Question 211240: How do I write an equality describing the amount of revenue that must be generated in order to break even or turn a profit?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the general formulas would be:
total cost = fixed cost plus incremental cost
incremental cost = number of units produced * cost per unit
revenue = number of units sold * revenue per unit
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example:
you sell cars
your fixed costs are $35,000,000
your incremental costs per car are $15,000
you want to sell the cars at $20,000 apiece
how many cars to you have to sell to make a profit?
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let x = number of cars you have to sell.
let r = revenue per car
let f = fixed cost
let i = incremental cost per car
let p = profit
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your general equation is:
p = r*x - i*x - f
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your break even is when your profit = 0.
it is at this point where you have received enough revenue to cover your costs but you haven't yet been able to turn a profit.
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let's see where that is:
we can factor x to make our equation equal to:
p = x*(r-i) - f
r = 20,000
i = 15,000
f = 35,000,000
p = 0
out equation becomes:
0 = x*(20,000 - 15,000) - 35,000,000
this becomes:
0 = 5,000*x - 35,000,000
add 35 million to both sides to get:
35,000,000 = 5,000*x
divide both sides by 5,000 to get:
35,000,000 / 5,000 = x
you wind up with:
x = 7,000
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you have to sell 7,000 cars just to break even.
anything over that will bring you profits.
anything under that will bring you losses.
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we can graph this equation to show you how it works.
the equation we would graph would be:
y = 5x - 35 which makes the dollar figures in millions.
x represents the number of cars being produced in thousands of units
y represents the cumulative profit in millions of dollars.
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you can see the break even at 7000 cars (x = 7)
you can see that when x goes about 7000 units, a profit is showing.
you can see that when x is below 7000 units, a loss is showing.
you should be able to see that at 35,000 units (x = 35), the profit is 140 million (y = 140).
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you could also have graphed revenue and costs separately on the same graph and then you would have seen where the revenues start taking over (become higher than) the costs.
that graph would look like this:
in this graph, it's easy to see where the revenue starts taking over the costs.
at 7000 units there is the crossover.
at 0 units (x = 0) the revenue is 0
at 0 units (x = 0) the cost is 35 million (the fixed cost)
it's not quite as easy to spot the profits, because they have to be calculated.
at 35000 units (x = 35), the revenue is 700 million dollars and the cost is 560 million dollars, making the profit equal to 700 - 560 = 140 million dollars.
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