Capítulo 8. Diseño metodológico
8.2 Diseño
8.2.3 Diseño computacional
Managers often want to know the number of sales required to break even or make a desired profit. Calculating that figure will allow managers to determine how many customers are required, and will provide an alternative means of determining whether financial goals are being met.
As previously discussed, the total of the contribution margins for all sales is used to cover fixed costs and provide a profit. If one knows the aver- age contribution margin per sale and the dollar figure for fixed costs, it is then possible to calculate the number of sales, or customers, needed to cover fixed costs and the desired profit.
For example, if the financial records of a small restaurant indicated sales of $48,000 and variable costs of $18,000 in a period when 3,000 custom- ers were served, then:
$ 48,000 sales 3,000 customers $ 16.00 average sales Similarly,
$ 18,000 variable costs 3,000 customers $ 6.00 average variable costs Using that information, it is possible to determine average contribution margin, defined previously as average sales minus average variable cost. Thus:
Average S $16.00 Average VC 6.00 Average CM $10.00
Before using this figure to complete calculations to determine the required number of customers, an important limitation on its use must be noted. An establishment with a stable sales mix can obtain more reliable data from the following calculations than can one with large fluctuations in the sales mix. Fluctuations in the sales mix typically cause the average sale and the average variable cost to change. These changes typically produce inaccu- rate results. Mathematically, the number of customers required to reach the break - even point may be calculated by the following formula:
Break - even in Customers Fixed costs Average Contribution Margin BEP in Customers FC Average CM
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If management wishes to determine the number of customers required to achieve a given profit, one simply adds profit to fixed cost and divides by average contribution margin. Thus:
Number of Customers FC Profit Average CM
In the small restaurant in our illustration, the average sale is $16.00, the average variable cost is $6.00, and the average contribution margin is $10.00. Assume that fixed cost for the period was $30,000. Thus:
Number of Customers $30,000 $10 3,000 customers
Applying this formula to the Grandview Bistro, we can find the number of customers necessary to break even or make a desired profit if we know the average sale and the average contribution margin.
In Chapter 1 , the average sale was computed to be $27.87. However, that figure was for food only and did not include liquor. For purposes of this discussion, we will assume that the average sale of $27.87 is correct for food and that there will be little, if any, fluctuation in that figure through- out the year.
Referring to the statement of income in Figure 1.3 , one can calculate that liquor sales represent 15 percent of total sales ($157,356 ÷ $1,049,043), and food sales represent 85 percent of total sales. Thus, the average total sale can be calculated by dividing $27.87 by .85:
$ 27.87 .85 $ 32.79 Total average sale
We previously calculated the average contribution rate of .567. Thus to find the average contribution margin, we multiply the average contribution rate times the average sales price.
Average sales price $32.79 Average CR 3 .567 Average CM $18.59
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COST CONTROL AND THE COST/VOLUME/PROFIT EQUATION
87
Fixed cost for the Grandview Bistro was previously calculated to be $466,106. Applying the formula for number of customers necessary to break even, we find that:
Number of Customers FC Average CM $466,106 $18.59 25,073
To determine the number of sales achieved for the profit shown in Figure 1.3 , the profit of $128,702 is added to fixed costs:
Number of Customers FC P Average CM
$466,106 $128,702 $18.59 $594,808 $18.59
31,996
To prove that the formula works, we multiply the number of sales (31,996) times the average sale ($32.79) to arrive at $1,049,149, the approxi- mate gross sales figure shown in Figure 1.3 . The small difference of $106.00 results from rounding.
Thus, the Grandview Bistro received 6,923 (31,996 25,073) more cus- tomers than were necessary to break even. Assuming that the restaurant is open 365 days during the year, the restaurant averaged 88 sales or covers each day (31,996 ÷ 365). Of course, some days had fewer customers and some days had more.
A detailed discussion of evaluating the contribution margin for individ- ual menu items is found in Chapter 11 .
COST CONTROL AND THE COST/VOLUME/PROFIT
EQUATION
Earlier in this chapter, we emphasized that cost must be controlled by the means discussed in Chapter 2 if an operation is to achieve planned profits. It is useful to consider what happens to planned profits when costs are not con- trolled. To illustrate, we refer to the operating budget for the Grandview Bistro for the coming year, developed in Chapter 2 and reproduced in Figure 3.9 .
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• FIGURE 3.9 •
The Grandview Bistro, Projected Operating Budget, Year Ended December 31, 20XX
Change Upcoming Year
Sales Food $891,687 $44,584 $ 936,271 Beverage $157,356 7,868 165,224 Total Sales $1,049,043 $52,452 $1,101,495 Cost of Sales Food $312,090 $15,605 $ 327,695 Beverage $39,339 1,967 41,306
Total Cost of Sales $351,429 $17,572 $ 369,001
Gross Profit $697,614 $34,880 $ 732,494
Controllable Expenses Fixed salaries and wages $125,885 $ 5,035 $ 130,920 Variable salaries and wages $83,924 4,085 88,009 Employee benefits $47,207 2,052 49,259 Other controllable expenses $162,602 6,500 169,102 Total Controllable Expenses $419,618 $17,672 $ 437,290 Income before Occupancy Costs, Interest, Depreciation, and Income Taxes $277,996 $ 295,204 Occupancy Costs $89,169 $ 2,000 $ 91,169 Interest $13,875 13,875 Depreciation $46,250 46,250 Total $149,294 $ 151,294 Restaurant Profit $128,702 $ 143,910 c03.indd Sec5:88 c03.indd Sec5:88 7/25/08 9:57:21 AM7/25/08 9:57:21 AM
COST CONTROL AND THE COST/VOLUME/PROFIT EQUATION
89
To determine the variable rate (VR) for the coming year, one must add the budgeted variable costs for food and beverages ($369,001) and the vari- able portions of salaries and wages and employee benefits.
In the discussion of the budget for the Grandview Bistro for the com- ing year in Chapter 2 , it was stated that sales were expected to increase by 5 percent and that variable costs would remain at the same percentages as before. Therefore, the ratio of variable costs to sales (the variable rate, or VR), calculated as .433 from figures in the income statement earlier in this chap- ter, is budgeted to remain the same for the coming year. Because this is true, the contribution rate (CR), defined as 1 VR, will also be the same: .567. Budgeted fixed costs for the coming year are as follows:
Fixed salaries and wages $130,920 Fixed employee benefits 32,730 Other controllable expenses 169,102 Occupancy costs 91,169
Interest 13,875
Depreciation 46,250
Total fixed costs $484,046
Assume that the new year has begun. The new budget has been adopted and is in effect. However, the manager has not been controlling variable costs adequately. As a result, excessive variable costs are developing, largely through inefficiency and waste. Such problems as spoilage of raw materials and poor scheduling of staff are common causes of these excessive costs.
Now assume that these excessive variable costs have had the effect of increasing the variable rate from .433, a figure calculated earlier from fig- ures in the income statement, to .515. This is the same as saying that the amount needed to cover variable costs has increased from a planned .433 to .515.
We now use the formula developed earlier in the chapter to determine the sales level required to earn the $143,910 profit indicated in the budget (Figure 3.9 ) if variable rate is .515. Using the formula
S FC P CR CR .485(1 .515)
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we substitute numbers in the formula to find that S $484,046 $143,910 .485
$627,956 .485 $1,294,755
This indicates that an additional $193,260 ($1,294,755 $1,101,495) in sales will be required to earn the target restaurant profit.
The reason these additional sales are required to earn the planned profit is simply that excessive variable costs have had the effect of increasing the variable rate unnecessarily. The planned profit could have been earned at the sales level of $1,101,495 if management had done a better job of con- trolling variable costs at the levels budgeted. And this could have been done, conceivably, without any change in quality or quantity standards and without raising prices.
This situation illustrates that an understanding of cost/volume/profit relationships is central to full comprehension of the need for cost control in food and beverage operations. On the one hand, one must understand that lowering contribution margins will necessitate increasing volume in order to achieve a given target profit. Sometimes the higher volume may not be attainable in a given operation because of limited seating capacity, realistic turnover rates, or even the limited size of the market. On the other hand, higher contribution margins, although requiring fewer customers, may not be an adequate answer if it means raising sales prices beyond the capacity or willingness of customers to pay. Some establishments with low menu prices and low contribution margins are very successful because they are able to maintain high volume. Some, with similar prices, contribution mar- gins, and sales volume, may be unsuccessful because of their higher fixed costs. There are other food and beverage operations with high contribution margins and low sales volume, some of which are successful, whereas others are not. The differences from one to another in their levels of profit and rela- tive success can normally be traced to differences in their fixed costs. The ideal restaurant would have high contribution margins, high sales volume, and low fixed costs.
Once satisfactory levels have been determined for costs, sales, and sales volume, it is clearly necessary for management to control costs if the enter- prise is to achieve the profit level planned in its budget.
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QUESTIONS AND PROBLEMS 91
CHAPTER ESSENTIALS
In this chapter, we have shown that knowledge of cost/volume/profit rela- tionships is important for those seeking to understand the need for control. We have given the basic formulas used in cost/volume/profit analysis and illustrated their use. We have defined several key terms, including break -
even point, variable rate, contribution rate , and contribution margin .
Finally, we have illustrated the effect of excessive or uncontrolled costs on profits.
KEY TERMS IN THIS CHAPTER
Break - even point Cost/volume/profit equation Contribution margin Variable rate
Contribution rate
QUESTIONS AND PROBLEMS
1. Given the following information, determine total dollar sales:
a. Cost of sales, $46,500; cost of labor, $33,247; cost of overhead, $75,883; profit, $3,129.
b. Cost of sales, $51,259; cost of labor, $77,351; cost of overhead, $42,248; loss, $41,167.
2. Given the following information, find contribution margin:
a. Average sales price per unit, $13.22; average variable cost per unit, $5.78
b. Average sales price per unit, $14.50; average variable rate, .36 c. Average sales price per unit, $16.20; average contribution rate, .55 d. Average variable cost per unit, $6.20; average variable rate, .3 e. Average variable cost per unit, $3.60; average contribution rate, .6
(From this point on, the term average is eliminated from the problems. This will affect neither the problems nor the solutions.)
3. Given the following information, find variable rate:
a. Sales price per unit, $19.25; variable cost per unit, $6.70
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b. Total sales, $164,328; total variable cost, $72,304.32 c. Sales price per unit, $18.80; contribution margin, $10.72
d. Sales price per unit, $16.37; total fixed costs, $142,408; total unit sales, 19,364; total profit, $22,952.80
4. Given the following information, find contribution rate:
a. Sales price per unit, $18.50; contribution margin, $10.08 b. Sales price per unit, $17.50; variable cost per unit, $6.95 c. Total sales, $64,726; total variable cost, $40,130.12
d. Sales price per unit, $16.50; profit, $33,381.80; number of customers, 18,440; total fixed costs, $136,137
5. Given the following information, find break - even point in dollar sales:
a. Fixed costs, $48,337.80; contribution rate, .6 b. Variable rate, .45; fixed costs, $155,410.31
c. Variable cost per unit, $5.85; sales price per unit, $17.40; fixed costs, $164,065.60
6. Given the following information, find break - even point in Number of
Customers:
a. Fixed costs, $113,231.64; contribution margin, $2.28
b. Sales price per unit, $17.22; fixed costs, $215,035.68; variable cost per unit, $6.98
c. Contribution rate, .6; sales price per unit, $18.20; fixed costs, $219,423.16
7. Given the following information, find dollar sales:
a. Fixed costs, $60,000; profit, $18,000; sales price per unit, $8.00; vari- able cost per unit, $5.00
b. Variable rate, .45; profit, $21,578.10; fixed costs, $58,382
c. Sales price per unit, $16.60; profit, $21,220; contribution margin, $9.29; fixed costs, $126,000
8. Given the following information, find number of customers:
a. Fixed costs, $58,922; profit, $9,838; contribution margin per unit, $3.82
b. Profit, $33,603; sales price per unit, $17.00; fixed costs, $97,197; con- tribution rate, .6
c. Variable cost per unit, $5.30; profit equal to 18 percent of $211,000; sales price per unit, $16.30; fixed costs, $86,609
d. Sales price per unit, $16.20; fixed cost, $129,425.36; variable rate, .4; profit, $44,000
9. Given the following information, find fixed costs:
a. Total sales, $104,672; profit, $18,000; variable rate, .42
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b. Profit, $12,000; number of customers, 32,392; variable cost per unit, $4.63; sales price per unit, $10.34
c. Sales price per unit, $14.60; profit, $34,000; number of customers, 26,712; variable rate, .35
d. Contribution rate, .65; sales price per unit, $18.40; number of custom- ers, 26,549; profit, $33,000
10. Given the following information, find profit:
a. Fixed costs, $82,449.40; total sales, $167,543.20; variable cost, $55,629.60
b. Variable rate, .4; number of customers, 26,412; fixed costs, $193,764.40; sales price per unit, $17.60
c. Total sales, $190,830.66; variable cost per unit, $5.64; fixed costs, $75,919.70; sales price per unit, $16.22
11. The owner of the Barn Lodge Restaurant estimates that fixed costs for
the coming year will be $360,000. Based on his investment in the busi- ness, he wants a profit of $120,000 for the year. Experience has shown that the average check is $12.00.
a. If total variable cost is $720,000, what level of dollar sales will be required to earn the target restaurant profit?
b. Given total variable cost and total sales figures calculated in Question 11a, what variable rate is the owner projecting?
c. Given the variable rate calculated in Question 11b, determine the contribution rate.
d. Given the contribution rate calculated in Question 11c, determine the average contribution margin based on a $12.00 average sale. e. At what level of dollar sales will the restaurant break even?
12. The following information is from the records of Daphne ’ s Restaurant:
Sales $800,000
Variable cost $342,400 Fixed cost $345,600
Assume that sales volume equals 40,000 covers: a. Calculate profit.
b. Calculate average dollar sale.
c. Calculate dollar sales required to earn a profit of $125,000, assuming variable rate does not change.
13. Define each of the key terms in this chapter.
QUESTIONS AND PROBLEMS 93
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