$$$..UNDERSTANDING BREAK-EVEN ANALYSIS.. $$$

This section addresses the concept of break-even analysis, a type of quantitative financial analysis. The advantages, terminology and mechanics of how to use its calculations will be demonstrated. How break-even can be applied and used in a variety of decision making situations will also be presented.

Article by Chef Mars
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· MBA, Miami University
· Cornell University School Of Hotel Administration
  - Professional Development Program
    º Accounting and Financial Management for Non Financial Managers
    º Hospitality Financial Management: Operational Decision Making
· BA Chemistry, Miami University
· 20 years experience in restaurants, clubs, inns and hotels
    California, Florida, Dominican Republic

Definition: a technique for analyzing a new investment (like a new kitchen, new walk-in, etc), a new product introduction (example: a new menu item, opening a new restaurant or adding a second unit), a price change or, and this is very critical, inaction in response to a competitor's moves.

GENERAL INFORMATION

This is a web reference document that focuses on using numbers and calculations that will help you succeed. Nothing presented here will be difficult or demand anything more than attention, intuition and a calculator or spreadsheet program. To apply break-even analysis it will be up to you to decide which elements or inputs are important or relevant to your calculation. Only you will be able to decide that.

To help all readers of this document, I will present an example as a learning tool.

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. The problem now reveals itself and it is that although we can calculate the revenue we do not have any cost information. Arriving at a pricing strategy is impossible. So we must start by investigating the concepts of fixed, variable and total costs and then combine the cost information with the price projections to determine unit contribution and total contribution.
We will begin by discussing the graph below:: Graph 1

TERMINOLOGY

Fixed Cost: Fixed costs are costs that do not vary with the output quantity. Fixed cost is the dotted line on the graph. Notice that the total cost curve (red line) does not begin at zero because of this fixed cost component, represented by the distance 0Z (referred to from this point on as $0Z), of total cost. An example of fixed cost would be the rent or lease expense on the property and building that continues to be paid even when you shut down each year for one month.

Variable Cost: This is the portion or component of the total cost that will vary and increase with output, sales or production of the new appetizer. Variable cost assignment is not an clear cut issue and there are a number of accepted methods to use. In this case variable unit-costs would-could include the food cost, labor cost, utility cost, facility maintenance cost etc. Variable cost could be effected by a quantity purchase agreement that would create the condition where costs would be increasing at a decreasing rate as you increase sales. It could also be impacted by the phenomena of the learning experience that has the effect of decreasing labor costs over time due familiarity of the process (no more training or learning to do). But for this tutorial we will assume that the total cost is linear as show in Graph 1 above.
The following equation will put together in numbers what we have discussed so far:: Equation 1

In the above equation. k is the constant unit-variable cost of producing one more new appetizer and in fact it is the slope of the red colored total cost line or curve in Graph 1. Not rocket science as you can see. The Total Cost to make the new dish is equal to:: the Fixed Costs of the entire operation + the Variable Cost of producing one more of the new appetizer multiplied times the Volume (quantity) you forecast to produce or sell.

Contributions: Now that we have provided the definitions for Fixed and Variable Costs we need to introduce the concept of contribution

Unit Contribution:
Letting k = constant unit-variable cost and P = Price received for the appetizer, then::

Unit Contribution in dollars = P - k

Total Contribution:
IF V = total volume or number the appetizers sold then::

Total Contribution in dollars = (P - k) · V
or the individual appetizer profit contribution times number of appetizers sold::

Total Contribution in dollars = PV - kV
(TC = Total Revenue - Total Variable Cost)
or, after the variable cost of the appetizer has been subtracted out of the total revenue from the sales volume of that appetizer the Total Contribution (TC) is the amount of dollars made available to the company to apply (cover or contribute) to the fixed cost and the profits.

Now let us apply what we have learned so far to our original forecast that was presented in Table 1. We will make the assumption that the forecasted unit sales are accurate and that k or the unit-variable cost = $3.00.

AT the $5.00 selling price::

Per Unit Contribution in dollars	= $P - k = $5.00 - $3.00 = $2.00
Total Contribution in dollars	= PV - kV
weekly Contribution in dollars	= $2.00 per appetizer · 1000 sold per week
bottom line	= $2,000.00 per week

AT the $6.00 selling price::

Per Unit Contribution in dollars	= $P - k = $6.00 - $3.00 = $3.00
Total Contribution in dollars	= PV - kV
weekly Contribution in dollars	= $3.00 per appetizer · 700 sold per week
bottom line	= $2,100.00 per week

AT the $7.50 selling price::

Per Unit Contribution in dollars	= $P - k = $7.50 - $3.00 = $4.50
Total Contribution in dollars	= PV - kV
weekly Contribution in dollars	= $4.50 per appetizer · 600 sold per week
bottom line	= $2,700.00 per week

Study the above closely. What can you deduce from the results based on the assumptions of the number sold and that the variable cost per each appetizer is constant at $3.00?

The best option for your company (and what you should recommend to the manager) is pricing the new appetizer at $7.50 will maximize the new appetizer's total contribution.

Run through the exercise above and assume the variable cost per each appetizer has changed to $1.00. Any difference in your recommendation to maximize the new appetizer's total contribution?

No, because at this lower variable cost maximizing total contribution would still occur at the $7.50 pricing level but the total contribution gap between it and the $5.00 appetizer has narrowed from a difference of $700 to only $300.

FOOD COSTING FORUM

Have Questions? Post them in the forum.