Cost-Volume-Profit Analysis

Cost-Volume-Profit, (CVP), Analysis: A Definition.

CVP is a management tool that expresses relationships among sales volume, costs and profits. CVP can be used in the form of a graph or an equation. Cost-volume-profit analysis can answer a number of analytical questions, such as:

What is the breakeven revenue of a restaurant?
How much revenue does a restaurant need to achieve a given profit?
What level of price change is needed to achieve a given profit?
What is the effect of cost changes on the profitability of an operation?
Many other "what if" type of questions

Variable versus fixed costs:

In order to use CVP analysis, Managers need to divide operating costs in to two categories. Variable expenses are those cost that vary with changes in sales volume. Fixed cost are those cost that remain constant with changes in sales volume. Quite often we run into expenses that are of a mixed nature; in this case managers needs to breakout the cost, as best they can, into its fixed and variable components.

Management may also designate fixed and variable expenses within their accounting system. In addition there are various other ways of breaking out cost. Consider the following analysis of a restaurant operation's high and low months:

 High month Low month Change Variable Fixed Meals 8,000 15,000 7,000 Per meal High month Low month Sales \$ 80,000 \$ 150,000 Cost of Sales (24,000) (45,000) (21,000) (3.00) - - Wages (22,000) (32,500) (10,500) (1.50) (10,000) (10,000) Other Controllable __(24,000) __(27,500) (3,500) (0.50) (20,000) (20,000) Operating Income \$ 10,000 \$ 45,000 ________ Variable (5.00) _________ _________ Fixed (30,000) (30,000)

By comparing a high and low months, estimates can be made of variable and fixed costs. Consider Wages. The difference between the two months is \$10,500. By dividing this amount by the change in meals, 7,000 meals, results in an estimated variable wage cost of \$1.50 per meal. We can then estimate the fixed cost by looking at either the high or the low month. For the high month variable wages are \$22,500 (\$1.50x 15,000 meals). Deducting the \$22,500 from total wages of \$32,500 equals an estimated fixed costs of \$10,000. Applying this technique to the low month will give the same results. Try it yourself!

Applying this procedure to all three expense categories results in total variable expense of \$5.00 per meal and total fixed costs of \$30,000. The relationship between sales, variable expense, fixed expenses and income can then be reflected in a simple formula. For the high month this is:

\$150,000-(\$5.00x15, 000 meals)-\$30,000=\$45,000

For the low month this is:

\$80,000-(\$5.00x8, 000 meals)-\$30,000=\$10,000

CVP Model

We are now going look at a larger example and use it to learn some concepts and see how CVP analysis can be applied. The following table shows an income statement of the NAU Grill with expenses broken out into variable and fixed:

 NAU Grill Income Statement Expense Variable Cost Amount Variable Fixed Ratio Per meal Sales Food \$ 1,000,000 Beverage ____200,000 _______ _______ Total sales 1,200,000 100.0% 12.00 Cost of Sales Food 310,000 \$ 310,000 25.8% 3.10 Beverage _____46,000 46,000 3.8% 0.46 Total cost of sales ____356,000 Gross profit 844,000 Controllable Expenses Salaries and wages 348,000 148,000 \$ 200,000 12.3% 1.48 Direct 72,000 22,000 50,000 1.8% 0.22 Utilities 40,000 13,000 27,000 1.1% 0.13 Marketing 25,000 - 25,000 0.0% - Repairs and maintenance 28,000 13,000 15,000 1.1% 0.13 Administration _____50,000 - 50,000 0.0% - Total controllable expense ____563,000 Operating profit 281,000 Non-controllable expenses Occupation expenses 60,000 - 60,000 Interest expense 15,000 - 15,000 Depreciation 35,000 - 35,000 Amortization ______3,000 - 3,000 Total non-controllable expenses ____113,000 Income before income taxes 168,000 Provision for income taxes @17% _____28,560 Net income \$ 139,440 Meals sold 100,000 Total variable costs \$ 552,000 46.0% 5.52 Total fixed costs \$ 480,000

The NAU Grill has total fixed costs of \$480,000. Variable cost is \$552,000, which when divided by meals sold give a variable cost per meal of \$5.52. Variable cost can also be expressed as a ratio of 46%. To facilitate looking at a number of "what if" situations, we have condensed the income statement in the following manner:

 NAU Grill Income Statement Variable Cost Amount Ratio Per meal Sales \$1 ,200,000 100.0% 12.00 Variable Costs ____552,000 ___46.0% _____5.52 Contribution Margin 648,000 54.0% 6.48 Fixed Costs ____480,000 Income before income taxes 168,000 Provision for income taxes _____28,560 Net income \$ 139,440

You will note a new term in our statement: "contribution margin." Contribution margin is defined as the excess of revenues over variable cost. The term contribution margin is used since this is the amount that is to cover fixed costs and provide a profit. NAU Grill's contribution margin ratio is 54%. Contribution margin per meal is \$6.48 per meal.

To continue our analysis, we will be using two equations where

S= sales,
F= fixed costs
I= income before taxes
CMm= contribution margin per meal
CMR= contribution margin ratio
M= number of meals

To determine sales:

 S = F + I CMR = 480,000 + 168,000 54% = 1,200,000

To determine meals:

 M = F + I CMm = 480,000 + 168,000 6.48 = 10,000 meals

We can now determine the breakeven point for the NAU Grill. In terms of sales it is:

 S = F + I CMR = 480,000 + 0 54% = 888,889

In terms of meals it is:

 M = F + I CMm = 480,000 + 0 6.48 = 7,074meals

From this point on we will be using the meal formula only since it is more flexible to use when dealing with different scenarios.

The column titled "Breakeven" shows the breakeven income statement:

 Start Breakeven Sales \$ 1,200,000 \$ 888,889 Variable Costs \$ 552,000 ____408,889 Contribution Margin 648,000 480,000 Fixed Costs ____480,000 ____480,000 Income before income taxes 168,000 - Provision for income taxes @ 17% _____28,560 - Net income \$ 139,440 \$ - Meals sold 100,000 74,074 Per Meal Sales 12.00 12.00 Variable Costs ______5.52 ______5.52 Contribution Margin 6.48 6.48

CVP analysis can also be visualized by means of a CVP graph: The point where revenue and total cost meet is the breakeven point; to the left the difference between the two lines is the loss; to the right it is the income before taxes. However, in order to obtain precise numbers we will need to use formulas

Let us look at two more situations. How many meals do we need to earn \$150,000 before taxes?

 M = F + I CMm = 480,000 + 150,000 6.48 = 97,222meals

Then, lets consider \$150,000 in net income. To do that we first need to calculate before tax income:

 I = ____N___ (100% - T) = __150,000__ (100% - 17%) = 180,723

Where:

N=net income
I= income before taxes
T=tax rate

Then we can calculate the required number of meals :

 M = F + I CMm = 480,000 + 180,723 6.48 = 101,963meals

The condensed income statement for these two cases is as follows:

 Before Tax Net Income Sales \$ 1,166,667 \$1,223,561 Variable Costs ______536,667 ______562,838 Contribution Margin 630,000 660,723 Fixed Costs ______480,000 ______480,000 Income before income taxes 150,000 180,723 Provision for income taxes @ 17% _______25,500 _______30,723 Net income \$ 124,500 \$ 150,000 Meals sold 97,222 101,963 Per Meal Sales 12.00 12.00 Variable Costs _________5.52 _________5.52 Contribution Margin 6.48 6.48

Two more cases and then we finished! Let's assume that NAU Grill experiences some costs increases: fixed expense go up by \$20,000 to \$500,000 and variable expense go from \$5.52 to \$6.82 per meal. Under these circumstances how many additional meals over the 101,963 need to be sold in order to maintain net income at \$150,000? Using the meal formula we can quickly calculate the requirement:

 M = F + I CMm = 500,000 + 180,723 5.18 = 131,414meals

 Cost increase example Sales \$ 1,576,964 Variable Costs _________896,241 Contribution Margin 680,723 Fixed Costs _________500,000 Income before income taxes 180,723 Provision for income taxes @ 17% __________30,723 Net income \$ 150,000 Meals sold 131,414 Per Meal Sales 12.00 Variable Costs ____________6.82 Contribution Margin 5.18

Let's assume that 131,000 meals is beyond reasonable expectations. Another approach would be a price increase in menu items. What average price per meal do we need in order to achieve net income of \$150,000 serving 100,000 meals? To calculate this we need to manipulate our formula in order to solve for the contribution margin per meal:

 M = F + I CMm

Then we solve for CMm:

 CMm = F + I M = 500,000 + 180,723 100,000 = 6.80723

We can then solve for the required average price per meal:
Where:

P= Average price per meal
Vm= Variable cost per meal=\$6.82
CMm= contribution per meal=\$6.81

P = Vm + Cm = 6.82 + 6.80723 = 13.62723
The condensed income statement will now be as follows:

 Price increase example Sales \$ 1,362,723 Variable Costs ____________682,000 Contribution Margin 680,723 Fixed Costs ____________500,000 Income before income taxes 180,723 Provision for income taxes @ 17% _____________30,723 Net income \$ 150,000 Meals sold 100,000 Per Meal Sales 13.62723 Variable Costs ____________6.82000 Contribution Margin 6.80723

What if management wanted to take a look at the effect of different price increases on the required number of meals needed to achieve a net income of \$150,000? One way to do this would be to try different prices in the above analysis and have the computer calculate the required number of meals. Spreadsheet programs, such as Excel, can simplify this task by use of a "table" feature. We have prepared such a table relating average meal prices in a range of \$12.60 to \$13.70 to the required number of meals in order to produce a net income of \$150,000. A graph was produced from the table showing the relationship in a graphic forme:

 Table for \$150K Net Income Price Meals 12.00 131,414 12.10 128,925 12.20 126,528 12.30 124,220 12.40 121,993 12.50 119,846 12.60 117,772 12.70 115,796 12.80 113,833 12.90 111,961 13.00 110,149 13.10 108,395 13.20 106,696 13.30 105,050 13.40 103, 453 13.50 101,905 13.60 100,401 13.70 98,942 There are many other ways to apply CVP analysis. Spreadsheet programs are well suited for this task. To experiment with the file used for the examples in this section, download here.

Are there any disadvantages to CVP analysis?
Yes. Some of the shortcomings are:

Cost volume profit analysis can get complicated when applying it to a multi-product operation, which is usually the case with restaurant operations. Each of the menu items on the restaurant's menu can have different variable cost ratios. To get around this problem an average variable cost ratio is used; this needs to be recognized when interpreting the analysis results.

Variable cost and fixed cost may differ from assumptions if the analysis is applied over a wide range of potential sales. Consequently the analysis technique needs to be restricted to a narrow range of sales volumes.

Cost volume profit analysis only provides approximate answers. In addition to quantitative studies, such as CVP analysis, management needs to investigate operations directly and to exercise judgement before making any changes to operations.

Once you have finished you should:

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