Question 72756: A company has a fixed cost of $75,000. Variable cost per unit is $25. Revenue unit is 75. Find the following:
a) Break Even Point
b) The profit or loss from producing 900 units.
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! Let's write two equations. The first equation will be for the Cost (let C represent Cost).
The Cost is comprised of two parts. The fixed cost of $75,000 and the variable cost that is
associated with the production. That cost is $25 per unit so its cost will be $25 times the
number of units produced. Let U represent the number of units produced. So our cost equation
is:
.
.
The amount of income or revenue is $75 per unit so that the revenue (call it R) is just the product
of the income for a single unit times the number of units produced. In equation form this is:
.
.
The break even point occurs when the revenue (R) just equals the cost C. We can determine this
by setting the right side of the cost and revenue equations equal to get:
.
.
Subtract 25*U from both sides to get:
.
.
And solve for U by dividing both sides by 50 to get:
.
.
When you produce 1500 units your income just equals your costs.
.
Another way of looking at this is on a per unit basis. Since it costs $25 dollars
to make a unit and you sell units for $75 each, then you are making 50 bucks a unit. And
you have to sell enough units to offset the $75000 of fixed costs. Therefore you again have
to divide $50 net income for each unit into the $75000 to find that 1500 units must be
made and sold to offset the costs.
.
You are also asked to calculate the profit or loss if you make and sell 900 units.
You can see that it will be a loss because you have to sell 1500 units to break even.
.
For 900 units, the cost is:
.
C 25*900 + 75,000 = 22,500 + 75,000 = $97,500
.
The income meanwhile is:
.
R = 75*900 = $67,500.
.
The result is that the costs exceed the income by $97,500 - $67,500 = $30,000 so you are out
$30,000 if you only sell 900 units.
.
Hope this helps you to understand the problem a little better.
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