Formula for profit volume ratio

Cost behavior, and Cost-volume-profit relationship

Cost 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 Cost

2. Variable cost

3. Semi-variable cost

Cost-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 overheads

Sales = Variable Cost + Fixed Cost + Profit

Sales – Variable cost = Fixed cost + Profit

Sales – Variable cost = Contribution

Contribution = Sales –Marginal cost

Contribution = Fixed cost + Profit

Contribution= Fixed cost – Loss

Profit = Contribution – fixed cost

Break – 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 or

Fixed cost / Selling price per unit – Variable cost per unit

BEP in Riyal (sales) = Fixed cost X Sales / Contribution or

Fixed cost /Profit Volume ratio

Profit 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 or

P/V Ratio = Fixed cost + Profit x100 / Sales or

P/V Ratio = Sales – Variable cost x100 /Sales or

P/V Ratio = Change in Profit x100 / Change in Sales

Margin 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, or

Margin of Safety = Profit / P.V. Ratio

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Questions:

Q. 1. From the following information, find out the amount of profit earned during the year using marginal cost technique:

Fixed Cost SR 500,000

Variable cost SR 10 per unit

Selling price SR 15 per unit

Output level 150,000 units

Q. 2. Calculate break- even point with the help of the following information:

Variable cost per unit SR 12

Fixed expenses SR 60,000

Selling price per unit SR 18

Q. 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 75

Fixed Expenses = SR 270,000

Selling Price per Unit = SR 100

Q. 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 100,000

Salaries SR 100,000

Variable expenses:

Materials SR 3 per unit

Labor SR 2 per unit

Selling price SR 10 per unit

Q. 6. Calculate Profit volume ratio with the help of the following information.

Marginal Cost SR 2,400

Selling Price SR 3,000

Q. 7. The sales turnover and profits during two periods are as under:

Period I : Sales SR 2,000,000 , Profits : SR 200,000

Period II: Sales SR 3,000,000 , Profits: SR 400,000

Calculate Profit volume ratio.

Q. 8. The following data are obtained from the records of a company:

First Year Second Year

Sales SR 80,000 SR 90,000

Profit SR 10,000 SR 14,000

Calculate break - even point.

Q. 9. From the following details find out; (a) Profit volume ratio , (b) BEP , (c) Margin of safety.

Sales SR 100,000

Total Costs SR 80,000

Fixed Costs SR 20,000

Net Profit SR 20,000

Q10.The following information was obtained from a Company in a certain year:

Sales SR 100,000

Variable Costs SR 60,000

Fixed Costs SR 30,000

Find 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 20,000

Variable Costs SR 10,000

Fixed Costs SR 6,000

Find 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 price

Q. 12. From the following information, prepare the Break-even chart.

Fixed Cost = SR 2,000

Variable Cost =SR 0.50 per unit

Sale SR 1 per unit

Units 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 750,000

Profit = Contribution - Fixed cost

Profit = 750,000 – 500,000 = SR 250,000

Solution-2: Break Eve Point (BEP) in Units = Fixed cost / Selling price per unit –variable cost per unit

Break Even Point (BEP) in Units = 60,000/18-12 = 10,000 Units

BEP Sales = 10,000 x18 = SR 180,000

Solution-3: BEP Sales = Fixed Cost xSales/Contribution

Contribution = Fixed cost +Profit ; 250,000+50,000= SR 300,000

BEP Sales= 250,000x993,000/300,000 = SR 827,500

Solution-4: BEP in Units = Fixed Cost/ contribution per unit

BEP in Units= Fixed Cost / SP per unit – VC per unit

270,000 /100 -75= 270,000 /25 = 10,800 Units)

Suppose Contribution per unit = X

9,000 = 270,000/x

9,000 x = 270,000 ; x = SR 30 per unit

Contribution per unit = Selling price per unit – Variable cost per unit

30 = SP -75 ; SP =105

or

Suppose selling price = X

BEP per unit = Fixed Cost / Selling price per unit – Variable Cost per unit

9,000 = 270,000 / X -75; 9,000 x X- 9,000 x75 = 1 x 270,000 = 9,000 X – 675,000 = 270,000

9,000 X =270,000 + 675,000; 9,000 X = 945,000; X = 945,000 / 9,000; X = 105 SR

Therefore, Selling price per unit = SR 105

Solution-5: BEP in Units = Fixed cost / SP – VC = 200,000 /10 -5 = 40,000 Units

If selling price is reduced by 10%

New Selling Price = 10 – (10x10/100); 10-1 = SR 9

New BEP = Fixed Cost /New SP-VC ; 200,000 / 9-5 = 50,000 units

Solution-6: Profit Volume Ratio = Contribution x100 /Sales

Contribution = SP – M.C.; 3,000 – 2,400 = 600

Profit Volume Ratio = 600 x100 /3,000 = 20%

Answer-7: Profit Volume Ratio= Change in profit x100 / change in sales

Profit 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. Ratio

P.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 – Profit

Fixed Cost = ( 80,000 x40 /100 ) – 10,000 = 32,000 – 10,000 = 22,000 or

Fixed Cost = (90,000 x 40 / 100) – 14,000= 36,000 – 14,000 = 22,000

BEP Sales = 22,000 /40% = 22,000 x 100 / 40 = SR 55,000

Answer-9: (a) P.V. Ratio = Contribution x100 / Sales;

Variable cost = Total cost – Fixed cost ; 80,000 – 20,000 = 60,000 SR

Contribution = Sales – Variable cost; 100,000 – 60,000 = 40,000 SR

P.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 or

Margin of Safety = Actual Sales – BEP Sales, 100,000 – 50,000 = 50,000 SR

Q. 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 SR

Q.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 costs

New 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 = 6,600

BEP 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 cost

New 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 price

New selling price = 20,000 + ( 20,000x10/100) = 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 price

New selling price = 20,000 - ( 20,000x10/100) = 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