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Aggregate Planning

Chapter 6: Cost-Volume-Profit Analysis and Relevant Costing



  1. The Breakeven Point
    1. The breakeven point (BEP) is the level of activity, in units or dollars, at which total revenues equal total costs.
    2. The following list summarizes the basic simplifying assumptions about revenue and cost functions:
    1. Relevant Range: A primary assumption is that the company is operating within the relevant range of activity specified in determining the revenue and cost information used in each of the following assumptions.
    2. Revenue: Total revenue fluctuates in direct proportion to units sold, while revenue per unit is assumed to remain constant; fluctuations in per-unit revenue for factors such as quantity discounts are ignored.
    3. Variable Costs: Total variable costs fluctuate in direct proportion to level of activity or volume. Variable costs per unit remain constant within the relevant range. Variable costs exist in all functional business areas including production, distribution, selling, and administration.
    4. Fixed Costs: Total fixed costs remain constant within the relevant range. Fixed cost per unit decreases as volume increases, and it increases as volume decreases. Fixed costs include both fixed factory overhead and fixed selling and administrative expenses.
    5. Mixed Costs: Mixed costs must be separated into their variable and fixed elements before they can be used in breakeven analysis. Any method that validly separates these costs in relation to one or more predictors may be used.
    1. Contribution margin (CM) id defined as selling price per unit minus all variable production, selling, and administrative costs per unit.
    2. Total contribution margin fluctuates in direct proportion to sales volume.
    3. The formula approach to breakeven uses an algebraic equation to calculate the breakeven point.
    1. The answer to the equation is not always acceptable and may need to be rounded to a whole number.
    2. Breakeven volume is equal to total fixed cost divided by the difference between revenue per unit and variable cost per unit.
    3. Algebraic breakeven computations use an equation that represents the income statement and groups costs by behavior to show the relationships among revenue, fixed cost, variable cost, volume, and profit as follows:

      R(X) – VC(X) – FC = P

      Where R = revenue (selling price) per unit

      X = number of units sold or to be sold

      R(X) = total revenue

      FC = total fixed cost

      VC = variable cost per unit

      VC(X) = total variable cost

      P = before-tax profit

    4. The equation represents an income statement, so P can be set equal to zero for the formula to indicate a breakeven situation.
    5. The breakeven point in units can be found by solving the equation for X:

      X = FC (R – VC)

    6. The contribution margin ratio (CM%) is contribution margin divided by revenue; indicates what proportion of selling price remains after variable casts have been covered.
    7. The BEP can be expresses in either units or dollars of revenue: (1) the BEP in sales dollars can be found by multiplying the BEP in units by the selling price per unit, or (2) the BEP in sales dollars can also be found by dividing total fixed cost by the CM%

X$ = FC CM%

Where X$ = breakeven point in sales dollars

CM% = contribution margin ratio = (R – VC) R

  1. CVP Analysis (See text Exhibits 6-2, 6-3, 6-4, and 6-5.)
    1. Cost-volume-profit analysis is a process of examining the relationships among revenues, costs, and profits for a relevant range of activity and for a particular time frame. The technique is applicable in all economic sectors (manufacturing, wholesaling, retailing, and service industries) since the same types of managerial functions are performed in each type of organization.
    2. CVP analysis uses the same algebraic income statement formula that is used for the calculation of the breakeven point, but includes a profit amount.
    3. A significant application of CVP analysis is the setting of a desired target profit and focusing on the relationships between it and specified income statement amounts to find an unknown.
    1. Volume is a common unknown in such applications since managers want to achieve a particular amount of profit and need to know what quantity of sales must be generated to accomplish this objective.
    2. Profits may be stated either as a fixed or variable amount and on either a before-tax or after-tax basis.
    1. The amount of profit may be specified – after the breakeven point is reached, each dollar of contribution margin is a dollar of profit.
    1. The formula would appear as follows for a fixed amount of profit before taxes:

      In units: R(X) – VC(X) = FC + PBT

      In sales dollars: X$ = (FC + PBT) CM%

      Where PBT = specified amount of profit before tax

    2. The formula would appear as follows for a fixed amount of profit after taxes:

R(X) – VC(X) – FC = PBT

And [(PBT)(TR)] = Tax Expense

PBT – [(TR)(PBT)] = PAT

Where TR = tax rate

PAT = specified amount of profit after tax

    1. Managers may want desired profit to be equal to a specified variable amount of sales.
    1. The formula would appear as follows for a variable amount of profit before taxes:

      R(X) – VC(X) – FC = PuBT(X)

      Where PuBT(X) = desired profit per unit before taxes

    2. The formula would appear as follows for a variable amount of profit after taxes:

R(X) – VC(X) – FC = PuBT(X)

And PuBT(X) [(1-TR0] = PuAT

So X = FC (CM – PuBT)

Where PuAT(X) = desired profit per unit after tax

  1. CVP Analysis in a Multiproduct Environment (See text Exhibit 6-6)
    1. A constant product sales mix or, alternatively, an average contribution margin ratio must be assumed in order to perform CVP analysis in a multiproduct company.
    2. The constant sales mix assumption compares the sales mix to a bag or package of items that are sold together.
    3. The computation of a weighted average contribution margin ratio for the bag of products being sold is necessary under the constant sales mix assumption.
    4. Any shift in the sales mix proportion of products will change the weighted average contribution margin and the breakeven point.
  1. Underlying Assumption of CVP Analysis
    1. The CVP model is a useful planning tool that can provide information on the impact on profits when changes are made in the costing system or in sales levels.
    1. The CVP model, like other human-made models, is an abstraction of reality and, as such, does not reveal all the forces at work. It reflects reality but does not duplicate it.
    2. CVP is a tool that focuses on the short-run partially because of the assumptions that underlie the calculations.
    3. The assumptions are necessary, but they limit the accuracy of the results.
    1. The underlying assumptions are:
    1. All variable cost revenue behavior patterns are constant per unit and linear within the relevant range.
    2. Total contribution margin is linear within the relevant range and increases proportionally with output.
    3. Total fixed cost is a constant amount within the relevant range.
    4. Mixed costs can be accurately separated into their fixed and variable elements. Such accuracy is especially unrealistic, but reliable estimates can be developed from the high-low method or least squares regression analysis
    5. Sales and production are equal; thus, there is no material fluctuation in inventory levels. This assumption is necessary because otherwise fixed costs might be allocated to inventory at different rates each year. The assumption is more realistic as more firms start to utilize JIT inventory systems.
    6. There will be no capacity additions during the period under consideration. If such additions were made, fixed ( and possible variable) costs would change, invalidating the first three assumptions.
    7. In a multiproduct firm, the sales mix will remain constant. If this assumption were not made, no useful weighted average contribution margin could be calculated for the company for CVP analysis.
    8. Either there is no inflation or, inflation affects all cost factors equally. Or. If factors are affected unequally, the appropriate effects are incorporated into the CVP figures.
    9. Labor productivity, production technology, and market conditions will not change. If any of these factors changed, costs would change correspondingly, and it is possible that selling prices would change, invalidating the first three assumptions.
  1. Costs and Quality
    1. Cost, price, and volume work hand-in-hand with a fourth factor, quality.
    2. The quality specifications of a product and its components will play an important part in influencing costs, and quality products are typically able to command higher selling prices.
    3. Consideration of the implications of quality changes on cost, price, and volume should assist managers in concentrating their attention on the long run more than on the short run.
  1. Analyzing Effects of Short-Run Operational Changes
    1. Many decisions are made on the basis of incremental analysis, which encompasses the concept of relevant costing, which allows managers to focus on pertinent facts and disregard extraneous data.
    2. While relevant costing decisions are often viewed by managers as short-run, each decision also has vital long-run implications.
  1. The Concepts of Relevance and Relevant Costing
    1. Relevant costs are costs that are pertinent to or logically associated with a specific problem or decision and that differ between alternatives.
    2. Two prevailing rules for short-run decision making are that
    1. most variable costs are treated as relevant and
    2. most fixed costs are not.
    1. Relevant costing is a process that allows managers to focus on pertinent facts and disregard extraneous information by comparing, to the extent possible and practical, the differential, incremental revenues and incremental costs of alternative decisions.
    2. Relevant information supports decision making, and information is relevant when it is logically related to the decision.
    3. Incremental revenue is the additional revenue resulting form a contemplated sale of a quantity of output.
    4. Incremental cost is the additional cost of producing or selling a contemplated quantity of output.
    5. Opportunity cost represents the benefit foregone when one course of action is chosen over another.
    6. The difference between the incremental revenue and incremental costs of a particular alternative is the positive or negative incremental benefit of that course of action.
    7. Management can compare the incremental benefits of various alternatives to decide on the most profitable or least costly alternative or set of alternatives.
    8. Sunk costs are the historical or past cost that is associated with the acquisition of an asset or a resource and that have no future recovery value.

  1. Relevant Costs in Scarce Resource Decisions
    1. A scarce resource is an item that is essential to production activity but that is available only in a limited quantity.
    2. Scarce resources create constraints on producing goods or providing services and can include money, machine hours, skilled labor hours, raw materials, and production capacity.
    3. Management may desire and be able to obtain a greater abundance of a scarce resource in the long run, but management must make the best current use of the scarce resources it has in the short run.
    4. The determination of the best use of a scarce resource requires that specific company objectives be recognized.
    5. The outcome of a scarce resource decision will always indicate that a single type of product should be manufactured and sold when one limiting factor is involved.
    6. One method of solving problems that have several limiting factors is linear programming, which finds the optimal allocation of scarce resources when there is one objective and multiple restrictions on achieving that objective.
    7. Company management must consider qualitative aspects of the problem in addition to the quantitative ones.
  1. Relevant Costs in Sales Mix and Sales Price Decisions
    1. Sales mix is the relative combination of quantities of sales of the various products that make up the total sales of a company.
    2. Some important factors that affect the appropriate sales mix are (1) product selling prices and (2) advertising expenditures. A change in one or both of these factors may cause a company’s sales mix to shift.
    3. Managers must constantly monitor the relative selling prices of company products, both in respect to each other as well as to competitor’s prices.
    4. Total contribution margin must be maximized in order to maximize profit.
    1. Unit contribution margin and sales volume should be evaluated together when profitability is assessed.
    2. The sales volume of a product or service is normally directly related to its selling price. When the selling price is increased and demand is elastic with respect to price, demand for the product or service decreases.
    1. In deciding to raise or lower prices, the relevant quantitative factors include:
    1. prospective or new contribution margin per unit of product;
    2. both short-term and long-term changes in product demand and production volume caused by the price increase or decrease; and
    3. best use of any scarce resources.
    1. Relevant qualitative factors that are related to price change decisions are:
    1. influence on customer goodwill;
    2. customer product loyalty; and
    3. competitor’s reactions.
    1. Special order pricing is the process of setting a sales price for manufacturing or service jobs that are outside the company’s normal production or service realm.
  1. Relevant Costs in Product Line Decisions
    1. Operating results of multiproduct environments are frequently presented in a format that indicates separate product lines in order to expedite performance evaluations.
    2. Managers, in reviewing such disaggregated statements, must distinguish relevant from irrelevant information in a manner that relates to the individual product lines.
    3. A common cost is a cost that cannot be associated with a particular cost object and is incurred because of general production activity.
    4. Product margin represents the excess of a product’s revenues over both its direct variable expenses and any avoidable fixed expenses related to the product.
    1. It is the amount remaining to cover unavoidable direct fixed

      expenses and common costs and then to provide profits.

    2. The product margin is the appropriate figure on which to base continuation or elimination decisions since it measures the segment’s contribution to the coverage of indirect and unavoidable costs.
  1. Graphic Approaches to Breakeven Analysis – Appendix 1
    1. A breakeven graph is a graphical depiction of the relationships among revenues, variable costs, fixed costs, and profits (or losses). (See text Exhibit 6-15)
    2. The following steps are required in preparing a breakeven graph.
    1. Label the x-axis as volume and the y-axis as dollars.
    2. Plot the variable cost line with a slope equal to total per-unit variable cost.
    3. Plot the revenue line with its slope equal to the unit sales price.
    4. To graph total cost, add a line parallel to the total variable cost line.
    5. The breakeven point is located where the revenue and total cost lines intersect.
    1. The format of the breakeven graph allows the following important observations to be made.
    1. Contribution margin is created by the excess of revenues over variable costs. If variable costs are greater than revenues, no quantity of volume will ever allow a profit to be made.
    2. Total contribution margin is always equal to total fixed cost plus profit or minus loss.
    3. Contribution margin must exceed fixed costs before profits can be generated.
    1. The profit-volume (PV) graph is a graphical presentation of the profit or loss associated with each level of sales.
    1. The horizontal axis on the PV graph represents unit sales volume and the vertical axis represents dollars.
    2. Amounts shown above the horizontal axis are positive and represent profits, while amounts below the horizontal axis are negative and represent losses.
  1. An Overview of Absorption and Variable Costing – Appendix 2
    1. Absorption costing is a cost accumulation method that treats the costs of all manufacturing components (direct materials, direct labor, variable overhead, and fixed overhead) as inventoriable, or product, costs; also known as full costing. (See text Exhibit 6-17)
    1. Total variable product costs increase with each additional product made or service rendered, and are therefore considered to be product costs and are inventoried until the product or service is sold.
    2. Fixed overhead does not vary with units of production or level of service; it provides the manufacturing capacity necessary for production to occur. Production could not take place without the incurrence of fixed overhead, so fixed overhead is considered to be inventoriable under absorption costing.
    3. Absorption costing presents expenses on an income statement according to their functional classification. A functional classification is a grouping of costs incurred for the same basic purpose.
    1. Variable costing is a cost accumulation method that includes only variable production costs (direct materials, direct labor, and variable overhead) as product or inventoriable costs and treats fixed overhead as a period cost; also known as direct costing. (See text Exhibit 6-18)
    1. A variable costing income statement or management report separates costs by cost behavior, although it may present expenses by functional classification within the behavioral categories.
    2. Cost of goods sold is more appropriately called variable cost of goods sold since it is composed of only the variable production costs related to the units sold.
    3. Product contribution margin is revenue minus variable cost of goods sold.
    4. Total contribution margin is revenue minus all variable costs regardless of the area (production or nonproduction) of incurrence.
    5. The accounting profession has unofficially disallowed the use of variable costing as a generally accepted inventory valuation method for external reporting purposes.
  1. Linear Programming – Appendix 3
    1. Linear programming (LP) is a method used to solve problems with one objective and multiple limiting factors; it determines the optimal allocation of scarce resources when the objective and the restrictions on achieving that objective can be stated as linear equations.
    2. The objective function is the mathematical equation that states the maximization or minimization goal of a linear programming problem.
    3. A constraint is a restriction on the ability to reach an objective.
    4. A feasible solution is an answer to a linear programming problem that does not violate any of the problem constraints.
    5. The optimal solution is the solution to a linear programming problem that provides the best answer to the allocation problem without violating any problem constraints.
    6. Simplex is an iterative technique used to solve multivariable, multiconstraint linear programming problems; usually requires the aid of a computer.


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