Calculate Break Even Point
In this lesson, you will learn to calculate the break even point. We will do so with some word problems
What is break even point? In economy, break even point is when you don't make a profit and you don't lose money either
In other words, your revenue is equal to your expenses
Say R = revenue and C = cost
R = C
Example #1:
It costs a publishing company 50,000 dollars to make books. The 50,000 is a fixed cost or a cost that cannot change.
To help the publishing company sell the books, a marketing company charges 4 dollars for each book sold. If the company charges 9 dollars per book, how many books should they sell to break even?
Solution #1:
Let x be the number of books sold
Let C be the cost of producing and selling x books
Let R be the revenue made for selling x books
R = selling price of 1 book × number of books sold
R = 9x
C = fixed cost + variable cost
variable cost = fee charged for 1 book × number of books sold
variable cost = 4x
C = 50000 + 4x
R = C
9x = 50000 + 4x
9x - 4x = 50000 + 4x - 4x
5x = 50000
x = 10000 since 5 × 10000 = 50000
The break even point is to sell 10000 books.
Example #2:
It costs a man 75 dollars to buy the things that he needs to make hotdogs. The city allows him to sell his hotdog somewhere near the city hall. However, the city hall charges him 1 dollar for each hotdog sold
Calculate the break even point if the price he charges for 1 hotdog is $1.50
Solution #2:
Let x be the number of hotdogs sold
Let C be the cost of buying and selling x hotdogs
Let R be the revenue made for selling x hotdogs
R = selling price of 1 hotdog × number of hotdogs sold
R = 1.50x
C = fixed cost + variable cost
variable cost = fee charged for 1 hotdog × number of hotdogs sold
variable cost = 1x
C = 75 + 1x
R = C
1.50x = 75 + 1x
1.50x - 1x = 75 + 1x - 1x
0.5x = 75
x = 150 since 0.5 × 150 = 75
The break even point is to sell 150 hotdogs.
Calculate Break even point using a formula
A break even point formula can be derived and you can just use the formula to calculate the break even point quicker
C = fixed cost + variable cost
Let x be the number of items sold and let c (lower case c ) be the fee charged for each item sold
variable cost = fee charged for each item sold × number of items sold
variable cost = c × x
C = fixed cost + cx
Let s be selling price of one item
R = s × x
R = C
sx = fixed cost + cx
sx - cx = fixed cost + cx - cx
sx - cx = fixed cost
x(s - c) = fixed cost
Divide both sides of the equation by s - c
In example 2, fixed cost = $75, s = $1.50, and c = $1. To calculate break even point, just put these numbers into the formula
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