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Long-term lower price limit

How to calculate the long-term lower price limit, what it says and the formula for it is in this article.

Would you like to have the calculation of the long-term floor price explained step by step? We have the right thing for you! Our Videoon the subject of LPU provides a clear explanation. Click directly inside!

Long-term lower price limit definition

The long-term lower price limit, also abbreviated LPU, corresponds to the amount of Cost and is the minimum of average unit cost. In contrast to short-term lower price limit will both the variables as well as the fixed costs taken into account in the calculation. With the long-term lower price limit, the company makes neither a loss nor a profit, since it covers its costs exactly.

Calculate long-term lower price limit

You can calculate the long-term floor price by using either the average cost function derive, set it to zero and use this value again in the unit cost function or consider the prime costs. So that you can calculate the LPU, let's first look at the formulas that you need for it.

Long-term floor price formula

If the cost function is in linear shape is available, you can easily calculate the long-term lower price limit with this formula:

So the aggregated unit costs plus the fixed costs are added up and then divided by the number of goods produced.

If the cost function has a higher degree, then the formula for the long-term floor price is:


From the cost function, the unit cost function is first determined, this is derived and then set to zero in order to increase the amount in Operating optimum to calculate. Then you insert x into the unit cost function to calculate the long-term lower price limit.

Long-term lower price limit and cost

Another simple formula is:

This is the case because the prime costs also result from the aggregated costs. Here, too, let's look at an example.

Calculation of long-term lower price limit example

Imagine your company produces office chairs. The cost function for your company looks like this:

If you produce an office chair, there are variable costs of 14 € and a total of fixed costs of 574 €. Now imagine you have produced 150 office chairs. Then you put the produced amount into the function and get a total cost of 2674 €. The long-term lower price limit is then


You have thus determined the LPU. It says at what price you won't make any profit or loss with your office chairs.

Calculate long-term lower price limit Example (non-linear)

Imagine we have a cost function that looks like this:

Then we first calculate our average unit cost by dividing the cost function by x. In our example we get:

Then we lead the Average cost and set this to zero to find a minimum. The derivation of the average cost is then:

The amount for the short-term lower price limit is x = 11.98. In the last step, we have to use this again in our function of average costs. This then looks like this

In the second case, the long-term lower price limit would be € 17.83 again

Calculation of the short-term lower price limit over cost

In addition to the calculation using the cost function, it is also possible to use the calculation of the prime costs. The addition of variable material costs and production costs as well as fixed overhead costs is divided by the number of items produced. For this we need the respective items in our Accounting. Your office chairs could look something like this:

Direct material costs
Seat, backrest of chair legs10€ * 150
Painting process1,23€ * 150
Manufacturing overheads
Assembly robot600€
administrative expenses