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# Cost Volume Analysis

2943 words - 12 pages

Lecture 5: Cost-Volume-Profit Analysis
In this module, we are going to discuss a simple concept yet a powerful financial planning and decision-making tool for managers. This concept is called CVP analysis or cost volume profit relationship. Profits are the difference between revenues and costs. Both revenue and cost depend on the volume of operations. So, in the short run whether you make a profit or a loss depends upon the volume of sales you make. What is the unknown for a manager when he or she tries to project profits for future? The managers know the costs and the selling price. So the only unknown is the volume of sales. The importance of CVP analysis flows from the fact ...view middle of the document...

We call ‘N’ as the activity volume in the sense that you need to do more activities if you are selling more u nits compared to selling less. The activity volume can be represented as the number of units sold, or sales revenue dollars or some measure of service quantity. For example, the activity level for a hospital is number of patient days and the activity level for an airline company is number of passenger miles. Depending upon how you measure the activity level, P and V are defined in accordance with the measure of activity. For example, for an airlines company that measures activity volume as the number of passenger miles, P is the price charged per passenger mile and V is the variable cost per passenger mile. The fixed costs, F is the sum of all costs in the organization that do not change with respect to the chosen activity measure. Let us now write out an expression for the profits of the firm. We know profits = Revenue – Costs. We can rewrite this as Profits = Revenue – Variable costs – Fixed costs. Given our notation, Profits = (NP) – (NV) – F = N (P-V) – F. Realize that P - V is the difference between revenue and cost per unit and we had earlier defined this as Unit Contribution Margin (UCM). The profit equation becomes Profits = N UCM – F. This approach of characterizing the firm profits as a function of UCM is called “UCM approach”. Alternatively, we could have characterized the profits as a function of (Contribution margin ratio) CMR and such characterization of profits is called “CMR approach”. What is Contribution Margin Ratio? CMR equals UCM divided by Revenue per unit. In other words, CMR represents the fraction of every sales dollar that turns into contribution. In order to characterize the profits of a firm as a function of CMR, take the profit equation that we developed earlier and multiply the right hand side of the equation by P/P. Since P/P is 1, the profit equation is still valid. We can rewrite the right hand side of the profit equation as (N × P) × (P-V)/P – F. Notice that (N × P) represents the total revenue generated and (P-V)/P is the CMR. Therefore, profits = Revenue × CMR – F. This version of the profit equation is called “CMR approach of characterizing the firm profits”.
Breakeven volume is defined as the level of sales at which revenue equals all costs and therefore the firm makes neither a profit nor a loss at the breakeven level. We can use the profit equation that we had developed earlier to find out the breakeven level. Substitute zero for profits in the profit equation that we had derived using the UCM approach. This leads to the following expression. 0 = NBEV × (P-V) – F where NBEV is the number of units to be sold for the firm to breakeven NBEV = F/(P-V). In other words, fixed costs divided by UCM will give the breakeven volume in number of units. We can convert the breakeven volume expressed in number of units to breakeven volume in sales dollars. In order to do this,...

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