COSTVOLUMEPROFIT ANALYSIS
INTRODUCTION. A company would not want to sell a product or render a service unless it is at least breaking even. To break even on your products or services, you must be able to calculate the sales volume needed to cover your costs, and how to use this information to your benefit. You must also be familiar with how your costs react to changes in volume, and how price change affects your profits. Further, you must know what effect expense reductions will have. Breakeven analysis aids in profit planning.
Breakeven formulas are useful to all businesses in determining the point at which a business can begin to turn a profit. The three most common breakeven formulas, described below, determine the breakeven point, the margin of safety, and the cash breakeven point.
1. BREAKEVEN POINT
Introduction. The breakeven point is the sales volume at which total revenue equals total costs, resulting in zero profit  that is, the minimum sales necessary to avoid a loss.
By knowing the breakeven point, you know which products and/or services to emphasize and which to deemphasize (perhaps even to drop). The knowledge allows you to improve operating results and facilities planning, because you know how much must sell of a new item even before you introduce it.
How Is It Computed? Breakeven is that point where total sales are exactly the same as total costs. That is:
S = VC + FC
S  VC = FC
where S = sales, VC = variable cost, (S  VC) = contribution margin, and FC = fixed cost.
Note: At the breakeven point, the contribution margin equals total fixed cost.
This approach allows you to solve for breakeven sales or for other unknowns as well. An example is selling price. If you want a desired beforetax profit (P), solve for P in the following equation:
S = VC + FC + P
The guidelines for breaking even are:

An increase in selling price lowers breakeven sales.

An increase in variable cost increases breakeven sales.

An increase in fixed costs increases breakeven sales.
Example 1. A product has a fixed cost of $270,000 and a variable cost of 70% of sales. The point of breakeven sales can be calculated as follows:
S 
= 
VC 
+ 
FC 
1 S 
= 
.7S 
+ 
$270,000 
0.3S 
= 


$270,000 
S 
= 


$900,000 
If the selling price per unit is $100, breakeven units are 9,000 ($900,000/$100). If desired profit is $40,000, the sales needed to obtain that profit (P) can be calculated as follows:
S 
= 
VC 
+ 
FC 
+ 
P 
1S 
= 
0.7S 
+ 
$270,000 
+ 
$40,000 
0.3S 
= 


$310,000 


S 
= 


$1,033,333 


Example 2. If the selling price per unit is $30, the variable cost per unit is $20, and the fixed cost is $400,000, the breakeven units (U) can be calculated as follows:
S 
= 
FC 
+ 
VC 
$30U 
= 
$400,000 
+ 
$20U 
$10U 
= 
$400,000 


U 
= 
40,000 


The breakeven dollar amount is:
Example 3. You sell 800,000 units of an item. The variable cost is $2.50 per unit. Fixed cost totals $750,000. The selling price (SP) per unit should be $3.44 to break even:
S = VC + FC 
$30U = $20U + $400,000 
$10U = $400,000 
U = 40,000 
Example 4. Assume your selling price is $40, your sales volume is 20,000 units, your variable cost is $15 per unit, your fixed cost is $120,000, your aftertax profit is $60,000, and your tax rate is 40%. To determine how much you have available to spend on research (R), consider this equation:
S = VC + FC + P + R 
($40 x 20,000) = ($15 x 20,000) + $120,000 + $ 100,000* + R 
$280,000 = R 
* Aftertax profit: 
$ 60,000 = 0.6 x beforetax profit 
$ 60,000 / 0.6 = beforetax profit 
$100,000 = beforetax profit 
Example 5. Assume your selling price is $40, your variable cost is $24, your fixed cost is $150,000, your aftertax profit is $240,000, and your tax rate is 40%. To determine how many units you must sell to earn the aftertax profit, consider the following equation:
S = FC + VC + P 
$40 U = $150,000 + $24 U + $400,000* 
$16 U = $550,000 
U = 34,375 
*0.6 x beforetax profit = aftertax profit 
0.6 x beforetax profit = $240,000 
Beforetax profit = $240,000 / 0.6 = $400,000 
Example 6. Assume your selling price is $50 per unit, your variable cost is $30 per unit, your sales volume is 60,000 units, your fixed cost is $150,000, and your tax rate 30%. To determine the aftertax profit, use the following equation:
S = VC + FC + P 
($50 x 60,000) = ($30 x 60,000) + 150,000 + P 
1,050,000 = P 
Aftertax profit = $1,050,000 x 0.70 = $735,000 
Example 7. You are considering making a product presently purchased outside for $0.12 per unit. The fixed cost is $10,000, and the variable cost per unit is $0.08. Use the following equation to determine the number of units you must sell so that the annual cost of your machine equals the outside purchase cost.
S = VC + FC 
$0.12 U = $0.08 U + $10,000 
$0.04 U = $ 10,000 
U = 250,000 
SALES MIX. Breakeven analysis requires some additional considerations when your company produces and sells more than one product. Different selling prices and different variable costs result in different unit contribution margins. As a result, breakeven points vary with the relative proportions of the products sold, called the sales mix. In breakeven analysis, it is necessary to predetermine the sales mix and then compute a weighted average contribution margin (CM). It is also necessary to assume that the sales mix does not change for a specified period.
How It Is Computed? The breakeven formula for the company as a whole is:
Break even sales in units (or in dollars) = Fixed Costs / Weighted Average Unit CM (or CM Ratio)
Example 8. Your company has fixed costs of $76,000 and two products with the following contribution margin data:

Product A 
Product B 
Selling price 
$15 
$10 
Less: Variable cost 
12 
5 
Unit CM 
$ 3 
$ 5 
Sales mix 
60% 
40% 
The weighted average unit contribution margin is:
$3(.6) + $5(.4) = $3.80 
Your company`s breakeven point in units is:
$76,000/$3.80 per unit = 20,000 units 
which is divided as follows:
Product A: 
20,000 units x 60% = 12,000 units 
Product B: 
20,000 units x 40% = 8,000 units 
2. MARGIN OF SAFETY
Introduction. The margin of safety is a risk indicator that stipulates the amount by which sales may decline before losses are experienced.
How Is It Computed?
Margin of safety = (Expected sales  Breakeven sales) / Expected sales 
The lower the ratio, the greater the risk of reaching the breakeven point.
Example 9. If expected sales are $40,000 and breakeven sales are $34,000, the expected margin of safety is:
Margin of safety = ($40,000  $34,000) / $40,000 = 15% 
3. CASH BREAKEVEN POINT
Introduction. The cash breakeven point is the sales volume that will cover all cash expenses during a period. Note that not all fixed operating costs involve cash payment (e.g., depreciation expenses).
How Is It Computed? The cash breakeven point equation is as follows:
S = VC + FC (after deducting depreciation) 
The cash breakeven point is lower than the usual breakeven point because noncash charges are subtracted from fixed costs.
Example 10. If the selling price is $25 per unit, the variable cost is $15 per unit, and total fixed cost is $50,000, which includes depreciation of $2,000, the cash breakeven point is:
$25U = $15U + $48,000 
$10U = $48,000 
U = 4,800 
HOW IS IT USED AND APPLIED? Costvolumeprofit analysis relates to the way in which profit and costs change with a change in volume. A relatively small percentage reduction in sales can cause a major decline in earnings. It is therefore important for the owner to keep sales at or exceeding planned levels, and above the breakeven point. Costvolumeprofit analysis examines the impact on earnings of changes in such factors as variable cost, fixed cost, selling price, volume, and product mix. It thus aids in the planning process. A breakeven analysis is used to determine whether or not the breakeven point can be achieved.
Breakeven analysis is used for many purposes, including to determine:

The sales volume required to break even.

The sales volume necessary to earn a desired profit.

The improvement in revenue required to "get out of the red".

The effect that changes in selling price, variable cost, fixed cost, and output have on profit.

The selling price that should be charged.

The desired variable cost per unit or fixed costs.
The applications of breakeven analysis are many, including introducing a new product or service, modernizing facilities, starting a new business, and evaluating production and administrative activities.
Breakeven analysis is used to organize thinking on important broad aspects of any business  for example, determining the breakeven occupancy rate for an inexpensive motel or the breakeven passenger load rate for a small chartered bus service.
The margin of safety is a measure of operating risk. The larger the ration, the safer is the situation is due to the reduction in risk in reaching the breakeven point.
The cash breakeven point is used when a business has a minimum cash available, or when the opportunity cost of holding excess cash is high.
Breakeven analysis is important when beginning a new activity, such as starting a new line of business, or introducing a new product or service.
Sales mix analysis is vital to the overall success of the business. It is needed at all managerial levels. Top managers may have to make important strategic decisions involving mergers, buyouts, acquisitions, and divestitures as part of diversification. Business owners may have to decide on which segments (e.g., product lines, services, divisions, sales, territories, departments, salespersons, etc.) to keep, drop, or add.
The managers of retail stores such as Thrifty and SaveOn must constantly check their product mix. For example, the retailer may have to decide which products to replace with highmargin vacation products before the summer begins.
Examples of questions that are commonly answered by breakeven formulas include the following:

What is the financial feasibility of a proposed investment?

Have the business` breakeven possibilities been improving or deteriorating?

Will advertising generate sufficient sales to justify the cost of a campaign?

Would introduction of a new product add or detract from profitability?

What will be the impact of labor negotiations?

Would modernization of production facilities pay for itself?

What bid price should be offered on a contract?

Should the contract with a vendor or customer be renegotiated?
See Sec. 124, Averages (Means): Simple and Weighted.