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# Cost volume profit analysis

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### Cost volume profit analysis

1. 1. Profit is a monetary gain a business produce after saleing products .a profit analysis is abreak down of a business applying a monetaryamount for each element and performingcalculations to determine what profit is .In the business world profit analysis most often referred to as cost volume profit (CVP) analysis.
2. 2. in managerial economics is a form of cost accounting . It is a simplified model, useful forelementary instruction and for short-rundecisions.It is a technique that examines changes in profits in response to changes in sales volumes,costs, and prices. Accountants often performanalysis to plan future levels of operating CVPactivity and provide information about:
3. 3. 1- Which products or services to emphasize 2- The volume of sales needed to achieve a targeted level of profit3- The amount of revenue required to avoid losses4- Whether to increase fixed costs 5- How much to budget for discretionary expenditures 6-Whether fixed costs expose the organization to an unacceptable level of risk
4. 4. CVP analysis begins with the basic profit  equation .Profit = Total revenue - Total costs  Separating costs into variable and fixed categories, we express profit as:  Profit = Total revenue - Total variable costs -  Total fixed costs
5. 5. The contribution margin is total revenue minus total variable costs. Similarly, the contribution margin per unit is the sellingprice per unit minus the variable cost per unit.Both contribution margin and contributionmargin per unit are valuable tools whenconsidering the effects of volume on profit
6. 6. Contribution margin per unit tells us how much revenue from each unit sold can betoward fixed costs appliedOnce enough units have been sold to cover all fixed costs, then the contribution margin per unit from all remaining sales becomes profit.If we assume that the selling price and variable cost per unit are constant, then total revenue
7. 7. is equal to price times quantity, and total variable cost is variable cost per unit times quantityWe then rewrite the profit equation of the contribution margin per unit Profit = P * Q - V * Q - F = (P - V ) * Q - F where P Selling price per unit V Variable cost per unit (P - V ) Contribution margin per unit Q Quantity of product sold (units of goods or services)F Total fixed costs 
8. 8. We use the profit equation to plan for different volume of operation CVP analysis can be performed using either : 1- Units (quantity) of product sold  2- Revenues (in dollars) CVP Analysis in Units We begin with the preceding profit equation. Assuming that fixed costs remain constant, wesolve for the expected quantity of goods or services must be sold to achieve a target level of profit
9. 9. CVP analysis employs the same basic assumptions as in breakeven analysis. Theassumptions underlying CVP analysis are:The behavior of both costs and revenues is linear throughout the relevant range of activity.(This assumption precludes the concept ofvolume discounts on either purchasedmaterials or sales.)
10. 10. cost can be classified accurately as either fixed or variable.Costs Changes in activity are the only factors that affect costs.All units produced are sold (there is no ending finished goods inventory).When a company sells more than one type of product, the sales mix (the ratio of eachproduct to total sales) will remain constant
11. 11. The components of CVP analysis are: Level or volume of activity Unit selling prices Variable cost per unit Total fixed costs Sales mix 
12. 12. CVP assumes the following: Constant sales price; Constant variable cost per unit; Constant total fixed cost; Constant sales mix; Units sold equal units produced. . 
13. 13. These are simplifying, largely linearizing, which are often implicitly assumed inelementary discussions of costs and profits. Inmore advanced treatments and practice, costsand revenue are nonlinear and the analysis ismore complicated, but the intuition afforded bylinear CVP remains basic and useful.
14. 14. One of the main methods of calculating CVP is profit–volume ratio: which is (contribution/sales)*100 = this gives us profit–volume ratio.contribution stands for sales minus variable costs.Therefore it gives us the profit added per unit of variable costs
15. 15. Basic graph of CVP, demonstrating relation of total costs, sales, and profit and lossThe assumptions of the CVP model yield the following linear equations for total cost and totalrevenue (sales):These are linear because of the assumptions of constant costs and prices, and there is nodistinction between units produced and units sold,as these are assumed to be equal. Note that whensuch a chart is drawn, the linear CVP model isassumed, often implicitly.In symbols: 
16. 16. TC=TFC+V.X TR=B.X where TC = Total costs TFC = Total fixed costs V = Unit variable cost (variable cost per unit) X = Number of units TR = S = Total revenue = Sales P = (Unit) sales price Profit is computed as TR-TC; it is a profit if positive, a loss if negative.
17. 17. Costs and sales can be broken down, which provide further insight into operations.Decomposing total cost as fixed cost plus variable cost.Decomposing sales as contribution plus variable costs
18. 18. Following a matching principles of matching a portion of sales against variable costs, one candecompose sales as contribution plus variablecosts, where contribution is "whats left afterdeducting variable costs". One can think ofcontribution as "the marginal contribution of aunit to the profit", or "contribution towardsoffsetting fixed costs".In symbols: 
19. 19. where C = Unit Contribution (Margin) Profit and loss as contribution minus fixed costsSubtracting variable costs from both costs and sales yields the simplified diagram andequation for profit and loss.Diagram relating all quantities in CVP. These diagrams can be related by a rather busydiagram, which demonstrates how if onesubtracts variable costs, the sales and total costs
20. 20. lines shift down to become the contribution and fixed costs lines. Note that the profit andloss for any given number of unit sales is thesame, and in particular the break-even point isthe same, whether one computes by sales =total costs or as contribution = fixed costs.Mathematically, the contribution graph isobtained from the sales graph by a shear, to beprecise , where V are unit variable costs.