Break-Even Analysis and the Break-Even Point
Posted by Professor Cram in Cost Accounting
Break-even
Let's start at the beginning: Profit is what is left from revenue after expenses are covered. Break-even is the point where revenue equals expenses and profit is zero. Break-even analysis is a tool businesses use to see whether selling/producing a proposed product or service can at least reach the break-even point. This in turn lets the business know whether the proposed product or service should be part of the company's product mix and business model.
We start from the base income formula:
- Revenue – Expenses = Profit
Since break-even is the point where revenue equals expenses and profit is zero, the base formula becomes:
- Revenue = Expenses
Let's look at each component.
Revenue
Revenue is income from sales and is determined by multiplying the selling price by the quantity sold. Revenue usually increases in a linear manner from zero at no sales, and stays directly proportional to sales unless you give quantity discounts, which we will ignore for this exercise. (Learn more about the different types of discounts.)
Revenue = (Price per unit) x (Quantity)
Revenue = P x Q
Expenses
Expenses can be categorized into either Fixed Costs, Variable Costs, or Mixed costs (some of both). Expenses don't start from zero, because unless you are out of business, there are some expenses even if you aren't making or selling anything. These expenses with no production are all fixed costs. Expenses then go up in proportion to sales because of variable costs. (See our article on Fixed Costs and Variable Costs, how to identify them, and how to split Mixed costs into their fixed and variable components.)
Expenses = Fixed Costs + Variable Costs
Expenses = F + V
Variable Costs are the cost per unit times the quantity
Variable Costs = Unit Cost x Quantity
V = C x Q
Expenses = F + (C x Q)
Now lets do a little algebraic substitution to combine these components to determine the formulas for break even.
Revenue = Expenses
P x Q = F + (C x Q)
Now we solve for Q (the quantity at which break even occurs).
P x Q = F + (C x Q)
(P x Q) – (C x Q) = F
Q(P -C) = F
Q = F/(P – C)
If you know the variable costs of production, the fixed costs of the business, and the selling price for the product or service, you can determine the quantity of sales that are required to cover all costs and break even. Sales beyond break even then result in profit to the extent that selling price exceeds the variable cost.
Example
Let's work an example:
Price is $25 (P)
Variable Cost is $10 per unit (C)
Fixed Cost is $900,000 (F)
Right off, we can see it will take a bunch of sales to make up $900,000 in fixed costs when we only clear $15 per unit sold. (Price of $25 minus Cost of $10 means we clear $15 per unit; this concept is related to marginal cost and marginal revenue.)
Let's plug this into our formula.
Q = F/(P – C)
Q = $900,000/($25 – 10)
Q = $900,000/($15)
Q = 60,000
In this example, the company needs to sell 60,000 units to break even. In comparing this to their sales projections and overall marketing plan, they can thus determine whether it makes financial sense for them to do so.
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How do I find break-even point in sales dollars,not units?
Thank you.
Multiply the break-even quantity by the unit price to get the sales dollars.
I would consider this website to very useful for our online revision.
How would I go about solving a problem like this:
Louder Company manufactures part MNO used in several of its truck models. 10,000 units are produced each year with production costs as follows:
Direct materials $ 45,000
Direct manufacturing labor 15,000
Variable support costs 35,000
Fixed support costs 25,000
Total costs $120,000
Louder Company has the option of purchasing part MNO from an outside supplier at $11.20 per unit. If MNO is outsourced, 40% of the fixed costs cannot be immediately converted to other uses.
What amount of the MNO production costs is avoidable?
Matt Reiss owns the Fredonia Barber Shop. He employs five barbers and pays each a base rate of $1,000 per month. One of the barbers serves as the manager and receives an extra $500 per month. In addition to the base rate, each barber also receives a commission of $5.50 per haircut.
Other costs are as follows.
Advertising $200 per month
Rent $900 per month
Barber supplies $0.30 per haircut
Utilities $175 per month plus $0.20 per haircut
Magazines $25 per month
Matt currently charges $10 per haircut.
Determine the variable cost per haircut and the total monthly fixed costs
Compute the break-even point ini units and dollars
Determine net income assuming 1.900 haircuts are given in a month.
@cathy :
variable cost : $6/haircut
fixed cost: $6800/month
break even point comes at 1700 haircuts/ month..
with 1900 haircuts..net income : $1800
When I put in 1800 as the net income it was wrong.