# Analysis that deals with how profits and costs change with a change in volume

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Published: *Mon, 5 Dec 2016*

## INTRODUCTION

Analysis that deals with how profits and costs change with a change in volume. More specifically, it looks at the effects on profits of changes in such factors as variable costs, fixed costs, selling prices, volume, and mix of products sold. By studying the relationships of costs, sales, and net income, management is better able to cope with many planning decisions. For example, CVP analysis attempts to answer the following questions: (1) What sales volume is required to break even? (2) What sales volume is necessary in order to earn a desired (target) profit? (3) What profit can be expected on a given sales volume? (4) How would changes in selling price, variable costs, fixed costs, and output affect profits? (5) How would a change in the mix of products sold affect the break-even and target volume and profit potential?

## COST VOLUME PROFIT ANALYSIS

Cost-volume-profit analysis (CVP), or break-even analysis, is used to compute the volume level at which total revenues are equal to total costs. When total costs and total revenues are equal, the business organization is said to be “breaking even.” The analysis is based on a set of linear equations for a straight line and the separation of variable and fixed costs.

## VARIABLE COST

Total variable costs are considered to be those costs that vary as the production volume changes. In a factory, production volume is considered to be the number of units produced, but in a governmental organization with no assembly process, the units produced might refer, for example, to the number of welfare cases processed.

There are a number of costs that vary or change, but if the variation is not due to volume changes, it is not considered to be a variable cost. Examples of variable costs are direct materials and direct labor.

## FIXED COST

Total fixed costs do not vary as volume levels change within the relevant range. Examples of fixed costs are straight-line depreciation and annual insurance charges. Total variable costs can be viewed as a 45 line and total fixed costs as a straight line. Linearity is an underlying assumption of CVP analysis. Although no one can be certain that costs are linear over the entire range of output or production, this is an assumption of CVP. To help alleviate the limitations of this assumption, it is also assumed that the linear relationships hold only within the relevant range of production. The relevant range is represented by the high and low output points that have been previously reached with past production. CVP analysis is best viewed within the relevant range, that is, within our previous actual experience. Outside of that range, costs may vary in a nonlinear manner. The straight-line equation for total cost is:

Total cost = total fixed cost + total variable cost

Total variable cost is calculated by multiplying the cost of a unit, which remains constant on a per-unit basis, by the number of units produced. Therefore the total cost equation could be expanded as:

Total cost = total fixed cost + (variable cost per unit number of units)

Total fixed costs do not change.

A final version of the equation is:

Y = a + bx

where a is the fixed cost, b is the variable cost per unit, x is the level of activity, and Y is the total cost. Assume that the fixed costs are $5,000, the volume of units produced is 1,000, and the per-unit variable cost is $2. In that case the total cost would be computed as follows:

Y = $5,000 + ($2 1,000) Y = $7,000

It can be seen that it is important to separate variable and fixed costs. Another reason it is important to separate these costs is because variable costs are used to determine the contribution margin, and the contribution margin is used to determine the break-even point.

## CONTRIBUTION MARGIN

The contribution margin is the difference between the per-unit variable cost and the selling price per unit. For example, if the per-unit variable cost is $15 and selling price per unit is $20, then the contribution margin is equal to $5. The contribution margin may provide a $5 contribution toward the reduction of fixed costs or a $5 contribution to profits. If the business is operating at a volume above the break-even point volume (above point F), then the $5 is a contribution (on a per-unit basis) to additional profits. If the business is operating at a volume below the break-even point (below point F), then the $5 provides for a reduction in fixed costs and continues to do so until the break-even point is passed.

Once the contribution margin is determined, it can be used to calculate the break-even point in volume of units or in total sales dollars. When a per-unit contribution margin occurs below a firm’s break-even point, it is a contribution to the reduction of fixed costs. Therefore, it is logical to divide fixed costs by the contribution margin to determine how many units must be produced to reach the break-even point: Assume that the contribution margin is the same as in the previous example, $5. In this example, assume that the total fixed costs are in creased to $8,000. Using the equation, we determine that the break-even point in units:

Now, if we want to determine the break-even point in total sales dollars (total revenue), we could multiply 1600 units by the assumed selling price of $20 and arrive at $32,000. Or we could use another equation to compute the break-even point in total sales directly. In that case, we would first have to compute the contribution margin ratio. This ratio is determined by dividing the contribution margin by selling price.

The financial information required for CVP analysis is for internal use and is usually available only to managers inside the firm; information about variable and fixed costs is not available to the general public. CVP analysis is good as a general guide for one product within the relevant range. If the company has more than one product, then the contribution margins from all products must be averaged together. But, any cost-averaging process reduces the level of accuracy as compared to working with cost data from a single product. Furthermore, some organizations, such as nonprofit organizations, do not incur a significant level of variable costs. In these cases, standard CVP assumptions can lead to misleading results and decisions.

## TARGET INCOME SALES VOLUME

Amount required to attain a particular income level or target net income. Target Income sales volume is computed as:

For example, assume that unit contribution margin is $15, fixed costs are $15,000, and target income is $15,000. Target income sales volume = ($15,000 + $15,000)/$15 = 2000 units. This means that 2000 units need to be sold to make $15,000 profit

## BREAK EVEN ANALYSIS

## DEFINITION

Financial analysis that identifies the point at which expenses equal gross revenue for a zero net difference. For example, if a mailing costs $100 and each item generates $5 in revenue, the break-even point is at 20 items sold. A profit will be made on items sold in excess of 20. A loss will result on sales under 20. The break-even point may be analyzed in terms of units, as above, or dollars.

## EXPLANATION

Branch of Cost-Volume-Profit (CVP) Analysis that determines the break-even point, which is the level of sales where total costs equal total revenue. Thus, zero profit results. Breakeven sales is computed as follows:

Break-even sales in units = Fixed costs/Unit contribution margin.

Break-even sales in dollars = Fixed costs/Contribution margin ratio.

For example, assume:

Fixed costs = $15,000.

Unit contribution margin (selling price – unit variable cost) = $15, and

Contribution margin ratio (unit CM/selling price) = .6

Then, break-even sales in units = $15,000/$15 = 1000 units and break-even sales in dollars = $15,000/.6 = $25,000.

A break-even chart is one in which sales revenue, variable costs, and fixed costs are plotted on the vertical axis while volume is plotted on the horizontal axis. The Break-Even Point is the point at which the total sales revenue line intersects the total cost line. See the sample chart below.

Break-even analysis is used in cost accounting and capital budgeting to evaluate projects or product lines in terms of their volume and profitability relationship. At its simplest, the tool is used as its name suggests: to determine the volume at which a company’s costs will exactly equal its revenues, therefore resulting in net income of zero, or the “break-even” point. Perhaps more useful than this simple determination, however, is the understanding gained through such analysis of the variable and fixed nature of certain costs. Break-even analysis forces the small business owner to research, quantify, and categorize the company’s costs into fixed and variable groups.

“Understanding what it takes to break even is critical to making any business profitable,” Kevin D. Thompson stated in Black Enterprise. “Incorporating accurate and thorough break-even analysis as a routine part of your financial planning will keep you abreast of how your business is really faring. Determining how much business is needed to keep the door open will help improve your cash-flow management and your bottom line.”

The basic formula for break-even analysis is as follows:

BEQ FC /(P-VC)

Where BEQ Break-even quantity

FC Total fixed costs

P Average price per unit, and

VC Variable costs per unit.

Fixed costs include rent, equipment leases, insurance, interest on borrowed funds, and administrative salaries-costs that do not tend to vary based on sales volume. Variable costs, on the other hand, include direct labor, raw materials, sales commissions, and delivery expenses-costs that tend to fluctuate with the level of sales. A key component of break-even analysis is the contribution margin, which can be defined as a product or service’s price (P) minus variable costs (VC) per unit sold. The contribution margin concept is grounded in incremental or marginal analysis; its focus is the extra revenue and costs that will be incurred with the next additional unit.

The first step in determining the level of sales needed for a small business to break even is to compute the contribution margin, by subtracting the variable costs per unit from the selling price. For example, if P is $30 and VC are $20, the contribution margin is $10. The next step is to divide the total annual fixed costs by the contribution margin. For example, a company with FC of $50,000 and a contribution margin of $10 would need to sell 5,000 units to break even. This number can easily be converted to the dollars of revenue the company would need to break even for the year. Simply multiply the break-even point in units by the average selling price per unit. In this case, a BEQ of 5,000 units multiplied by a P of $30 per unit yields break-even revenue of $150,000.

Break-even analysis has numerous potential applications for small businesses. For example, it can help managers assess the effect of changing prices, sales volume, and costs on profits. It can also help small business owners make decisions regarding whether to expand their operations or hire new employees. Break-even analysis would also be useful in the following situation: a small business owner is skeptical of her marketing manager’s projection for sales of 15,000 units of a new product, and wants to know what minimum quantity of units must be sold to avoid losing money, assuming a selling price of $25, fixed costs of $100,000, and variable costs of $15. The equation tells her that these parameters will require a break-even volume of 10,000 units; fewer than that level yields losses, more than that level yields profits. This perspective of analysis may be employed where the analyst is highly confident of the estimates for price and costs, but feels less certain about the assessment of market demand. In this case, the small business owner might be interested in how low sales could fall below the marketing manager’s forecast without causing an embarrassment at year-end reporting time.

Another scenario may involve the question of how to manufacture a product, in terms of the nature of operations and how they will affect fixed costs. Here, a small business owner may have a good handle on the quantity expected, the likely selling price, and the variable costs involved, but be undecided about how to structure the new operation. If the volume is expected to be 10,000 units, at a selling price of $5 and variable costs of $3.50, the break-even equation tells him that fixed costs can be no greater than $15,000. “The bottom line is that, especially for small businesses, the margins for error are much too narrow to make business decisions on gut instinct alone,” Thompson concluded. “Every idea, whether it is the introduction of a new product line, the opening of branch offices, or the hiring of additional staff, must be tested through basic business analysis.”

The break-even point for a product is the point where total revenue received equals the total costs associated with the sale of the product (TR = TC).[1] A break-even point is typically calculated in order for businesses to determine if it would be profitable to sell a proposed product, as opposed to attempting to modify an existing product instead so it can be made lucrative. Break even analysis can also be used to analyze the potential profitability of an expenditure in a sales-based business.

break even point (for output) = fixed cost / contribution per unit

contribution (p.u) = selling price (p.u) – variable cost (p.u)

break even point (for sales) = fixed cost / contribution (pu) * sp (pu)

## Margin of Safety

Margin of safety represents the strength of the business. It enables a business to know what is the exact amount he/ she has gained or lost and whether they are over or below the break even point.[2]

margin of safety = (current output – breakeven output/current output margin of safety% = current output – breakeven output/current output x 100 If P/V ratio is given then profit/ PV ratio

## In unit sales

If the product can be sold in a larger quantity than occurs at the break even point, then the firm will make a profit; below this point, the firm will make a loss. Break-even quantity is calculated by:

Total fixed costs / (selling price – average variable costs).

Explanation – in the denominator, “price minus average variable cost” is the variable profit per unit, or contribution margin of each unit that is sold.

This relationship is derived from the profit equation: Profit = Revenues – Costs where Revenues = (selling price * quantity of product) and Costs = (average variable costs * quantity) + total fixed costs.

Therefore, Profit = (selling price * quantity) – (average variable costs * quantity + total fixed costs).

Solving for Quantity of product at the breakeven point when Profit equals zero, the quantity of product at break even is Total fixed costs / (selling price – average variable costs).

Firms may still decide not to sell low-profit products, for example those not fitting well into their sales mix. Firms may also sell products that lose money – as a loss leader, to offer a complete line of products, etc. But if a product does not break even, or a potential product looks like it clearly will not sell better than the break even point, then the firm will not sell, or will stop selling, that product.

An example:

Assume we are selling a product for £2 each.

Assume that the variable cost associated with producing and selling the product is 60p.

Assume that the fixed cost related to the product (the basic costs that are incurred in operating the business even if no product is produced) is £1000.

In this example, the firm would have to sell (1000 / (2.00 – 0.60) = 715) 715 units to break even.

Total Income (Net profit) = Total expenses (costs)

NI = TC = Fixed cost + Variable cost

Selling Price x Quantity = Fixed cost + Quantity x Variable cost (cost/unit)

SP x Q = FC + Q x VC

Quantity x (SP-V) = Fc

Break Even = FC / (SP âˆ’ VC)

where FC is Fixed Cost, SP is Selling Price and VC is Variable Cost

## Internet research

By inserting different prices into the formula, you will obtain a number of break even points, one for each possible price charged. If the firm changes the selling price for its product, from $2 to $2.30, in the example above, then it would have to sell only (1000/(2.3 – 0.6))= 589 units to break even, rather than 715.

To make the results clearer, they can be graphed. To do this, you draw the total cost curve (TC in the diagram) which shows the total cost associated with each possible level of output, the fixed cost curve (FC) which shows the costs that do not vary with output level, and finally the various total revenue lines (R1, R2, and R3) which show the total amount of revenue received at each output level, given the price you will be charging.

The break even points (A,B,C) are the points of intersection between the total cost curve (TC) and a total revenue curve (R1, R2, or R3). The break even quantity at each selling price can be read off the horizontal, axis and the break even price at each selling price can be read off the vertical axis. The total cost, total revenue, and fixed cost curves can each be constructed with simple formulae. For example, the total revenue curve is simply the product of selling price times quantity for each output quantity. The data used in these formulae come either from accounting records or from various estimation techniques such as regression analysis.

## Limitations

Break-even analysis is only a supply side (i.e. costs only) analysis, as it tells you nothing about what sales are actually likely to be for the product at these various prices.

It assumes that fixed costs (FC) are constant. Although, this is true in the short run, an increase in the scale of production is likely to cause fixed costs to rise.

It assumes average variable costs are constant per unit of output, at least in the range of likely quantities of sales. (i.e. linearity)

It assumes that the quantity of goods produced is equal to the quantity of goods sold (i.e., there is no change in the quantity of goods held in inventory at the beginning of the period and the quantity of goods held in inventory at the end of the period).

In multi-product companies, it assumes that the relative proportions of each product sold and produced are constant (i.e., the sales mix is constant).

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