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# Business Economics 08 Breakeven Analysis

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### Business Economics 08 Breakeven Analysis

1. 1. Breakeven Analysis or Profit Contribution Analysis or Cost-volume-profit (CVP) Analysis
2. 2. <ul><ul><li>Breakeven analysis – useful in planning, studies the relationship between TC, TR, total losses and profits over the whole range of output </li></ul></ul><ul><ul><li>Linear cost and revenue functions </li></ul></ul><ul><ul><li>TC = 100 + 10Q, TR = 15Q </li></ul></ul><ul><ul><li>Breakeven Q (Qe) TR = TC 20 </li></ul></ul><ul><ul><li>or PQ=FC+Q.AVC </li></ul></ul><ul><ul><li>or FC/P-AVC 20 </li></ul></ul>
3. 3. <ul><ul><li>Operating losses (TC>TR) </li></ul></ul><ul><ul><li>Operating profit (TR>TC ) </li></ul></ul><ul><ul><li>Profit contribution (P-AVC) - revenue on the sale of a unit of output after variable costs are covered represents a contribution towards profit </li></ul></ul><ul><ul><li>Contribution margin ratio = P - AVC/P </li></ul></ul><ul><ul><li>Criticism of linear functions- linear revenue and non linear cost functions </li></ul></ul>
4. 4. Non linear costs and revenue functions TFC TVC TR TC  Q1 Q2 Q3 TC TR,TC,  A B a b C D losses profits
5. 5. Managerial uses of breakeven analysis <ul><ul><li>Margin of safety – refers to the extent to which the firm can afford a decline in sales before it starts incurring losses. </li></ul></ul><ul><li> MS = S - BEP </li></ul><ul><ul><li>where MS = margin of safety, </li></ul></ul><ul><ul><li>S = sales (planned), BEP = breakeven point </li></ul></ul><ul><ul><li>It reflects resistance capacity to avoid losses </li></ul></ul>
6. 6. Margin of safety <ul><li>Case -1 </li></ul><ul><li>MS = 8000 – 5000 = 3000 Q </li></ul><ul><li>Or (S – BEP).100/S = 37.5% </li></ul><ul><li>Case - 2 </li></ul><ul><li>MS = (4000 – 5000).100/4000 = 25% </li></ul>
7. 7. Required rate of profit (  R ) Q <ul><li> R = PQ - [ (Q.AVC) + FC] </li></ul><ul><li>Q = FC +  R /P – AVC = 100 + 200/15 – 10=60 </li></ul>
8. 8. Change in price <ul><li>P contribution margin and vice versa </li></ul><ul><li>P not always demand – it depends on E d </li></ul><ul><li>Increasing sale price increases MS and vice versa </li></ul><ul><li>Q n = FC +  / SP n – AVC </li></ul><ul><li>Where Q n = new volume of sales, SP n = new selling price </li></ul>
9. 9. <ul><li>Case – 1 </li></ul><ul><li>100 +200/15 – 10 = 60 </li></ul><ul><li>Price reduced to 13 </li></ul><ul><li>Q n = 100 + 200/13 – 10 = 100 </li></ul><ul><li>Case – 2 </li></ul><ul><li>If price increased to 17 </li></ul><ul><li>Q n = 100 + 200/17 – 10 = 44 </li></ul>
10. 10. Change in cost <ul><li>High ratio of TFC to TC allows high profits with increasing sales </li></ul><ul><li>Low ratio of TFC to TC has larger MS </li></ul>
11. 11. Change in fixed cost <ul><li>New output level </li></ul><ul><li>Q n = Q + FC n – FC/P – AVC </li></ul><ul><li>60 + 150 – 100/15 – 10 = 70 </li></ul><ul><li>New selling price </li></ul><ul><li>P n = P + FC n – FC/Q </li></ul><ul><li>= 15 + 150 – 100/60 </li></ul><ul><li>= 16 </li></ul>
12. 12. Change in variable costs <ul><li>New output level </li></ul><ul><li>Q n = FC +  / P – VC n </li></ul><ul><li>= 100 + 200/15 – 12 = 100 </li></ul><ul><li>The new selling price </li></ul><ul><li>P n = P + (VC n + VC) </li></ul><ul><li>= 15 + (12 – 10) </li></ul><ul><li>=17 </li></ul>
13. 13. Operating leverages <ul><li>A firm is said to be highly leveraged if fixed costs are large relative to variable costs and experiences more variation in profits for a given % ∆ Q than does a less leveraged firm. </li></ul>
14. 14. Leverage is analyzed using profit elasticity an indicator of risk
15. 15. Operating leverages <ul><li>If price is constant, E  depends on </li></ul><ul><ul><ul><li>the level of output </li></ul></ul></ul><ul><ul><ul><li>the level of TFC </li></ul></ul></ul><ul><ul><ul><li>AVC </li></ul></ul></ul><ul><ul><ul><li> = PQ – (AVC) (Q) – TFC </li></ul></ul></ul><ul><li>And ∆  = P (∆Q) – (AVC) (∆Q) </li></ul>
16. 16. <ul><li>Therefore </li></ul><ul><li>E  = [P( ∆Q) – (AVC) ( ∆Q) ] / [PQ – (AVC)(Q) - TFC] / ∆Q/Q </li></ul><ul><li>Or E  = Q(P – AVC)/ Q(P – AVC) - TFC </li></ul>
17. 17. Example Operating profit elasticity for two firms VG/lv/P-II-6 firm a firm b price = 10 price = 10 AVC = 5 AVC = 2 AFC = 1000 TFC = 4000 Output sale profit E  firm A firm B firm A firm B 1000 4000 4000 1.25 2.00 1500 6500 8000 1.15 1.50 2000 9000 12000 1.11 1.33 2500 11500 16000 1.09 1.25 3000 14000 20000 1.07 1.20
18. 18. Policy guidelines emanating from break even analysis <ul><li>A high BEP indicates vulnerability of the profit position of the firm </li></ul><ul><li>The higher the contribution margin, the higher is the endurance of business and vice versa </li></ul><ul><li>During boom, a firm with a higher percentage of fixed costs to sales earns higher profits as compared to a business with a higher percentage of variable expenses to sales. During depression. the leveraged firm suffers greater losses than others. </li></ul>VG/lv/P-II-6