Break even point problems and solutions pdf

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Break even point problems and solutions pdf

Here is a collection of top eight problems on break-even analysis with their relevant solutions. Break-Even Analysis: Problem with Solution #1. From the following information, calculate: (i) Break-even points in terms of sales value and in units. (ii) The number of units that must be sold to earn a profit of Rs. 90,000.Solution: Break-Even Analysis: Problem with Solution #2. From the following data, you must calculate: (a) P/V ratio(b) Break-even sales using P/V ratio. (c) Sales required to earn a profit of Rs. 4,50,000Fixed Expenses = Rs. 90,000Variable Cost per unit: Direct Material = Rs. 5Direct Labour = Rs. 2Direct Overhead = 100% of Direct LabourSelling Price per Unit = Rs. 12.Solution: Break-Even Analysis: Problem with Solution #3. From the following data, you are required to calculate the break-even point and net sales value at this point: If the sale is 10% and 25% above the pausek and even volume, determine the net profit. Solution: Break-Even Analysis: Problem with Solution #4. From the following information, find out break-even-point: What should be the sale price per unit, if the break-even point should be brought down to 6,000 units? Solution: Break-Even Analysis: Problem with Solution #5. The fixed costs amount to Rs. 50 000, and the percentage of variable costs of sale is given to be 66 2/3%. If 100% capacity sales are Rs. 3 00 000, you can find out the break-even point and percentage sales when it occurred. Determine profit of 80% capacity:Solution: Break-Even Analysis: Problem with solution #6. From the following information, determine how much the value of sales must be increased by the company to break-even: Solution: Break-Even Analysis: Problem with Solution #7. Calculate: (i) The amount of fixed expenses. (ii) Number of units to break-even. (iii) The number of units to make a profit of Rs. 40,000.The sale price per unit can be assumed at Rs. 100.The Company sold in two consecutive periods 7,000 units and 9,000 units and has incurred a loss of Rs. 10,000 and earned Rs. 10,000 as profit respectively. Solution: Break-Even Analysis: Problem with Solution #8. A company makes a loss of Rs. 40,000 and relevant information is as follows: Sales Rs. 1,20,000; Variable costs Rs. 60 000; Fixed costs Rs. 1,00,000.Loss can be done well either by increasing the sales price or by increasing the sales volume. What is Break self sales if (a) Current sales level is maintained and the sales price is increased. (b) If the current sales price is maintained and the sales volume is increased. What would be sales if a profit of Rs. 1,00,000 is required? Solution: This article provides an overview of Break Even Analysis:- 1. The meaning of Break-Even Analysis 2. Prerequisites for break-even analysis 3. Break Even Point 4. Types of break-even point 5. Graphic method 6. Prerequisites Underlying break-even charts 7. Benefits of Break-Even Charts 8. Limitations of Break-Even Charts 9. Safety margin 10. Angle of the 11th of the Result volume 12. Curvilinear.Contents: The meaning of breakeven analysisAssumptions of Break-Even AnalysisBreak Even PointTypes of Break-Even PointGraphic Method of Break-Even AnalysisAssumptions Underlying Break-Even ChartsAdvantages of Break-Even ChartsLimitations of Break-Even ChartsMargin of SafetyAngle of Incidence of SafetyAngleVolume GraphCurvilinear Break-Even Analysis (Two Break-Even Points) 1. Meaning of Break-Even Analysis: The study of cost volume profit analysis is often referred to as break-even analysis and the two terms are used interchangeably by many. This is so, because break-even analysis is the most wellknown form of cost-volume-profit analysis. The term break-even analysis is used in two senses - narrow sense and broad sense. In its broad sense, break-even analysis refers to the study of the relationship between cost, volume and profit at different levels of sales or production. In its narrow sense, it refers to a technique for determining the level of operation at which total revenue corresponds to total expenses, that is, the point of no profit, no loss. 2. Prerequisites for break-even analysis: The break-even analysis is based on the following assumptions: (i) All elements of costs, that is, production, administration and sales and distribution can be segregated into fixed and variable components. (ii) Variable costs remain constant per production unit regardless of the output level and thus fluctuate directly in relation to changes in production volume. (iii) Fixed costs remain constant at all production volumes. (iv) Unit price per unit remains unchanged or constant at all levels of production. (v) Production volume is the only factor affecting costs. (vi) There will be no change in the overall price level. (vii) There is only one product or in the case of multi-products, the sales mix remains unchanged. (viii) There is synchronization between production and sales. 3. Break Even Point: The break-even point can be defined as the sales volume where total revenue equals total costs. It's a point of no profit, no losses. A business is said to break even when the total sales are equal to the total cost. The break-even point refers to the level of production that uniformly breaks costs and revenue and thus the name. At this point is contributions, it will want sales minus marginal costs equal to the fixed costs, and thus this point is often called as Critical Point or Equilibrium Point or Balancing Point or no profit, no loss. If production/sales are increased beyond this level, there should be profits for the organization, and if it is reduced from this level, there shall be losses for the organization. Break-even point can be specified in the form of an equation: Sales revenue at break-even point = fixed costs + variable costs. Breakeven point calculation: Break-even point can be calculated using the following methods: (i) The algebraic formula method (ii) Graphic or Diagram Method.Algebraic Method for Beregning av Break-Even Point: The Algebraic Formula Method(ii) Graphic or Chart Method.Algebraic Formula Method for Computing the Break-Even Point: The Algebraic Formula Method(ii) Graphic or Chart Method.Algebraic Formula Method for Computing the Break-Even Point: The Algebraic Formula Method(ii) Graphic or Chart Method.Algebraic Formula Method for Computing the Break-Even Point: The Algebraic Formula Method(ii) Graphic or Chart Method.Algebraic Formula Method for Computing the Break-Even Point : The Algebraic Formula Method(ii) Graphic or Chart Method.Algebraic Formula Method for Computing the Break-Even Point: The Algebraic Formula Method(ii) Graphic or Chart Method.Algebraic Formula Method for Computing Computing point can be calculated in the form of: (a) Sales Units. (b) Budget total or in the form of monetary value. (c) As a percentage of estimated capacity. (a) Break-Even Point in Units: As break-even point, the point of no profit is no loss, It is the level of output where the total contribution corresponds to the total fixed costs, It can be calculated using the following formula: (b) Break-even Point in terms of budget-total or monetary value: (c) Break-even Point as a percentage of estimated capacity: Break-even point can also be calculated as a percentage of estimated sales or capacity by splitting break-even sales of capacity sales. For example, if a company has an estimated capacity of 1,00,000 units of products and the break-even point is reached at 50,000 units, the break-even point is 50% of the capacity (1,00,000/50,000). If there is information about total contributions at full capacity, the break-even point exists as a percentage of estimated capacity as below: B.E.P (as % capacity age) = Fixed cost/total contributionIllustration 1: From the following information, calculate break-even point in units and in value: Output = 3000 unitsSelling price per unit = Rs. 30Variable cost per unit = Rs. 20Total fixed cost = Rs. 20.000Solution: 4. Types of Break-Even Point:(i) Cash Break-Even Point: In today's competitive world of business, it can be difficult for new industrial units to achieve break-even point in the first few years. Thus, the concept of cash break-even point has appeared. The cash break point can be defined as the sales volume where the total revenue equals total cash costs. At this point, cash contributions (which are calculated after adjustment for the variable part of the depreciation, etc.) are the cash fixed cost, it will result in fixed costs excluding depreciation and deferred costs. This point allows management to determine the level of activity below which liquidity position of the company will be negatively affected. Thus, cash break-even points can be calculated as below: Cash Break- Even Point (in units) = Cash Fixed Cost / Cash Contribution per unitIllustration 2: From the following information, calculate cash Break-Even Point: Solution:(ii) Composite Break-Even Point: So far we have processed break-even point of companies producing single product. We can also calculate the compound break-even point for a company that produces multiple products, as below: Composite Break-Even Point (in sales value) = Total fixed cost / composite P / V Ratioand, Composite P/V ratio = Total contribution/total sales ? 100Illustration 3: From the following information about a company producing three products, you must calculate:(a) Composite P/V Ratio and(b) Composite Break-Even Point.Fixed cost: Rs. 50,000.Solution: 5. Graphical method of break-even analysis: Break-even point can also be calculated graphically. A break-even chart is a graphical representation of marginal costings. Break-even 'Depicts a pictorial view of the relationship between cost, volume and profit.'It shows break-even point and also indicates estimated profits or losses at different levels of production. The break-even point as specified in the chart is the point at which the total cost line and the total sales line intersect. There are three methods to draw a break-even chart. These methods of drawing break-even chart have been explained using the following illustration. Figure 4: Draw the following data on a chart (break-even chart) and determine: (a) Break-even point(b) Profit if the output is 25,000 units. Solution: First method: Under this method, the following steps are taken to draw the break-even chart:i. Volume of production/output or sales is plotted on horizontal axis, that will the X-axis. The volume of sales or production can be expressed in the form of rupees, units or as a percentage of capacity.ii. Costs and sales revenue are represented on the vertical axis, that is, said Yaxis.iii. Fixed cost line is drawn parallel to the X axis. The line indicates that fixed expenses remain constant at all task levels.iv. The variable costs for different task levels are drawn above the fixed cost line. The variable cost line is appended to the fixed cost line at the zero task level. As the variable cost line is drawn over the fixed cost line, it represents the total cost at different levels of output/sales.v. Sales values at different output levels are plotted, and a line is drawn along with these plotted points. This line is called the Sales file (line.vi. The intersection of total cost line and sales line (revenue) is called break-even point.vii. The number of units to be produced at break-even points can be determined by drawing a perpendicular to the X-axis from the intersection of cost and sales line.viii. Sales revenue at break-even point can be determined by drawing a perpendicular to the X-axis from the point between cross-section of cost and sales line.ix. The area below the break-even point represents the loss area as the total sales and less than the total cost, and the area above the break-even point indicates the profit range for which sales revenue exceeds the total cost. Second method: Break-even chart can also be drawn by another method that is a variant of the first method. Under this method, the variable cost line is drawn first, and then the fixed cost line is pulled over and parallel to the le variable cost line. The fixed cost line, then deducted, represents the total cost (Variable + Fixed) at different levels of output because it is pulled over the variable cost line. This method is useful for decision-making management because it reveals additional information: (a) The variable costs are displayed directly for different levels of production/sales. (b) Marginal contribution at different sales levels is clearly indicated by the difference between sales line and variable cost line. (c) It indicates the recovery of fixed costs production levels. A small variant of this method is to show the various elements of fixed and variable costs, such as large cost elements such as direct material costs, labor costs, variable factory cost, variable sale of indirect costs, and fixed costs. Third method ? Contribution Violation Chart: This is a modified form of a single break-even chart as shown in the first two methods above. Under this method, the total cost line is not drawn, but another line called contribution line is taken from its origin, and this line goes up with the increase in the output level. The fixed cost line is drawn in parallel with the x-axis as in the first method. The sales line is also drawn as usual. In this method, the question about the intersection of sales line with the total cost line does not occur because there is no cost line. The break-even point is the point where the contribution line crosses the fixed cost line. At this time, the total contribution is equal to the total fixed cost, and thus there is no profit or loss. As the contribution increases more than the fixed costs, profits shall arise for the organization, and as the contribution decreases from the fixed costs, there shall be losses for the organization. The deposit break chart clearly shows contributions at different activity levels and indicates that all levels below the break-even point cannot cover the fixed costs. In the example above, on the level of production/sales of 25,000 units, there is a profit of Rs. 50,000 as indicated by break-even charts under the three methods. 6. Prerequisites Underlying break-even charts: There are a number of prerequisites that are made while drawing a break-even chart, such as: (i) All costs can be divided into fixed and variable costs. (ii) Fixed costs remain constant at all activity levels. (iii) Variable costs fluctuate directly in relation to changes in production volume. (iv) Sales prices per unit remain constant at all activity levels. (v) There is no opening or closing stock. (vi) There will be no change in operational efficiency. (vii) The product mix remains unchanged or there is only one product. (viii) The volume of production or production is the only factor affecting costs. 7. Benefits of Break-Even Charts: Calculation of break-even point or presentation of cost, volume and profit ratio using break-even charts has the following advantages: i. Information provided by the break-even chart is in a simple form and is clearly understandable even for a layman. The whole idea of the problem is presented in an instant.ii. The break-even chart is very useful for management to make management decisions because the chart studies the relationship between cost, volume and profit at different levels of production. The effect of changes in fixed costs and variables costs at different levels of production and that of changes in the sales price of the profit can very clearly using break-even charts.iii. Break-even charts charts to know and analyze the profitability of different products under different circumstances.iv. A break-even chart is very useful for forecasts (costs and profits), planning and growth.v. The Break-even chart is a management tool for controlling costs as it shows the relative importance of fixed costs in the total cost of a product.vi.

Besides determining the break-even point, profits at different levels of production can also be determined using break-even charts.vii. The break-even charts can also be used to study the comparative plant effectiveness of business. 8. Limitations of Break-Even Charts: Despite many advantages, a breakeven chart suffers of the following limitations: in. A break-even chart is based on a number of assumptions, discussed above, that may not hold well in all circumstances. For example, fixed costs do not remain constant after a certain level of activity. variable costs do not always vary in direct relation to changes in production volume due to the laws of decreasing and increasing returns; sales prices do not remain the same forever and for all levels of production due to competition and changes in the overall price level; etc.ii. A break-even chart provides only a limited information. We need to draw a series of charts to study the impact of changes in fixed costs, variable costs and sales prices on profitability. In such cases, it becomes rather more complicated and difficult to understand.iii. Break-even charts present only cost-volume profit relationships, but ignore other important considerations such as the amount of capital investments, marketing issues and government policy, etc.iv. A break-even chart suggests no action or remedies to management as a tool for management decisions.v. More often, a break-even chart presents only a static view of the problem under consideration. The excess of actual or budgeted sales over break-even sales is known as the safety margin. That's the difference between actual sales minus sales at break-even point. It represents the amount that sales revenue may fall after before a loss is incurred. As at the break-even point there is no profit no loss, sales beyond the breakeven point represent margin of certainty because any sale over break-even point will make some profit. Thus, Margin of Safety = Total Sales - Sales at Break-Even Point.Say, actual current sales are Rs. 5,00,000 and break-even sales are Rs. 4,00,000, then the safety margin is equal to Rs. 1,00,000, that is, 5,00,000 - 4,00,000.Margin of Safety can also be expressed as a percentage. For example, if a company can break even with 60 percent of expected sales; then it has a safety margin of (100-60) 40 percent. In the previous example, the percentage safety margin can be calculated as 1,000,000/5,000,000 ? 100 = 20% safety margin calculated as a percentage, is also called safety margin and can be expressed as:M.S. Ratio =M.S./Sales ? 100= ? Sales on B. E. P./Sales ? 100 Margin of security can also be calculated using the following formula: Margin of Safety (M/S) = Profit/P/V RatioThis is so because margin of security is the volume of sales beyond break-even point and all sales above break-even point give some profit, which can be calculated as:Profit = Safety margin ? P/V ratioor M.S.= Profit/P/V RatioThe size of the safety margin is an important indicator of the strength of a business. The large safety margin indicates that the business is good, and even if there is a significant fall in sales, there will still be some profit. On the other hand, a small margin of safety indicates that the position of the business is relatively weak, and even a slight decrease in sales will negatively affect the company's profits and can lead to losses. The safety margin can be improved by taking the following steps: i. By increasing production levels in 2014. By increasing the selling price. By reducing the fixed costiv. By reducing the variable costv. By replacing unprofitable products with profitable productswe. By increasing the contribution by changing the sales mix or by releasing unprofitable products. The angle of the instance is the angle between the sales line and the total cost line that is formed at the break-even point where the sales line and the total cost line intersect. The angle of the occurrence indicates the profit earning capacity of a business. A large instance angle indicates a high profit, and on the other hand, a small instance angle indicates a low profit. Typically, the angle of the instance and the safety margin are assessed together to indicate the sound of a business. A large instance angle with a high safety margin indicates the most favorable position of a business. Profit-volume graph is a pictorial representation of the profit-volume ratio. This graph shows results at different sales volumes. It is said to be a simplified form of break-even chart as it clearly represents the ratio of profit to volume of sales. A profit volume graph also called P/V graph or profit graph can be constructed from any data related to a business for which a break-even chart can be drawn. The result volume graph may be preferred to a break-even chart because profits or losses can be read directly at different activity levels. But the basic limitation of a P/V graph is that it does not show how costs vary with the change in activity level. For this reason, the break-even chart and profit-volume graph should both be pulled together to derive the maximum benefit of both. The construction of a profit-volume graph involves the following steps: i. Sales line (in volume or value) is drawn on horizontal or x-axis.ii. Profits and losses are given on vertical or y-axis.iii. The area above the horizontal of the x-axis is called the profit area, and the area below the horizontal axis is the loss area.iv. Profits and at different activity levels are plotted against corresponding sales, and then those points are merged and expanded. This line is called profit line. In more than one product, a separate profit line for each product should be deducted. The point at which the profit line crosses with the sales line is the break-even point. Figure 5: Prepare a P/V graph from the following data: Show expected sales in the chart when the profit to be earned is Rs. 87 500.Solution: Arithmetic Verification: Sales (in units) = Fixed expenses + Profit/ Contributions per unit = 1.50.000 + 87,500/5 = 2,37,500/5 = 47,500 units ... Sales = = 47,500 units @ Rs. 15 = Rs. 7,12,500Illustration 6: The following figures apply to one-year work at the 100 percent capacity level in a production business: Fixed indirect costs - Rs. 1.20.000Variable indirect costs ? Rs. 2.00.000Direct pay ? Rs. 1.50.000Direct materials ? Rs. 4.10.000Sales ? Rs. 10.00.000Represent the above figures on a break-even chart and determine from the break-even point chart. Confirm the result by calculations: Solution: Arithmetic confirmation: Contributions = Sales ? Marginal costs= Rs. 10.00.000 ? Rs. 7.60.000= Rs. 2.40.000P/V Ratio = Contributions/Sales2.40.000/10.00.000 = 24/100 or 24%. Break-Even Point = Fixed Expenses / P/V Ratio = 1,20,000/24/100 = 1,20,000 ? 100/24 = Rs. 5,00,000At Rs. 10,00,000 sales, 100% capacity has been reached ... At Rs. 5,00,000 sales, 50% capacity is reachedHence, break-even point is reached at a 50% capacity utilization. Figure 7: You get the following data for the coming year of a factory: Draw a break-even chart showing break-even points. If the sale price is reduced to Rs. 18 per unit, what will be the new break-even point? Solution: Illustration 8: AB Ltd. and XY Ltd. expect sales of Rs. 25 00 000 10% of this is expected to be profits if each achieves 100% of normal capacity. The variable costs are Rs. 13,50,000 for AB Ltd. and Rs. 20,00,000 for XY Ltd.Present the necessary details graphically on a single break-even chart, and determine from there from the capacity of each of the break-even points:Solution: 12. Curvilinear Break-Even Analysis (Two Break-Even Points): The marginal cost recognition is based on the basic assumption that the sales price and variable cost per unit will remain constant at all activity levels or, in other words, the cost-volume-profit ratio is linear. But in actual practice, the sale prices do not remain the same forever and for all levels of production due to competition and changes in the overall price level etc. Furthermore, it may not be possible to increase sales volume without offering concessions in price to customers. Similarly, variable costs per unit can also increase with the increase in production levels due to operational efficiency and the law on declining returns. Thus, the profits can be increased only up to a certain point, in which time it will decrease until it is converted into a The break-even chart will then be curvilinear instead of linear. It can show more than one break-even point, one at a lower level of output and another at a higher level of output. In such a case, increasing production/sales volume beyond the first break-even point will increase profits, but increases in volume beyond the second break-even point will result in losses. The optimal production level should be reached at the point where the difference between the total turnover and the total cost is the highest. Highest.

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