# CMA311S NOTES UNIT 1: COST-VOLUME-PROFIT ANALYSIS

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1 CMA311S NOTES UNIT 1: COST-VOLUME-PROFIT ANALYSIS Example 1: Tokio Ltd manufactures and sells only one product. The product is sold at N\$10 per unit. Other details are as follows: Variable cost per unit N\$5 Fixed cost per month N\$ Normal sales per month units 1. Calculate the contribution per unit. 2. Calculate the contribution ratio (P/V ratio). 3. Calculate the break-even point in units. 4. Calculate the break-even point in sales value (N\$). 5. Calculate the margin of safety and the margin of safety ratio. 6. Draw a break-even graph which clearly indicates the break-even point. 7. Calculate the net profit per month if units are sold. 8. Suppose the variable cost increases to N\$6 per unit and the fixed cost decreases to N\$ Calculate how many more units have to be sold in order to break-even. 8.2 Calculate the number of units to be sold in order to earn a net profit of N\$7 500 per month. Solution to Example 1 1. Contribution per unit = Selling price per unit variable cost per unit = N\$10 N\$5 = N\$5 2. Contribution ratio = Contribution per unit Selling price per unit = N\$5 N\$10 = 0,5 (or 50%) 3. Break-even point (in units) = Fixed cost Contribution per unit = N\$ N\$5 = units 4. Break-even point (in sales value) = Fixed cost Contribution ratio = N\$ ,5 = N\$ OR Break-even point (in sales value) = Break-even units x Selling price per unit = x N\$10 = N\$ Margin of safety (in units) = Sales Break-even sales = = units OR Margin of safety (in sales value) = Sales Break-even sales = N\$60 000¹ N\$ = N\$ ¹ Normal sales = units x N\$10 Margin of safety ratio = (Margin of safety Sales) x 100% = ( ) x 100% 1

2 OR = 33,3% Margin of safety ratio = (Margin of safety Sales) x 100% = (N\$ N\$60 000) x 100% = 33,3% 6. Graphical presentation of break-even point (break-even graph, break-even chart): Costs and revenue (N\$ 000) Y Profit area 60 Sales revenue Break-even point Total cost line 40 Margin of Safety Loss area Variable cost 20 Fixed cost X Units of Production and Sales ( 000) 7. Sales revenue (5 000 units x N\$10) N\$ Variable cost (5 000 units x N\$5) N\$ = Contribution N\$ Fixed cost N\$ = Net profit (net income) N\$ Break-even sales (in units) = Fixed cost Contribution per unit = N\$ N\$4 = units New break-even point (4 500 units) less Previous break-even point (4 000 units) = Difference (500 units) Thus: the company will have to sell 500 more units in order to break even. 8.2 If the company sells units, the profit is zero (break-even point). However, for every additional unit in excess of 4 500, the profit is N\$4. Therefore, in order to show a profit of N\$7 500, the company will have to sell an additional units per month (N\$7 500 N\$4). Contribution chart This is an alternative presentation of the break-even point. In this case the variable cost line is drawn first. The fixed costs are represented by the difference between the total cost line and the variable cost line, with 2

3 the result that the total cost line is parallel to the variable cost line. The advantage of this form of presentation is that the total contribution is emphasised in the graph, and is represented by the difference between the total sales revenue line and the total variable cost line. Costs and Revenue (N\$ 000) Y 60 Break-even point Profit area Sales revenue Total cost 40 Loss area Fixed cost 20 Margin of Safety Variable cost X Units of Production and Sales ( 000) Profit-volume graph The break-even and contribution charts above do not highlight the profit or loss at different volume levels. To ascertain the profit or loss figures from a break-even chart, it is necessary to determine the difference between the total-cost and total-revenue lines. The profit-volume graph is a more convenient method of showing the impact of changes in volume on profit. The horisontal axis represents the various levels of sales volume, and the profits and losses for the period are recorded on the vertical scale. Y 20 Break-even point Profit (N\$ 000) 10 Loss area Profit area X 10 Units of Production and Sales Loss (N\$ 000) 20 Y 1 3

4 Expected profit after tax: Example 2 Easysteam Ltd manufactures and sells steam irons. The irons sell at N\$190 per unit and the variable costs amount to N\$81,70 per unit. The company s fixed costs are N\$ per year and the current tax rate is 35%. Calculate what the company s sales value (N\$) must be if management expects a net income of N\$ after income tax. Solution to Example 2 Required sales value = Fixed costs + [Expected after-tax profit (1 Tax rate)] Marginal income ratio N\$ [N\$ (1 0,35)] = N\$108,30 N\$190 N\$ (N\$ ,65) = 0,57 N\$ N\$ = 0,57 N\$ = 0,57 = N\$ Activity 1: A summary of a manufacturing company s budgeted profit statement for its next financial year, when it expects to be operating at 75% of capacity, is given below: (N\$) (N\$) Sales units at N\$ Less: Direct materials Direct wages Production overhead: Fixed Variable Gross Profit Less: Administration, selling And distribution costs Fixed Varying with sales volume Net profit Calculate the break-even point in units and in N\$-value 1.2 Draw a contribution (profit-volume) graph which indicates what profit could be expected if the company operated at full capacity. 1.3 It has been estimated that: if the selling price per unit were reduced to N\$28, the increased demand would utilise 90% of the company s capacity without any additional advertising expenditure; and 4

5 1.3.2 to attract sufficient demand to utilize full capacity would require a 15% reduction in the current selling price and a N\$5 000 special advertising campaign. You are required to present a statement showing the effect of the two alternatives compared with the original budget and to advise management which of the three possible plans should be adopted, i.e. the original budget plan or above or above. 1.4 An independent market research study shows that by spending N\$ on a special advertising campaign, the company could operate at full capacity and maintain the selling price at N\$32 per unit. You are required to: advise management whether this proposal should be adopted; and state any reservations you might have. Solution to Activity Variable costs = N\$ N\$ N\$ N\$ = N\$ Variable cost per unit = N\$ units = N\$19 per unit Fixed costs = N\$ N\$ = N\$ Break-even point (in units) = Fixed cost Contribution per unit = N\$ (N\$32 N\$19) = N\$ N\$13 = units Break-even point (in sales value) = B/E point in units x Selling price per unit = x N\$32 = N\$ Profit-volume graph 75% Capacity = Sales of N\$ (9 000 units) This was given in the question N\$ (9 000 units) 100 Therefore, 100% Capacity = 1 X 75 = N\$ ( units) X-axis: Volume (Sales) 0 N\$ N\$ Y-axis: Net income N\$ (Fixed costs) 0 (B/E point) N\$

6 Y Profit (N\$ 000) Loss area Break-even point At sales of N\$ Profit area X Units of Production and Sales Loss (N\$ 000) 80 Fixed cost = N\$ Y Proposal 1: Total contribution = (90% x units x N\$9) = N\$ Less fixed overheads = N\$ Net income = N\$ Proposal 2: Total contribution = ( units x N\$8,20) = N\$ Less fixed overheads = (N\$ N\$5 000) = N\$ Net income = N\$ Recommendation: Based on the above information management should adopt the original budget plan as this yields the largest profit Contribution = units x N\$13 = N\$ Less fixed costs (N\$ N\$15 000) = N\$ Net income = N\$ Recommendation: This proposal yields the largest profit and therefore should be accepted However, there is a risk that the estimated sales demand will not be obtained and this could result in a reduced profit since the N\$ will be a committed cost irrespective of the outcome. Management would need some assurance that the market research company is reliable and has a good track record. 6

7 Cost-volume-profit analysis: Multi-products In today s complex production times no company produces a single product only. In other words, the previous discussions based on a single product were too simplistic. Often companies produce and sell more than one product. Breakeven analysis under these circumstances is somewhat more complex than discussed earlier in this chapter. The reason is that different products will have different selling prices, different costs, and different contribution margins. Consequently the breakeven point will depend on the mix in which the different products are sold. Businesses try to achieve the combination (or mix) that will yield the greatest amount of profits. Most companies produce several products and often these products are not equally profitable. Where this is true, profits will depend to some extent on the company s sales mix. Profits will be greater if high-margin rather than low-margin items make up a relatively large proportion of total sales. Changes in sales mix can cause interesting variations in a company s profits. A shift in the sales mix from high margin items to low margin items can cause total profits to decrease even though total sales may increase. Conversely, a shift in the sales mix from low margin items to high margin items can cause total profits to increase even though total sales may decrease. It is one thing to achieve a particular sales volume; it is quite a different thing to sell the most profitable mix of products! Calculation of break-even point in units You will recall from the previous paragraphs above that the break-even point in units is calculated as follows: Total fixed costs Break-even point in units = Contribution per unit When there is more than one product, the formula is adjusted as follows: Total fixed costs Break-even point in units = Average contribution per unit Example 3 Hangana Ltd supplied the following information regarding its three products: Sales in units Selling price per unit Variable cost per unit Total fixed cost = N\$ Compute the company s break-even point in units. Product A Product B Product C N\$20 N\$50 N\$40 N\$16 N\$36 N\$28 7

8 Solution to Example 3 Compute the average contribution per unit. This can be done in one of the following two ways: Method 1: Product Sales price per unit Variable cost per unit = Contribution per unit x Number of units = Total contribution A B C N\$20 N\$50 N\$40 N\$16 N\$36 N\$28 N\$ 4 N\$14 N\$ N\$ N\$ N\$ Totals N\$ Average contribution per unit (N\$ units) N\$11,00 Method 2: Product Contribution per unit x Sales mix¹ = Weighted contribution² A B C N\$ 4 N\$14 N\$12 0,20 ( ) 0,30 ( ) 0,50 ( ) N\$ 0,80 N\$ 4,20 N\$ 6,00 Average contribution per unit N\$11,00 ¹ The sales mix is the proportion of each product s sales in units to total sales in units. ² Each product has a different contribution, and it is necessary to reduce the separate contributions to a weighted average contribution of all products. Note that the average contribution is not simply the sum of N\$4, N\$14 and N\$12 divided by 3, because the products are not sold in equal proportions. The contribution of product C, which constitutes 50% of unit sales, must be weighted more heavily than the contributions of products A and B. The weighted average contribution, therefore, represents the contribution of all separate products with a specific sales mix. The break-even point can now be computed: Fixed costs Break-even point in units = Average contribution per unit N\$ = N\$11 Activity 2 = units Chem-Sol Ltd produces and sells two chemicals called Solvex and Dysolve. The following data regarding these two products is available: Solvex Selling price per unit N\$10 Variable cost per unit N\$ 7 Sales mix 60% Total fixed cost = N\$ Dysolve N\$20 N\$12 40% 2.1 Compute the company s break-even point in units. 8

9 2.2 Calculate how many more (or fewer) units have to be sold if the sales mix is changed to 50% for each product. Individual product break-even points In Example 3 above the break-even point was units for all three products combined. However, production planning and scheduling require break-even data for individual products. The sales mix used to calculate the weighted average contribution per unit is now used to extract the individual product break-even points. Total break-even units are multiplied by the individual sales mix percentages to determine the breakeven point for individual products. The calculation is as follows: Product Total units A B C Example 4 x Sales mix 0,20 0,30 0,50 = Individual Product B/E in units x Selling price N\$20 N\$50 N\$40 = Individual Product B/E in N\$ N\$ N\$ N\$ N\$ Flupp Ltd produces 3 products and has fixed costs of N\$ per year. Other data for the year is as follows: A B C Selling price per unit N\$18 N\$12 N\$36 Variable cost per unit N\$12 N\$7 N\$27 Relative sales mix 0,4 0,3 0,3 4.1 Calculate the break-even point in units for each product individually. 4.2 Determine how many units of each product must be sold to earn a net income of N\$ Solution to Example 4 Weighted contribution Product Selling price Variable cost Contribution Sales mix A N\$18 N\$12 N\$6 0,4 N\$2,40 B N\$12 N\$ 7 N\$5 0,3 N\$1,50 C N\$36 N\$27 N\$9 0,3 N\$2,70 Average contribution per unit N\$6,60 Break-even point (in units) = Fixed costs Average contribution per unit = N\$ N\$6,60 = units Individual break-even sales in units: A B C x 0,4 = units x 0,3 = units x 0,3 = units units 9

10 4.2 Required sales = (Fixed costs + Expected profit) Average contribution per unit = (N\$ N\$99 000) N\$6,60 = units Individual break-even sales in units: A B C x 0,4 = units x 0,3 = units x 0,3 = units units Activity 3 Dynatone Tape Company produces two types of blank recording tapes that it distributes through wholesalers or sells directly to large retailers. The following data apply to these products: Product Sales price Variable costs Contribution Expected % of units sold Cassette N\$2,00 N\$0,60 N\$1,40 60 Cartridge N\$3,00 N\$1,10 N\$1,90 40 Total fixed costs = N\$ Calculate the break-even point in units and in N\$ for each product individually. 3.2 Calculate the number of units and sales value in N\$ of each product necessary to achieve a net income of N\$600. Calculation of break-even point in sales value In the previous paragraphs above you learned that the break-even point in sales value could be determined in two different ways: Break-even point in sales value = Break-even point in units x Selling price per unit OR Total fixed costs Break-even point in sales value = Contribution ratio In a multi-product situation, the break-even point in sales value can also be calculated in two different ways by adjusting these two formulas. By using the weighted average selling price per unit One way of calculating the break-even point in sales value is to compute the weighted average selling price per unit and then applying the following formula: Break-even sales value = Break-even quantity x Weighted average selling price per unit Example 5 Refer to Example 3 above. Compute the break-even point in sales value by first computing the weighted average selling price per unit. 10

11 Solution to Example 5 Product Sales price per unit x Sales mix = Weighted selling price A B C N\$20 N\$50 N\$40 0,20 0,30 0,50 N\$ 4 N\$15 N\$20 Weighted average selling price per unit N\$39 Break-even point in sales value = Break-even point in units x Weighted average selling price per unit = x N\$39 = N\$ Activity 4 A company manufactures and sells two products, X and Y. Forecast data for a year are: Product X Product Y Sales (units) Sales price (per unit) N\$12 N\$8 Variable cost (per unit) N\$ 8 N\$3 Annual fixed costs are estimated at N\$ What is the break-even point in sales revenue with the current sales mix? A N\$ B N\$ C N\$ D N\$ (Hint: First calculate the break-even point in units). By using the average contribution ratio If the average contribution ratio is known, the break-even point in sales value can be computed by means of the following formula: Total fixed costs Break-even point in sales value = Average contribution ratio Example 6 Refer to Example 3 above Calculate the break-even point in sales value by first computing the average contribution ratio. Solution to Example 6 Average contribution per unit Average contribution ratio = Average selling price per unit N\$11 = N\$39 = N\$0,28205 OR 11

12 Product Units x Sales price = Sales revenue Variable cost = Contribution A B C N\$20 N\$50 N\$40 N\$ N\$ N\$ N\$ N\$ N\$ N\$ N\$ N\$ Totals N\$ N\$ N\$ Total contribution Average contribution ratio = Total sales N\$ = N\$ = 0,28205 Fixed costs Break-even point in sales value = Average contribution ratio N\$ = 0,28205 Activity 5 = N\$ Refer to Activity 3 above. Repeat the question without first calculating the break-even point in units. Activity 6 H Limited manufactures and sells two products, J and K. Annual sales are expected to be in the ratio of J:1 and K:3. Total annual sales are planned to be N\$ Product J has a contribution to sales ratio of 40%, whereas that of product K is 50%. Annual fixed costs are estimated to be N\$ The budgeted break-even sales value (to the nearest N\$1 000) is: A N\$ ; B N\$ ; C N\$ ; D N\$ E Cannot be determined from the above data. Activity 7 Z plc currently sells products Aye, Bee and Cee in equal quantities and at the same selling price per unit. The contribution to sales ratio for product Aye is 40%; for product Bee it is 50% and the total is 48%. If fixed costs are unaffected by mix and are currently 20% of sales, the effect of changing the product mix to: Aye 40%; Bee 25%; Cee 35% is that the total contribution : total sales ratio changes to: A 27,4% B 45,3% C 47,4% D 48,4% E 68,4% Activity 8 PE Limited produces and sells two products, P and E. Budgets prepared for the next six months give the following information: 12

13 Product P per unit Product E per unit Selling price N\$10,00 N\$12,00 Variable costs: Production and selling N\$ 5,00 N\$10,00 Common fixed costs: Production and selling (for six months) N\$ You are required in respect of the forthcoming six months to: 8.1 state what the break-even point in N\$ s will be and the number of each product this figure represents if the two products are sold in the ration 4P to 3E; 8.2 state the break-even point in N\$ s and the number of products this figure represents if the sales mix changes to 4P to 4E (ignore fractions of products); 8.3 advise the sales manager as to which product mix should be better, that in 8.1 or that in 8.2 above. Graphical presentation for multiple products In the paragraphs above you learned that the relationship between cost, volume and profit could be presented by a graph. You also learned that there are three types of graphs namely the break-even chart, the contribution chart and the profit-volume graph. When the details of more than one product have to be presented graphically, more lines have to be drawn and this can become very cumbersome as well as confusing. However, the easiest method is to make use of the Profit-volume graph. Example 7 An enterprise supplied the following information regarding its three products: Details Product A Product B Product C N\$ N\$ N\$ Sales Variable cost Contribution NIL Total fixed cost N\$ Plot the above information on a Profit-volume graph and indicate the break-even sales clearly. Solution to Example 7 Step 1: Calculate the contribution ratio of each product separately and rank them in order from the largest to the smallest: Product A Product B Product C Contribution ratio N\$ x 100% N\$ x 100% N\$0 x 100% N\$ N\$ N\$ Ranking = A, B, C. = 50% (0,5) = 25% (0,25) = 0% (0) 13

14 Step 2: Determine the cumulative sales and cumulative profit figures in the order established in Step 1 above: A A + B A + B + C X-axis (Cumulative sales) N\$0 N\$ N\$ N\$ Y-axis (Cumulative profit) (N\$40 000) N\$ N\$ N\$ Step 3: The profit-volume graph can now be plotted as follows: Net income N\$ 000 Product C 80 Profit area 70 Product B Product A Volume (sales) units Break-even point (N\$ ,33) Loss area -40 Fixed costs N\$

15 Example 8 Nerina CC supplied the following information regarding their four products for the year 2005: 1. Sales, Variable costs and Contributions: Sales Variable costs Contribution Product A Product B Product C Product D N\$ N\$ N\$ N\$ (5 000) Fixed costs: N\$ Plot the relevant information on a Profit-volume graph (P/V chart) and indicate the break-even sales clearly. 8.2 Check the correctness of your answer by calculating the break-even sales with the aid of an applicable formula. Solution to Example 8 Step 1: Calculation of individual as well as average contribution ratios: Product A Product B Product C Product D Total Calculations N\$ N\$ N\$ N\$ N\$ Sales Less Variable costs = Contribution Less Fixed costs = Net income (5 000) Contribution ratio - 0,025 0,125 0,125 0,30 0,111 Ranking = D, B, C, A. Step 2: Calculation of cumulative sales and cumulative net income: D D + B D + B + C D + B + C + A N\$ N\$ N\$ N\$ N\$ Sales (X-axis) Net income (Y-axis) (50 000) (20 000) Step 3: The profit-volume graph can now be plotted as follows: 15

16 Y Net income N\$ 000 Profit area Product A 50 Product C Product B X -10 Volume (sales) units Break-even point (N\$ ) Product D Loss area -50 Fixed costs N\$ Break-even sales = Fixed costs Average contribution ratio = N\$ ,111 = N\$

17 Activity 9 Desert Ltd supplied the following information regarding their three products for the year 2010: 1. Sales, Variable costs and Contribution: Product A Product B Product C N\$ N\$ N\$ Sales Variable costs Contribution Fixed costs: N\$ Plot the relevant information on a Profit-volume graph (P/V chart) and indicate the break-even sales clearly. 9.2 Check the correctness of your answer by calculating the break-even sales with the aid of an applicable formula. Activity 10 Namsa Ltd supplied the following information regarding their three products for the year 2010: 1. Sales, Variable costs and Contribution: Product A Product B Product C N\$ N\$ N\$ Sales Variable costs Contribution Fixed costs: N\$ Plot the relevant information on a Profit graph (P/V chart) and indicate the break-even sales clearly Check the correctness of your answer by calculating the break-even sales with the aid of an applicable formula. Cost structure and the operating leverage factor The concept cost structure refers to the relative relationship between fixed and variable costs in an enterprise. During recent years the cost structure of manufacturing enterprises has changed in that costs have become more fixed as a result of automation. More machines and less manual labour are used in production. Enterprises with a high percentage fixed costs are more sensitive to changes in sales than enterprises with a low percentage fixed costs. For example, consider a firm with relatively high fixed costs (ie, relatively low variable costs and consequently a high profit-volume ratio). If sales should increase, profit will increase as a higher rate than for a firm with relatively low fixed costs, because of the high profit-volume ratio. However, if sales should drop, profit will also drop at a higher rate because, although variable costs will drop as well, the fixed costs (rent, salaries, etc) must still be paid. 17

18 Example 9 The following details regarding two different firms are available: Company A Company B N\$ % N\$ % Sales Variable cost = Contribution Fixed cost = Net profit Calculate the increase in profit for each company if sales were to increase by 20%. 9.2 Calculate the decrease in profit for each company if sales were to decrease by 20%. Solution to Example 9 Details Sales Variable cost = Contribution Fixed cost = Net profit % increase in Profit Company A Company B Presently 20% increase Presently 20% increase N\$ N\$ N\$ N\$ % 40% Conclusion: Company A has relatively high fixed costs. However, because it has a high P/V-ratio, profit will also increase at a higher rate than that of Company B. Details Sales Variable cost = Contribution Fixed cost = Net profit % decrease in Profit Company A Company B Presently 20% decrease Presently 20% decrease N\$ N\$ N\$ N\$ % 40% Conclusion: Company A has relatively high fixed costs. Therefore, because it has a high P/V-ratio, profit will also decrease at a higher rate than that of Company B. The operating leverage factor reflects how much influence a percentage change in sales volume has on net profit. A specific operating leverage factor is valid for a specific sales volume and changes as the sales volume changes. The operating leverage factor is calculated as follows: Contribution Operating leverage factor = Net profit 18

19 The operating leverage is a management instrument that shows, relatively easily, the effect of a change in turnover on net income, without detailed statements having to be prepared. Example 10 The management of Shilongo Ltd supplied the following details: N\$ Sales Variable cost Fixed cost Calculate the operating leverage factor 10.2 Use the operating leverage factor calculated in 10.1 above to compute the increase in net income if sales were to increase by 15%. Solution to Example Operating leverage factor = Contribution Net profit = N\$ N\$ = % increase in net income = % increase in sales x operating leverage factor = 15% x 2 = 30% Activity 11 The following income statement has been supplied to you: Sales revenue N\$ Less: Variable costs = Contribution Less: Fixed costs = Net income Show the firm s cost structure by indicating the percentage of the firm s revenue represented by each item on the income statement Suppose the firm s revenue declines by 15%. Use the contribution % to calculate the resulting decrease in net income Compute the firm s operating leverage factor when sales revenue is N\$ Use the operating leverage factor to calculate the increase in net income resulting from a 20% increase in sales revenue. 19

20 Activity 12 George Awarab recently opened a shop that specialises in car polish, a product that he has developed himself. He has just received a diploma in accounting and is anxious to apply the principles he has learned at the Polytechnic. As a first step, he has prepared the following analysis for his new store: Sales price per tin N\$40 Variable costs per tin 16 Marginal income per tin N\$24 Fixed costs per year: Rent on building N\$ Depreciation on equipment Selling expenses Administrative expenses Total fixed costs N\$ Determine how many tins of polish must be sold each year in order to break even. What does this represent in total N\$ sales? 12.2 George has decided that he must earn at least N\$ during the first year to justify his time and effort. Determine how many tins of polish he must sell to reach this target profit George now has a part-time sales person working in the store. It will cost him an additional N\$8 000 per year to convert the part-time position to a full-time post. George believes that the change would bring in an additional N\$ in sales each year. Determine whether he should convert the position. Use the incremental approach (do not prepare an income statement) Refer to the original data. During the first year, the store sold only tins of polish and reported the following operating results: Sales (3 000 tins) N\$ Less variable costs Marginal income Less fixed costs Net income N\$ Determine the store s degree of operating leverage George is confident that with a more intense sales effort and with a more creative advertising program he can increase sales by 50% next year. Determine what the expected percentage increase in net income would be (use the degree of operating leverage to compute your answer). Cost-volume-profit analysis assumptions It is highly unlikely that selling price and variable costs per unit as well as fixed costs in total will remain constant for a given period. Therefore, certain assumptions are part of break-even analysis. These assumptions have given rise to criticism against CVP analysis. However, despite this criticism it remains a useful management tool for short-term decision-making and profit planning. Summary CVP analysis is a useful tool with which to do certain short-term investigations and make decisions. It puts an enterprise in a position to calculate its sales in order to make an expected profit level. It is therefore also useful in evaluating the effect of operating changes on profit. These changes include changes in the selling price and fixed costs. CVP analysis is liable to contain certain simplified assumptions that are necessary to make the analysis clear and understandable. 20

21 Solution to Activity Product Contribution x Sales mix Weighted contribution Solvex N\$3 0,6 N\$1,80 Dysolve N\$8 0,4 N\$3,20 Weighted average contribution per unit N\$5,00 Break-even point = Fixed costs Average marginal income per unit = N\$ N\$5 = units 2.2 Product Contribution x Sales mix Weighted contribution Solvex N\$3 0,5 N\$1,50 Dysolve N\$8 0,5 N\$4,00 Weighted average contribution per unit N\$5,50 Break-even point = Fixed costs Average marginal income per unit = N\$ N\$5,50 = units Solution to Activity 3 Product Selling price Variable cost Contribution Sales mix Weighted contribution per unit Cassette N\$2 N\$0,60 N\$1,40 0,6 N\$0,84 Cartridge N\$3 N\$1,10 N\$1,90 0,4 N\$0,76 Weighted average contribution per unit N\$1,60 Break-even point (in units) = Fixed cost Average contribution per unit = N\$3 000 N\$1,60 = units Individual break-even sales in units: Cassettes: x 0,6 = units Cartridges: x 0,4 = 750 units units Break-even point (in sales value): Cassettes: units x N\$2 = N\$2 250 Cartridges: 750 units x N\$3 = N\$2 250 Total sales to break even = N\$ Required sales = (Fixed cost + Expected profit) Average contribution per unit = (N\$ ) N\$1,60 = units Individual break-even sales in units: Cassettes: x 0,6 = units Cartridges: x 0,4 = 900 units units 21

22 Break-even point (in sales value): Cassettes: units x N\$2 = N\$2 700 Cartridges: 900 units x N\$3 = N\$2 700 Total sales to break even = N\$5 400 Solution to Activity 4 Product Contribution per unit x Sales mix = Weighted contribution X Y N\$4 N\$5 0,80 ( ) 0,20 ( ) N\$3,20 N\$1,00 Weighted average contribution per unit N\$4,20 Fixed costs Break-even point in units = Average contribution per unit Solution to Activity 5 N\$ = N\$4,20 = units Product Selling price Variable cost Contribution Sales mix Weighted contribution Cassette N\$2 N\$0,60 N\$1,40 0,6 N\$0,84 Cartridge N\$3 N\$1,10 N\$1,90 0,4 N\$0,76 Average N\$1,60 Break-even point (in units) = Fixed cost Average marginal income = N\$3 000 N\$1,60 = units Individual break-even sales in units: Cassettes: x 0,6 = units Cartridges: x 0,4 = 750 units Break-even point (in sales value): Cassettes: units x N\$2 = N\$2 250 Cartridges: 750 units x N\$3 = N\$2 250 Total sales to break even = N\$ Required sales = (Fixed cost + Expected profit) Average marginal income = (N\$ ) N\$1,60 = units Individual break-even sales in units: Cassettes: x 0,6 = units Cartridges: x 0,4 = 900 units Break-even point (in sales value): Cassettes: units x N\$2 = N\$2 700 Cartridges: 900 units x N\$3 = N\$2 700 Total sales to break even = N\$

23 Solution to Activity 6 Product Sales revenue x P/V ratio = Contribution J K N\$ ¹ N\$ ² 0,4 0,5 N\$ N\$ Totals N\$ N\$ ¹ 1 N\$ X 1 ² 3 N\$ X 1 Total contribution Average contribution ratio = Total sales N\$ = N\$ = 0,475 Fixed costs Break-even point in sales value = Average contribution ratio Therefore, answer = C Solution to Activity 7 N\$ = 0,475 = N\$ ,57 The average contribution to sales ratio is 48% (given in question) 48% x 3 = 144% Therefore, Product Cee = 144% (40% + 50%) = 54% Product Contribution x Sales mix = Weighted contribution Aye 0,40 (40%) 0,40 0,16 Bee 0,50 (50%) 0,25 0,125 Cee 0,54 (54%) 0,35 0,189 Weighted average contribution 0,474 (47,4%) Answer = C Solution to Activity Product Contribution x Sales mix = Weighted contribution P N\$5 4/7 2,857 E N\$2 3/7 0,857 Weighted average contribution per unit 3,714 Break-even point (in units) = Fixed cost Average contribution per unit = N\$ ,

24 = units Individual break-even sales in units: Product P = x 4/7 = units Product E = x 3/7 = units units Break-even point in sales value: Product P = units x N\$10 selling price = N\$ Product E = units x N\$12 selling price = N\$ N\$ When the products are sold in equal proportions the average contribution is calculated by simply dividing the total contribution by two. Thus: Average contribution per unit = (N\$5 + N\$2) 2 = N\$3,50 Break-even point (in units) = Fixed cost Average contribution per unit = N\$ N\$3,50 = units (consisting of units of each product). Break-even point in sales value: Product P = units x N\$10 selling price = N\$ Product E = units x N\$12 selling price = N\$ N\$ Advice to management: The product mix in 9.1 above is preferable because it yields the higher average contribution per unit and consequently the break-even point is reached sooner. Solution to Activity 9 Product A Product B Product C Total 9.1 Calculations N\$ N\$ N\$ N\$ Sales Less Variable costs = Contribution Less Fixed costs = Net income Contribution ratio 0,02 0,08 0,25 0,08 Ranking = C, B, A. C C + B C + B + A Cumulative figures N\$ N\$ N\$ N\$ Sales (X-axis) Net income (Y-axis) (40 000)

25 Profit-volume graph (P/V chart) Net income N\$ Profit area 60 Product A Product B Product C Volume (sales) units Break-even point (N\$ ) Loss area -40 Fixed costs 9.2 Break-even sales = Fixed costs Contribution ratio = N\$ ,08 = N\$ Solution to Activity Calculations: Product A Product B Product C Total N\$ N\$ N\$ N\$ Sales Variable costs Contribution Fixed costs Net income

26 Contribution ratio 0,30 0,10 0,067 0,10 A A + B A + B + C N\$ N\$ N\$ N\$ Sales Net income (50 000) (20 000) Contribution graph (Profit-volume chart): Profit-volume graph (P/V chart): Net income N\$ 000 Profit area Product C Product B Volume (sales) units Product A Break-even point (N\$ ) Loss area Fixed costs 10.2 Break-even sales = Fixed costs Marginal income ratio = N\$ ,10 = N\$

27 Solution to Activity Income Statement Amount Percentage Sales revenue N\$ % Less: Variable costs % = Contribution % Less: Fixed costs % = Net income % 11.2 Contribution = 40% of sales revenue = 40% of N\$ (N\$ less 15%) = N\$ Net income = Contribution Fixed costs = N\$ N% = N\$ Therefore, net income has decreased by 60% (from N\$ to N\$20 000) 11.3 Operating leverage factor = Contribution Net profit = N\$ N\$ = % increase in net income = % increase in sales x operating leverage factor = 20% x 4 = 80% Solution to Activity Break-even point (in units) = Fixed costs Marginal income per unit = N\$ N\$24 = tins Break-even point (in N\$) = x N\$40 = N\$ Required sales = (Fixed costs + Target profit) Marginal income per unit = (N\$ N\$18 000) N\$24 = N\$ N\$24 = tins 12.3 Incremental sales N\$ Incremental marginal income = N\$ Incremental fixed costs = Incremental net income = N\$ Yes, he should convert this position because he will earn an extra N\$ Operating leverage = Marginal income Net income = N\$ N\$ = Percentage increase in net income = Percentage increase in sales x operating leverage = 50% x 6 = 300% 27

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