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4Cost behavior, and Cost-volume-profit relationshipCost behavior:Costs are defined as variable or fixed with respect to a specific activity and for a given time period. It represents the resources sacrificed to achieve benefits. A variable cost changes in total in proportion to changes in the related level of total activity or volume. A fixed cost remains unchanged in total for a given period despite wide changes in the related level of total activity or volume. Cost incurred by a business may be classified in various ways which are given below:1. Fixed Cost2. Variable cost3. Semi-variable costCost-Volume-Profit Analysis:The cost volume-profit analysis is the analysis of three variables, viz., cost, volume and profit. In CVP analysis an attempt is made to measure variations of costs and profit with volume. The cost volume profit analysis helps the management in profit planning. In order to increase the profit, a concern must increase the output. When the output is at maximum, within the installed capacity it adds to the contribution. When the output increases, the fixed cost per unit decreases. Generally, cost may not change in direct proportion to the volume. Thus, a small change in the volume will affect the profit.The management is always interested in knowing that which product or product mix is most profitable, what effect a change in the volume of output will have on the cost of production and profit etc. All these problems are solved with the help of the cost-volume-profit analysis.To know the cost volume profit relationship, a study of marginal cost formulae, break-even analysis, and profit volume ratio is essential.Marginal Cost Equations:Marginal Cost = Prime cost + Variable overheadsSales = Variable Cost + Fixed Cost + ProfitSales – Variable cost = Fixed cost + ProfitSales – Variable cost = ContributionContribution = Sales –Marginal costContribution = Fixed cost + ProfitContribution= Fixed cost – LossProfit = Contribution – fixed costBreak – Even Point:Break – even point is that point on which sales revenue and costs are equal. At this point of activity, a producer neither earns any profit nor incurs any loss. That is why it is also called as “No profit, No loss point”. If sales exceed break-even point, profit arises and if sales fall below break-even point, loss emerges. Following are the formulae for calculating break-even point.BEP in Units = Total fixed cost / Contribution per unit orFixed cost / Selling price per unit – Variable cost per unitBEP in Riyal (sales) = Fixed cost X Sales / Contribution orFixed cost /Profit Volume ratioProfit Volume Ratio:Profit volume ratio, which is popularly known as P/V ratio, expresses the relationship of contribution to sales. Another name for this ratio is contribution-sales ratio, marginal-income ratio. The formula for computing the P/V ratio is given below:P/V Ratio = Contribution x 100 /Sales orP/V Ratio = Fixed cost + Profit x100 / Sales orP/V Ratio = Sales – Variable cost x100 /Sales orP/V Ratio = Change in Profit x100 / Change in SalesMargin of Safety:Margin of safety is an important concept in Marginal Costing. Actual sale minus break-even sale is known as the margin of safety. If the margin of safety is large, it is a sign of soundness of the business. The margin of safety is a reliable indicator of the business strength and soundness. Following are the formulae for calculating margin of safety:Margin of Safety = Actual Sales – BEP Sales, orMargin of Safety = Profit / P.V. Ratio,Questions:Q. 1. From the following information, find out the amount of profit earned during the year using marginal cost technique:Fixed Cost SR 500,000Variable cost SR 10 per unitSelling price SR 15 per unitOutput level 150,000 unitsQ. 2. Calculate break- even point with the help of the following information:Variable cost per unit SR 12Fixed expenses SR 60,000Selling price per unit SR 18Q. 3. A company estimates that next year it will earn a profit of SR 50,000. The budgeted fixed costs and sales are SR 250,000 and SR 993,000 respectively. Find out the break-even point for the company.Q. 4. From the following particulars, find out the selling price per unit if BEP is to be brought down to 9,000 units.Variable Cost per unit = SR 75Fixed Expenses = SR 270,000Selling Price per Unit = SR 100Q. 5. From the following data, calculate break-even point expressed in terms of units and also the new BEP, if selling price is reduced by 10%.Fixed cost:Depreciation SR 100,000Salaries SR 100,000Variable expenses:Materials SR 3 per unitLabor SR 2 per unitSelling price SR 10 per unitQ. 6. Calculate Profit volume ratio with the help of the following information.Marginal Cost SR 2,400Selling Price SR 3,000Q. 7. The sales turnover and profits during two periods are as under:Period I : Sales SR 2,000,000 , Profits : SR 200,000Period II: Sales SR 3,000,000 , Profits: SR 400,000Calculate Profit volume ratio.Q. 8. The following data are obtained from the records of a company:First Year Second YearSales SR 80,000 SR 90,000Profit SR 10,000 SR 14,000Calculate break – even point.Q. 9. From the following details find out; (a) Profit volume ratio , (b) BEP , (c) Margin of safety.Sales SR 100,000Total Costs SR 80,000Fixed Costs SR 20,000Net Profit SR 20,000Q10.The following information was obtained from a Company in a certain year:Sales SR 100,000Variable Costs SR 60,000Fixed Costs SR 30,000Find out Profit volume ratio, Break-even point and margin of safety.Q. 11. The following information is obtained from a Company for 2006:Sales SR 20,000Variable Costs SR 10,000Fixed Costs SR 6,000Find the Profit volume ratio, Break-even point and Margin of Safety at this level, and the effect of :(a) 20% decrease in fixed costs;(b) 10% increase in fixed costs;( c ) 10% decrease in variable costs;( d) 10% increase In selling price;( e) 10% decrease in selling priceQ. 12. From the following information, prepare the Break-even chart.Fixed Cost = SR 2,000Variable Cost =SR 0.50 per unitSale SR 1 per unitUnits produced and sold 2,000; 4,000; 6,000; 8,000; and 10,000.Solution-1: Contribution = Selling price – variable cost (Marginal cost)Contribution = 2,250,000 -1,500,000 = SR 750,000Profit = Contribution – Fixed costProfit = 750,000 – 500,000 = SR 250,000Solution-2: Break Eve Point (BEP) in Units = Fixed cost / Selling price per unit –variable cost per unitBreak Even Point (BEP) in Units = 60,000/18-12 = 10,000 UnitsBEP Sales = 10,000 x18 = SR 180,000Solution-3: BEP Sales = Fixed Cost xSales/ContributionContribution = Fixed cost +Profit ; 250,000+50,000= SR 300,000BEP Sales= 250,000×993,000/300,000 = SR 827,500Solution-4: BEP in Units = Fixed Cost/ contribution per unitBEP in Units= Fixed Cost / SP per unit – VC per unit270,000 /100 -75= 270,000 /25 = 10,800 Units)Suppose Contribution per unit = X9,000 = 270,000/x9,000 x = 270,000 ; x = SR 30 per unitContribution per unit = Selling price per unit – Variable cost per unit30 = SP -75 ; SP =105orSuppose selling price = XBEP per unit = Fixed Cost / Selling price per unit – Variable Cost per unit9,000 = 270,000 / X -75; 9,000 x X- 9,000 x75 = 1 x 270,000 = 9,000 X – 675,000 = 270,0009,000 X =270,000 + 675,000; 9,000 X = 945,000; X = 945,000 / 9,000; X = 105 SRTherefore, Selling price per unit = SR 105Solution-5: BEP in Units = Fixed cost / SP – VC = 200,000 /10 -5 = 40,000 UnitsIf selling price is reduced by 10%New Selling Price = 10 – (10×10/100); 10-1 = SR 9New BEP = Fixed Cost /New SP-VC ; 200,000 / 9-5 = 50,000 unitsSolution-6: Profit Volume Ratio = Contribution x100 /SalesContribution = SP – M.C.; 3,000 – 2,400 = 600Profit Volume Ratio = 600 x100 /3,000 = 20%Answer-7: Profit Volume Ratio= Change in profit x100 / change in salesProfit Volume Ratio = 400,000 – 200,000 x 100 /3,000,000 – 2,000,000 = 200,000 x100 /1,000,000 = 20%Answer-8: BEP Sales = Fixed Cost / P.V. RatioP.V. Ratio = Change in Profit x 100 / Change in Sales = 14,000 – 10,000 x100 /90,000 -80,000 =4,000 x100 / 10,000 = 40 %Fixed Cost = Contribution – ProfitFixed Cost = ( 80,000 x40 /100 ) – 10,000 = 32,000 – 10,000 = 22,000 orFixed Cost = (90,000 x 40 / 100) – 14,000= 36,000 – 14,000 = 22,000BEP Sales = 22,000 /40% = 22,000 x 100 / 40 = SR 55,000Answer-9: (a) P.V. Ratio = Contribution x100 / Sales;Variable cost = Total cost – Fixed cost ; 80,000 – 20,000 = 60,000 SRContribution = Sales – Variable cost; 100,000 – 60,000 = 40,000 SRP.V. Ratio = 40,000 x100 /100,000 = 40%(b) BEP sales = Fixed cost /P.V.Ratio = 20,000 x100 /40 = 50,000 SR( c) Margin of Safety = Profit /P.V. Ratio = 20,000 x100 /40 = 50,000 SR orMargin of Safety = Actual Sales – BEP Sales, 100,000 – 50,000 = 50,000 SRQ. 10. (i) P.V. Ratio = 100,000 – 60,000 x100 /100,000= 40%(ii) BEP Sales = 30,000 x100 / 40 = 75,000 SR(iii)Margin of Safety = Actual Sales – BEP Sales; 100,000 – 75,000 = 25,000 SRQ.11. (a) P.V. Ratio = 20,000 – 10,000 x100 /20,000 = 50%, 10,000 x100 /20,000= 50%(b) BEP Sales = 6,000 x100 /50 = 12,000 SR( c ) Margin of Safety = 20,000 – 12,000 = 8,000 SR(i) 20% decrease in fixed costsNew fixed cost = 6,000 – (6,000 x20 /100)= 4,800 SR, 6,000 – 1,200 = 4,800 SR(a) P.V. Ratio= No change(b) BEP Sales = New Fixed cost / PV Ratio = 4,800 x100/ 50 = SR 9,600( c ) Margin of safety = 20,000 – 9,600 = 10,400 SR(ii) (a) P.V. Ratio= No change (50%)(b) New fixed Cost = 6,000 + ( 6,000 x 10 / 100); 6,000 +600 = 6,600BEP Sales = New Fixed Cost / P.V. Ratio = 6,600 x 100 / 50 = 13,200( c ) Margin of safety = Actual Sales – BEP Sales; 20,000 – 13,200 = 6,800(iii) 10% decrease in Variable costNew Variable cost =10,000 – ( 10,000 x10 /100); 10,000 -1,000 = SR 9,000(a) PV Ratio = 20,000 – 9,000 x 100/20,000 = 11,000 x100 /20,000 = 55%(b) BEP Sales = 6,000 x100 /55 = 10,909 SR( c ) Margin of safety = 20,000 – 10,909 = 9,091 SR(iv) 10% increase in selling priceNew selling price = 20,000 + ( 20,000×10/100) = 20,000 +2,000 = 22,000 SR(a) PV Ratio = 22,000 –10,000 x 100/22,000 = 12,000 x100 /22,000 = 54.55%(b) BEP Sales = 6,000 x100 /54.55 = 10,999 SR( c ) Margin of safety = 22,000 – 10,999 = 11,001 SR(V) 10% decrease in selling priceNew selling price = 20,000 – ( 20,000×10/100) = 20,000 -2,000 = SR18,000(a) PV Ratio = 18,000 –10,000 x 100/18,000 = 8,000 x100 /18,000 = 44.44%(b) BEP Sales = 6,000 x100 /44.44 = 13,500 SR( c ) Margin of safety = 18,000 – 13,500 = 4,500 SR———————————————–