### Profit volume relationship

One cannot assume, however, that “good” cost-to-sales relationships automatically result in profit for a restaurant or that higher or lower cost percentages are necessarily desirable for a given restaurant. Indeed, it is possible that a higher food cost percent— obtainable by lowering menu prices or by increasing food costs, thus giving each customer more for his or her money—may result in sufficient additional customers to increase profitability in spite of the higher food cost percent. It is also possible that lower cost percentages (achieved by raising menu prices or lowering costs) may result in fewer customers and lower profits.
Another possibility is that lower menu prices will lessen profit because there is an insufficient increase in the number of customers to offset the higher cost percentage. Nevertheless, it is obvious that the ratio of total costs—food, plus beverage, plus labor, plus all other costs—to total sales cannot exceed 100 percent if the operation is to be profitable. These possibilities are examined in the following paragraphs.
At the given level of sales (\$925,000) and costs (\$818,625) as shown in picture 1, satisfactory profit (\$106,375) has been earned. However, it is also possible to earn acceptable profit at some sales level other than \$925,000 even if prime cost, as a percentage of sales, increases. picture 1 illustrates this.
 picture 1

 picture 2

Although the costs and cost-to-sales ratios for the components of prime cost have increased (cost of sales from 33.5 percent to 40 percent, and cost of labor from 25 percent to 30 percent), a satisfactory profit was still realized, because lowered menu prices resulted in many new customers and the number of dollars required for overhead was the same in both cases. Consequently, as sales volume increases, the number of dollars required for overhead has represented a smaller percentage of sales. Profit as a percentage of sales is considerably lower, but the dollar amount of profit is higher.
On the other hand, suppose that lowering menu prices resulted in relatively few new customers—only a sufficient number to maintain total sales at the given level of \$925,000. In that case profit would be reduced to zero, as shown in picture 3.
In the preceding illustration, total sales remained at the original figure, but prime costs expressed as a percentage of sales increased because of lowered menu prices and increased labor cost to service the increased number of customers.
Now assume a decrease in sales in the restaurant, as illustrated in picture 4.
In this instance cost percents for the components of prime cost are the same as they were in picture 1. However, the operation shows a loss rather than a profit, because of fewer customers. The fixed element for overhead, still \$277,500, now accounts for 46.25
 picture3

Fig 3.3
 picture 4

Fig 3.4
percent of sales dollars, rather than the 30 percent it represented at the sales level illustrated in  picture 1 .
A key lesson in the preceding examples, then, is that although percentages are very useful in comparing operations and judging a single operation, one should not be rely on them to provide all of the information necessary to judge profitability. There are many restaurants that operate with relatively high food cost percentages or beverage cost percentages and at the same time are
able to earn a satisfactory profit. Each operation must establish the cost percentages that are suitable for that particular operation.
The key to understanding cost/volume/profit relationships lies in understanding that there are fixed costs in any operation, regardless of sales volume, and that it is necessary to generate sufficient total volume to cover both fixed and variable costs. This is not to say, however, that ratios of variable costs to sales are to be ignored. In fact, if the ratio of variable costs to sales is very high, it may not be possible to generate sufficient volume to cover fixed costs. After all, the seats in a dining room can be turned over only a limited number of times in any given meal period. Conversely, if the ratio of variable costs to sales is too low, it may not be possible to generate adequate sales volume, simply because potential customers perceive that prices are too high for the value they receive. If this is the case, they are likely to dine elsewhere.

#### The cost volume/Volume/Profit Equation

There is a close relationship between sales, cost of sales, cost of labor, cost of overhead, and profit. In fact, these relationships can be expressed as follows:
Sales =  Cost of sales+  cost of labor + cost of overhead + profit
\$925,000 = 309,875 + 231,250 + 277,500 + 106,375
Because cost of sales is variable, cost of labor includes both fixed and variable elements, and cost of overhead is fixed, one could restate this equation as follows:
Sales = Variable cost + fixed cost + profit
In fact, this is the basic cost/volume/profit equation.
Using the first letters of the terms to stand for those terms, this basic equation can be written as a formula:
S = VC + FC + P
Throughout this topic, then,
S=  Sales
VC=  Variable cost
FC = Fixed cost
P = profit
In proceeding with the chapter, the reader will do well to keep three points in mind:
1. Within the normal range of business operations, there is a relationship between variable costs and sales that remains relatively constant. That relationship is a ratio that is normally expressed either as a percentage or as a decimal.
2. In contrast, fixed costs tend to remain constant in dollar terms, regardless of changes in dollar sales volume. Consequently, whether expressed as a percentage or as a decimal, the relationship between fixed cost and sales changes as sales volume increases and decreases.
3. Once acceptable levels are determined for costs, they must be controlled if the operation is to be profitable. Before considering cost/volume/profit relationships in detail, it is necessary to understand some important concepts, abbreviations, and terms.
These are illustrated using figures from the statement of income for the Graduate Restaurant, reproduced in Figure 3.5.
The first step is to determine total variable cost for the Graduate Restaurant. Total variable cost consists of food cost, beverage cost, and the variable portion of labor cost. As we know the cost of labor includes both a fixed element and a variable element. Figure 3.6,
is the basis for the following discussion.
 income starement of a restaurant

Fig 3.5
By referring to Figure 3.5, one can determine that food cost is \$275,187 and beverage cost is \$34,688. The variable portion of labor cost will be 40 percent of total payroll expense (salaries and wages, plus employee benefits). Total payroll expense is \$231,250, and 40 percent of that total is \$92,500. One can then determine total variable cost by adding the following three figures:
Food cost \$275,187
Beverage cost 34,688
Variable labor cost 92,500
Total variable cost \$402,375
The next step is to determine total fixed cost for the restaurant. Total fixed cost includes all costs other than the variable costs. From Figure 3.1, these are the fixed portion of the labor cost
(60 percent of \$231,250, or \$138,750), other controllable expenses (\$138,750, by coincidence), occupancy costs (\$78,625), interest (\$13,875), and depreciation (\$46,250). One can then determine total fixed cost quite simply by adding these five figures:
Fixed labor cost \$138,750
Other controllable expenses 138,750
Occupancy costs 78,625
Interest 13,875
Depreciation 46,250
Total fixed cost \$416,250
Given the preceding figures, the basic cost/volume/profit equation for the Graduate Restaurant at the level of sales indicated is
Sales (\$925,000) = Variable cost (\$402,375) + fixed cost (\$416,250) + profit (\$106,375)
or
S (\$925,000) = VC (\$402,375) + FC (\$416,250) + P (\$106,375)

Variable Rate
Variable rate is the ratio of variable cost to dollar sales. It is determined by dividing variable cost by dollar sales and is expressed in decimal form. It is similar to a cost percent:
Variable cost
Variable rate = _______________
Sales
Variable rate is normally abbreviated as VR, so the equation can be written
VC
VR = _______________
S
In the preceding example, variable cost (VC) is \$402,375, and sales (S) are \$925,000. Therefore,

Variable cost (402,375)
Variable rate = ______________________________
Sales (925,000)

VR= 0.435

This is the same as stating that 43.5 percent of dollar sales is needed to cover the variable costs, or that \$.435 of each dollar of sales is required for that purpose. As sales increase, the total dollars spent to cover these costs will increase, but the percentage will not change.

### Contribution Rate

If 43.5 percent of dollar sales is needed to cover variable costs, then the remainder (56.5 percent) is available for other purposes, namely:
1. Meeting fixed costs
2. Providing profit
As sales increase, an increasing number of dollars will be available to be used to meet fixed costs and provide increased profit.

Thus, \$.565 of each dollar of sales is available to contribute to covering fixed costs and providing profit. Indeed, one can easily see that if fixed costs were to remain the same, increased dollars resulting from the contribution rate of the increased sales would all be used to increase profit. This percentage (or ratio, or rate) is known as the contribution rate, abbreviated as CR. Thus,
CR = Contribution rate
The contribution rate is determined by subtracting the variable rate from 1.
CR = 1 - VR
For the Graduate Restaurant, the CR is .565, determined by subtracting the VR of .435 from 1.
CR = 1 - .435
CR = .565

### BREAK EVEN POINT

One will recognize at once that no business enterprise can be termed profitable until all of the fixed costs have been met. If dollar sales volume is insufficient to cover both variable and fixed costs, the enterprise will clearly operate at a loss. If dollar sales are sufficient to cover both variable and fixed costs exactly, but insufficient to provide any profit (i.e., profit is zero), the business is said to be operating at the break-even point. The break-even point, usually abbreviated as BE, is defined as the point at which the sum of all costs equals sales, so that profit equals zero. Thus,
BE=  break-even point

#### COST/VOLUME/PROFIT

Sales = \$925,000
Variable costs = \$402,375
Fixed costs = \$416,250
Profit = \$106,375
Variable rate=  .435
Contribution rate = .565
An additional formula must be introduced at this point.

fixed costs+ profit
Sales = ________________
Contribution rate
which is abbreviated as:
FC + P
S _______
CR
This formula can be used to determine the level of dollar sales required to earn any profit that one might choose to put into the equation.
To prove that the formula works, one can substitute the preceding figures in the formula, as follows:

\$416,250 + \$106,375
\$925,000 = ___________________
.565
\$522,625
\$925,000 = ________
.565
\$925,000 = \$925,000
To determine the break-even point for the Graduate Restaurant, the point at which profit would be equal to zero dollars, one would simply let P  0 and solve the equation as follows:
FC+ P
S = ________
CR

\$416,250 +0
S = __________
.565
S = \$736,726
The calculations assume that the variable rate and the contribution rate will remain the same at the reduced sales volume. At that level of sales, variable costs (VC) remains at 43.5 percent of
sales, or \$320,476. Thus, VC of \$320,476 plus FC of \$416,250 equals S, or \$736,726, leaving no profit.

S (\$736,726) = VC (\$320,476) + FC (\$416,250) +P (0) \$736,726 = \$736,726

No profit-oriented business ever wants to operate at BE, and the Graduate Restaurant was no exception. The sales level achieved in the Graduate Restaurant was \$925,000, which was
\$188,274 beyond BE. Although there are no additional fixed costs to cover after the break-even point is reached, each additional dollar of sales does have variable costs associated with it. In
the Graduate Restaurant these were identified as \$.435 for each dollar of sale, which is the same as saying that VR = .435. Variable cost can be determined by multiplying S (sales) by VR (variable rate).
VC=  S + VR
VC = \$188,274 x .435
VC=  \$81,899
If one multiplies dollar sales of \$188,274 by VR .435, one determines that variable costs associated with those sales beyond BE is \$81,899. If this \$81,899 in variable costs is subtracted
from sales of \$188,274, the result (\$106,375) is equal to the profit (P) for the period. It consists of \$.565 of each dollar sale beyond BE.
P (\$106,375) = S (\$188,274) x CR (.565)
\$106,375 =  \$106,375
It must be stressed that this is true only for sales beyond BE: Before BE, there is no profit.
 fixed and variable cost in a restaurant

### Contribution Margin

Each dollar of sales, then, may be divided imaginatively into two portions:
1. That which must be used to cover variable costs associated with the item sold
2. That which remains to cover fixed costs and to provide profit The dollar amount remaining after variable costs have been subtracted from the sales dollar is defined as the contribution
margin, abbreviated as CM. Thus,
CM  contribution margin
CM = Selling price - variable costs of that item
Thus, if a menu item sells for \$12.00 and its cost is \$5.00, the contribution margin is \$7.00
\$7.00 = \$12.00 - \$5.00
This holds true for each menu item and for the total of all menu items. Again considering the statement of income for the Graduate Restaurant, food sales were \$786,250 and food costs were
\$275,188. The contribution margin of food sales at the Graduate Restaurant was:
Food sales = \$786,250
- Food costs = 275,188
Contribution margin = 511,062
The final figure is also referred to as the gross margin and the gross profit on sales.
When sales reach a level sufficient to cover all variable costs and all fixed costs, with an additional amount left over, that additional amount is obviously profit. Moreover, because the contribution margin must go to cover fixed costs until break-even is reached, after break-even is reached, the contribution margin becomes profit.
The importance of the contribution margin in food and beverage management cannot be overemphasized. Clearly, any item sold for which variable cost exceeds sales price results immediately in a negative contribution margin, which is an immediate financial loss to the business. A prime sirloin steak with a variable cost of \$4.00 must be sold for an amount greater than \$4.00, or there will be such a loss. Furthermore, in establishing a sales price for the steak, provision must be made for each sale to result in an adequate contribution margin. An adequate contribution margin is one that, when taken with all other contribution margins from all other sales, will be sufficient not only to cover fixed costs of operation, but also to provide for an additional amount beyond break-even that will be the desired profit.

### Break even analysis

Break-even analysis is a technique widely used by production management and management accountants. It is based on categorizing production costs between those which are "variable" (costs that change when the production output changes) and those that are "fixed" (costs not directly related to the volume of production).

Total variable and fixed costs are compared with sales revenue in order to determine the level of sales volume, sales value or production at which the business makes neither a profit nor a loss (the "break-even point").

The Break-Even Chart

In its simplest form, the break-even chart is a graphical representation of costs at various levels of activity shown on the same chart as the variation of income (or sales, revenue) with the same variation in activity. The point at which neither profit nor loss is made is known as the "break-even point" and is represented on the chart below by the intersection of the two lines:
 break even chart

In the diagram above, the line OA represents the variation of income at varying levels of production activity ("output"). OB represents the total fixed costs in the business. As output increases, variable costs are incurred, meaning that total costs (fixed + variable) also increase. At low levels of output, Costs are greater than Income. At the point of intersection, P, costs are exactly equal to income, and hence neither profit nor loss is made.

Fixed Costs

Fixed costs are those business costs that are not directly related to the level of production or output. In other words, even if the business has a zero output or high output, the level of fixed costs will remain broadly the same. In the long term fixed costs can alter - perhaps as a result of investment in production capacity (e.g. adding a new factory unit) or through the growth in overheads required to support a larger, more complex business.

Examples of fixed costs:
- Rent and rates
- Depreciation
- Research and development
- Marketing costs (non- revenue related)

Variable Costs

Variable costs are those costs which vary directly with the level of output. They represent payment output-related inputs such as raw materials, direct labour, fuel and revenue-related costs such as commission.

A distinction is often made between "Direct" variable costs and "Indirect" variable costs.

Direct variable costs are those which can be directly attributable to the production of a particular product or service and allocated to a particular cost centre. Raw materials and the wages those working on the production line are good examples.

Indirect variable costs cannot be directly attributable to production but they do vary with output. These include depreciation (where it is calculated related to output - e.g. machine hours), maintenance and certain labour costs.

Semi-Variable Costs

Whilst the distinction between fixed and variable costs is a convenient way of categorising business costs, in reality there are some costs which are fixed in nature but which increase when output reaches certain levels. These are largely related to the overall "scale" and/or complexity of the business. For example, when a business has relatively low levels of output or sales, it may not require costs associated with functions such as human resource management or a fully-resourced finance department. However, as the scale of the business grows (e.g. output, number people employed, number and complexity of transactions) then more resources are required. If production rises suddenly then some short-term increase in warehousing and/or transport may be required. In these circumstances, we say that part of the cost is variable and part fixed.

1. If Sales \$300000, P/V 33% and Fixed Cost \$75000 then what is (I) BEP (II) Variable Cost and (III) Net Profit?
-Thank You

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