appendixa - A1 A. APPENDIX A Linear Applications A.1...

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A1 A PPENDIX A Linear Applications A.1 Cost-volume-profit Analysis A. Cost-volume-profit relationships In our discussion of break-even analysis in Chapter 5, we used graphs to show the relationship between revenue and costs at different levels of output. We intro- duced the formulae that are used in cost-volume-profit analysis. We will begin this appendix by presenting the formulae from Chapter 5 in mathematical notation. The following components are basic to cost-volume-profit relationships. The mathematical notations shown below will be used for these components through- out this appendix. X 5 Volume of output P 5 Selling price (revenue) per unit of output TR 5 Total revenue TC 5 Total cost FC 5 Fixed cost TVC 5 Total variable cost VC 5 Variable cost per unit of output NI 5 Net income (profit) Recall that fixed costs are those costs that remain constant over the time period considered for all levels of output. Variable costs are those costs that are constant per unit of output regardless of volume. Variable costs fluctuate in total amount as volume fluctuates. The accounting relationship (income statement equation) is basic to cost-vol- ume-profit analysis. —————————————— Formula A.1 The following relationships are also useful. —————————————— Formula A.2 TR 5 (X)(P) TOTAL REVENUE 5 VOLUME 3 UNIT REVENUE TR 5 1 NI TOTAL REVENUE 5 TOTAL COST 1 NET INCOME
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————————————— Formula A.3 ————————————— Formula A.4 ——————————— Formula A.5 B. Algebraic analysis of cost-volume-profit relationships Recall from Chapter 5 that break-even analysis is a method of determining the level of output at which a business neither makes a profit nor sustains a loss. The break-even point is the level of output at which net income is zero. On a break- even chart , total revenues and total costs are shown for different levels of output. The point at which the total revenue line crosses the total costs line is the break- even point, since this is the level of output where no profit or loss is made. (See Chapter 5, page 206 for an example of a break-even chart.) Break-even analysis focusses on one particular level of operations. However, the accounting relationship TR 5 FC 1 TVC 1 NI ———————— Formula A.5 can be used to extend cost-volume-profit analysis to any desired level of opera- tions. It is possible to determine the net income at any level of operations and to analyze what effect changes in selling price, fixed cost, or variable costs have on profitability at any level of operations. EXAMPLE A.1A Market research for a new product indicates that the product can be sold at $50.00 per unit. Cost analysis provides the following information.
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This note was uploaded on 08/22/2009 for the course MATH 1101 taught by Professor Tonycirusolo during the Fall '05 term at Niagara College.

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appendixa - A1 A. APPENDIX A Linear Applications A.1...

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