HC - $1,750 - $40,000 - $6 * HC = 0
Simplifying the equation:
$6 * HC - $41,750 = 0
Now solve for HC by isolating it:
$6 * HC = $41,750
HC = $41,750 / $6
HC ≈ 6,958.33
Therefore, the new annual break-even point, in number of haircuts, is approximately 6,958 haircuts.
To solve each of the questions, we need to use the equation for break-even point and adjust it according to the given conditions.
1. Determine the annual break-even point, in number of haircuts:
Break-even occurs when total costs equal total revenue. The total costs consist of rent and other fixed expenses, annual wage expenses, and the cost of shampoo per haircut. The total revenue is the unit price of the haircut multiplied by the number of haircuts.
The equation for break-even is: Total revenue - Total costs = 0
So, the equation will be: 12 * HC - 1750 - 99000 - 0.4 * HC = 0
Solve for HC (number of haircuts) in this equation.
2. What will be the operating income if 20,000 haircuts are performed:
To find the operating income, we need to calculate the total revenue and subtract the total costs. Use the equation: Total revenue - Total costs = Operating income
Replace HC with 20,000 in the equation and solve for the operating income.
3. What if Andre revises the compensation method:
If Andre changes the compensation method, we need to adjust the equation by considering the new fixed cost of labor and the variable cost of each haircut.
Let's say the new fixed cost of labor is F and the variable cost of each haircut is V.
The new equation for break-even will be: Total revenue - Total costs = 0
Total costs now include the new fixed cost of labor, the variable cost of each haircut, and the rent and other fixed expenses.
So the equation will be: 12 * HC - F - (4 * 40 * 50 * 5) - (V * HC) - 1750 = 0
Now, solve for the new contribution margin per haircut and the new annual break-even point in numbers of haircuts.