$$$..APPLYING BREAK-EVEN VOLUME ANALYSIS.. $$$

The "Break-Even Volume (BEV)" is a very powerful tool. It represents a statistic that can be computed by plugging in numbers and comparing the results.

Definition: The "Break-Even Volume" is the volume at which the company's total revenues equal the total costs. Below the BEV point the company is losing money. Above the BEV point profits are realized.

GENERAL INFORMATION

Recall the situation, that you are the Chef and have requested that a new appetizer be placed on the menu. The general manager of your operation has tasted the appetizer and agrees it will be a winner but needs to know what it should be priced at, so he comes to you. He presents you with the following preliminary forecast for weekly sales at differing prices:

Table 1

VOLUME		SELLING PRICE
1,000 units		$5.00 per unit
700 units		$6.00 per unit
600 units		$7.50 per unit

and asks you what you think the best selling price for the company would be. We have investigated the concepts of fixed, variable and total costs and have combined the cost information with the price projections to determine the critical pricing concepts of unit contribution and total contribution.

We will begin our BEV discussion by examining the graph below which contains both hypothetical and previously presented data:: Graph 2

TECHNICALITIES

Method: Understanding Graph 1 in the previous section is critical in being able to apply the Break Even tutorial and use it in your operation. In this hypothetical situation, your manager has accepted your recommendation of $7.50 as the selling that will best maximizes the new appetizer's total contribution to the company. He then throws you a surprise and asks you how many we would have to sell to make a profit (essentially, where is the break even point)? Thoughtful reflection on this material so far presented in this tutorial shows you how you can obtain the answer in two different approaches.

: Graphical Solution:
Simply drawing a graph as presented above in Graph 2, which is the same graph as Graph 1 of the web resource document Understanding Break-Even Analysis except a Total revenue line has been added and the fixed cost established at $2,500 (recall that in Graph 1 fixed cost was established at $2,000). The Graphical Solution answer is obtained by drawing the BEV from where Total Revenues and Total Costs intersect down to the Appetizers volume axis.
: Algebraic Solution:
This other solution utilizes the Algebraic approach. We have established above that BEV is where total revenues and total costs are equal (or the point where the lines cross each other), therefore::

Equation 2
Total Costs in dollars = Total Revenue in dollars
Fixed Cost + (k · BEV) = Price · BEV

Solving Equation 2 we get::

Simplifying (for the $7.50 selling price example) we then obtain::

and see that to BREAK-EVEN within our selected accounting period, we would have to sell 556 of the new appetizers (all other factors ,such as fixed and variable costs, remaining unchanged).

Equation 2
Total Costs in dollars	= Total Revenue in dollars
Fixed Cost + (k · BEV)	= Price · BEV

UTILIZATION

Applying Break-Even Volume: As stated before, this is not rocket science. The BEV calculation is quite simple. BEV is used as a tool in helping to make all kinds of decisions that require analysis, especially those regarding pricing, variable cost changes, fixed cost level for a business and unit contributions. These are all "life blood" decisions for a company that wants to enter into business or to remain competitive.

: Unit Contribution:
Let's first look at leveraging unit contribution data to make decisions.
Above we have seen that pricing the appetizer at $7.50 the break-even point (BEV) is 556. Any price (and/or cost) change will effect the BEV because of its impact on the unit contribution. If we were to raise the price of the appetizer to $8.00 the unit contribution would increase by $0.50 and the BEV would go down to 500 appetizers and after that profit is earned. Lowering the price from $7.50 to $7.00 moves the BEV UP to 625 appetizers in order to begin making a profit. Your decision here is what is the viable and competitive and profitable price range--> and you must ask yourself of all the price and volume choices, what do I have the best chance of selling? Many factors need to be considered at this decision point like ::

where are my competitors priced?
how big is the current market for this product?
how big could the future market be for this product?
: Non Break-Even Profit Calculations:
If your company wants to make a profit of $2,000 per week above its fixed costs of $2,500 per week, break-even analysis can calculate the sales-volume numbers needed. We can in fact determine the volume or number of appetizers we would need to sell at any given price using BEV tool. For an example IF we continue to assume that the selling price is $7.50 and the unit contribution is $4.50 ==> then::

If your company would like to budget $5,000 per month to market and advertise this new appetizer you can use BEV to tell you how many extra appetizers you need to sell to cover this additional $5,000 expense.
: Fixed Cost Analyzation:
The new appetizer is a gastronomic hit and a very profitable menu addition. Your manager has approached you for your opinion on an expansion idea ==> to build a small kitchen to wholesale the new appetizer to other restaurants and to a large grocery store chain.

Using the formula above all you would need to do is plug in the numbers to arrive at the numeric answer.

SUMMARY

FINAL WORDS OF CAUTION: This tutorial on Break-Even Analysis has demonstrated a process that takes numerical data, crunches it, returns sets of other numerical data that must then either be ignored or acted upon. Be clear on the point that there are no absolute correct numbers. You have to determine what are relevant numbers for your own particular circumstances. In the example we used, fixed cost is $2,500, selling price is $7.50, unit contribution is $4.50 and Break-Even volume is therefore ==> 556 appetizers.

: The Meaning of the Numerical Data Sets:

is our fixed cost reasonable?
is the unit contribution enough?
can we sell 556 appetizers?

Once again, to answer these and many other questions regarding your pricing strategy you will need a background to reflect your Numerical Data against and make a comparison. The combination of reliable and accurate data and benchmarks to measure them against is the combination you must have and use to make successful and competetive decisions.

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