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CVP problems

# CVP problems - TECHNIQUES FOR SOLVING CVP PROBLEMS The...

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TECHNIQUES FOR SOLVING CVP PROBLEMS The following symbols are used below to illustrate the various techniques used in cost-volume-profit analysis. P = Sales price. V = Variable costs per unit. Note: This is not inventory cost because it includes both variable manufacturing costs as well as variable selling and administrative expenses. X = The number of units produced and sold. A unit is a common way to describe an output, but an output may be expressed in pounds, gallons, board feet, cubic feet, etc. TR = S = Total revenue, or sales dollars. TVC = Total variable costs = VX TFC = Total fixed costs. TC = Total costs = TFC + TVC. P-V = Contribution margin per unit. This is the amount of sales revenue that each unit provides towards covering the fixed costs and providing a profit, i.e., what's left over after the variable costs associated with the unit have been covered. TCM = Total contribution margin = (P-V)(X). CMR = (P-V)÷P = (TR-TVC)÷TR = (PX-VX)÷PX = 1-(V÷P). These are just different ways to define the contribution margin ratio. They all work because the functions are linear. There are many algebraic equations illustrated on the next several pages that may appear to require memorization. However, every equation is simply a variation of the following basic concepts: Total Revenue = Total Cost + Profit TR = TC + NIBT TR = TFC + TVC + NIBT TR - TVC = TFC + NIBT TCM = TFC + NIBT Total revenue, or sales dollars, less total variable costs equals total contribution margin. Contribution margin is the revenue over and above the variable costs that contributes towards covering the fixed costs and also towards providing a profit after the fixed costs have been covered. Practically any cost-volume-profit problem can be solved with the last equation stated above and an understanding of the concepts involved. SOLVING SINGLE PRODUCT CVP PROBLEMS IN UNITS A summary of the cost volume profit equations for single product problems is presented in Exhibit 11-1. All five equations are variations of the basic conceptual equation stated above. To reinforce the concept, each equation is developed and illustrated below.

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EXHIBIT 11-1 SUMMARY EQUATIONS FOR SOLVING SINGLE PRODUCT CVP PROBLEMS IN UNITS NUMBER EQUATION USED TO DETERMINE [1] (P-V)X = TFC Units needed to break-even. [2] (P-V)X = TFC + NIBT Units needed to generate a target net income before taxes. [3] (P-V)X = TFC + [NIAT ÷ (1-T)] Units needed to generate a target net income after taxes. [4] (P-V)X = TFC + (R)(PX) Units needed to generate a target NIBT stated as a proportion (R) of sales dollars (PX). [5] (P-V)X = TFC + [(R)(PX) ÷ (1-T)] Units needed to generate a target NIAT stated as a proportion (R) of sales dollars (PX). UNITS NEEDED TO BREAK-EVEN
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CVP problems - TECHNIQUES FOR SOLVING CVP PROBLEMS The...

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