Chapter7 - CVP

Cost-volume-profit (CVP) analysis focuses on the relationships of prices, costs, volume, and mix of products. It is useful for determining the amount of units or total sales revenue the company must earn at a particular level of profit desired. CVP analysis is based on the on the profit equation:

In most situations, you will solve for x, the number of units. Note the format of the equation includes the components of the variable costing income statement. Although some textbooks provide specific formulas, the formulas are not very flexible. The profit equation approach is easier to remember given that you already know the income statement format. The key is to remember that selling price and variable costs are in units and fixed cost is a total. Total sales revenue is determined after you solve for the number of units to be sold. If you buy 3 beers at an NFL football game for $8 each, sales revenue for the vendor at the stadium will be 3 times $8, or $24.

When relying on analysis using CVP, we must remember four assumptions so we can understand the limitations of the analysis: The assumptions are:

b. Both unit variable costs and total fixed costs remain constant within the relevant range.

Using the profit equation, you can solve for both of the following at any level of activity:

The break-even point is the point where sales revenue equals total cost and where profit is zero. Replace profit with zero in the profit equation to create a breakeven profit formula:

By inserting the appropriate sales price per unit, variable cost, and fixed cost information, the above equation can be solved for the break-even point in units. Assume that a company sells one product for $10 with a unit variable cost of $4 and a total fixed cost of $15,600. To determine breakeven, we plug the amounts given as follows:

Solving for x, we determine the number of units the company must sell to breakeven, x = 2,600 units.

To determine the sales revenue at breakeven point, think about the two components of total sales revenue. Sales revenue is determined by multiplying the number of units sold times the selling price per unit.

Recall your early algebra classes in eighth grade. You had to check your work by plugging your answer back into the equation to verify the accuracy of your answer. The same holds true with the profit equation. Plugging 2,600 units in the equation for x:

The math works! This tells you your answer is correct. Its a good idea to always check your work by plugging back into the equation to avoid errors. Alternatively you could construct a variable costing income statement using the 2,600 units where sales revenue equals $10 times 2,600 units and variable costs equal $4 times 2,600 units:

Sales revenue	$26,000
Less variable costs	10,400
Less fixed costs	15,600
Profit	$ 0

It may not be sufficient for companies to calculate the break even point if a higher level of profit is desired. Target profit is the profit level a company desires. To calculate the target profit, we use the same profit equation and replace a profit of zero with whatever profit level is desired. Let's use the same example for a company that sells one product for $10 with a unit variable cost of $4 and a total fixed cost of $15,600. However, instead of breakeven, or no profit expected, assume the company wants to earn $12,000 of profit. We use the same profit equation, but instead substitute the desired profit level of $12,000:

Solving for x, we get 4,600. The company must sell 4,600 to earn a profit of $12,000. How much total revenue will this be? At $10 sales price per unit times 4,600 units, total revenue is $46,000.

Managers are pleased when they earn lots of profit. Managers with operations that are not highly profitable are often stressed when sales drop in an effort to avoid having a 'loss.' To most managers, earning a profit of $1 is incredibly better than having a loss of one cent. To determine if the manager's unit will have profit or a loss, lots of accounting must take place so its likely the manager won't find out he has a loss until the accounting period has ended and its too late to do something about it.

That's where the margin of safety comes in. Its a calculation of how much 'sales revenue' can drop before the manager will incur a loss. It can be calculated in sales units, or when a company has more than one product, in sales revenue dollars. Margin of safety is calculated as the difference between expected sales and the break-even point:

Note that a company's current sales level can be used instead of expected sales level if you need to determine the margin of safety the company has achieved. More often, managers want to know what the expected margin is before sales have occurred instead of after the fact so they can do something to prevent a loss.

Contribution margin is the difference between sales and variable costs. The unit contribution margin is the difference between selling price per unit and the variable cost per unit.

Unit contribution margin is the amount each unit contributes to covering fixed costs and increasing profits. Above the break-even point, every additional unit sold increases profit by the amount of the unit contribution margin.

Let's assume the vendor at the Jacksonville Municipal Stadium sells draft beer for $8 each. The vendor's cost is $1.20 per beer, and its fixed costs total $800 for one day of football. Each additional beer that is sold will generate an additional $6.80 of profit, the amount of the contribution margin. In other words, each beer contributes $1.20 towards covering the fixed costs and they what is left over contributes to profit.

The contribution margin ratio (CMR) is similar to the gross profit ratio you learned in financial accounting. Recall that the gross profit ratio is the amount of gross profit divided by sales revenue. Likewise, the contribution margin ratio can be expressed based on sales as well:

Because the ratio is an expression of the amount of the contribution margin to sales revenue, you get the same ratio regardless if you calculate per unit or in total. The CMR expresses the contribution margin as a percentage of sales. The CMR measures the amount of each sales dollar that is contributed to covering fixed costs and generating profit. For each beer sold, the vendor generates 85 cents to cover fixed costs and go towards profit:

The profit equation lends itself very well to what-if analysis. It is easy to change components based on possible changes to selling price, fixed costs, or variable costs. a manager may anticipate. Suppose the beer vendor wants to know what will happen to the break even point if he changes to a new lager that requires less labor because of speedier pouring into cups reducing labor cost by 15%. However, the new lager requires a new refrigeration unit costing 10% more per day to rent for each football game. First, calculate the breakeven point with the changes:

However, since only full beers are sold, we must round up to 118. Rounding down (even if less than 0.5) causes a loss to result. Remember that managers become very disappointed with losses!

The variable and fixed costs are changed in the profit equation to reflect the proposed changes:

Because a portion of a beer cannot be sold, you must round up to 127 beers. The vendor must now sell 127 beers to breakeven rather than 118, or 9 additional beers. Selling more units is more work for the vendor, so you should recommend that the proposed change should not be made.