Break-even analysis with changed cost structures?
Hello everyone,
I'm taking an exam in Production Management on Monday, and it will likely be on break-even analyses. In the lecture so far, we've only covered simple problems involving determining the break-even point. Now it's been announced that transfer problems might be included in the exam.
An example would be: You initially have a normal total cost function (fixed costs and variable costs). However, at a certain production volume (eg, 5,000 units), a robot is introduced that increases normal costs (eg, by €2,000 per month) but simultaneously reduces variable costs (eg, by €0.50 per unit). The task would then be to calculate the new break-even point at which total costs (including the robot) and revenue are equal again.
I've attached a diagram that shows how this situation could be represented. This is exactly how it should be calculated. How do you go about it, and what does the calculation look like?
Thank you in advance!
Our professor drew this for us. The orange line shows the total costs, the old break-even point, and then the new break-even point. How do I calculate the new point?
It's really very urgent.
Thank you very much:)
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Moin, what you're describing here are so-called jump-fixed costs, ie additional fixed costs, which only come from a certain amount of production, for example, because the production capacities of a machine are expelled.
The trick is that there can even be several break-even points here, as shown in your sketch. The one for the first point is your "normal" cost function, i.e. you assume that the production amount is smaller than the 5,000 units. If you find an x smaller than 5,000, that's a break-even point.
For the other break-even point, you first calculate the total cost for the 5,000 units plus the cost of the robot. Now you can set up a new cost function, with the fixed costs being the value just calculated. But you now do not consider the costs depending on the total amount x, but on the amount that goes beyond 5,000 units.
By the way, an interesting transfer task would also be asked from which quantity of goods it makes sense to get the robot. The diagram shows that at 5,001 units the costs with the acquisition of the robot are above the turnover. This would not make it useful.
Thank you for your detailed answer.
Just for understanding.
The break-even point is determined by setting your sales equal to the cost. And here it is that you make your sales equal to the cost of the 5,000 units, ie the 5,000 euros plus, for example, the 2 euro variable costs once 5,000 units. And then you're still counting plus the 2000 euros for the robot, plus the variable costs for the robot are then 50 cents minus, ie 1.50 euros. Then you'll get the costs together and then you'll have your total cost plus the 1.50 Euro times X, a certain amount. And then you'll get it off normal to X and then somehow get a new point out, for example 7333 pieces, and that's your new break-even point.
So I really understood that you will then make the total cost for the 5000Stk plus the 2000 Euro for the robot and then again plus these variable costs and then just change it to X
Right. To make it clearer, maybe you should work with 2 variables, once with x_1 for your "normal" cost function and with x_2 as the amount that goes beyond x_1.
Thank you.