Chapter 20

Break-Even and Cost-Volume-Profit Analysis

Discussion Questions

1) The break-even point is the point at which costs and revenue are in equilibrium, showing neither profit nor loss for the business.2) (a) The conventional income statement must be restated for computation of the break-even point because it does not show fixed and variable costs. (b) The new income statement distinguishes between variable and fixed costs. It emphasizes the margin available to cover fixed cost and profit after variable cost has been deducted from sales.3) The contribution margin is the result of subtracting variable cost from the sales figure. The contribution margin indicates the amount available for the recovery of fixed cost and for profit.4) (a) R (BE) = F 1 – Vor (in words):Revenue at the = Total fixed costbreak-even point Contribution margin per dollar of sales

(b) Q (BE) = F P – Cor (in words):Units of sales at = Total fixed costbreak-even point Contribution margin per unit of sales5) (1) Dollars of revenue and costs. (2) Volume of output, expressed in units, percent of capacity, sales, or some other measure. (3) Total cost line. (4) Variable cost area. (5) Fixed cost area. (6) Break-even point. (7) Loss area. (8) Profit area. (9) Sales line.6) An analysis of the expected behavior of a firm’s expenses and revenue for the purpose of constructing a break-even chart is usually restricted to the output levels at which the firm is likely to operate. Assumptions about the level of fixed cost, the rate of variable cost, and sales prices are based on the operating conditions and managerial policies that will be in effect over the expected output levels.These expected output levels represent the firm’s relevant range, and the cost-volume-profit relationships shown in a break-even chart are applicable only to output levels within this range. The behavior of fixed cost, variable cost, and sales prices at levels of output below or above the relevant range are likely to result in an entirely different set of cost-volume-profit relationships because of changed operating conditions or managerial policies. The fact

that the cost and revenue lines on a break-even chart are typically extended past the upper and lower limits of the relevant range should not, therefore, be interpreted to mean that they are valid for these levels of output. A break-oven chart showing cost-volume-profit relationships for all levels of output could be developed. The shapes of the cost and revenue lines in such a chart could not, however, be expected to approximate straight-line (linear) patterns. By restricting the underlying cost and revenue behavior assumptions in breakeven analyses to a relatively narrow output range (the range over which the firm is likely to operate), it is usually possible to assume linear behavior patterns without any significant distortions in cost-volume-profit relationships, thereby simplifying the analysis. If the range over which a firm is likely to operate is quite wide, curvilinear functions may be employed; or it may be desirable to develop a number of break-even charts, each having its own relevant range, for which the underlying cost and revenue behavior assumptions are valid.7) Weaknesses inherent in the preparation and use of break-even analysis are: (a) When more than one product is produced, the contribution margin of each product will probably differ. Accordingly, a break-even analysis for the whole operation will not indicate the contribution of each product to fixed cost and the volume required for each product. (b) Some costs are almost impossible to classify conclusively as being either fixed or variable. (c) General economic conditions and other external factors may affect the data used in the analysis. (d) In the final analysis, fixed cost is related to production and sales and, therefore, may decrease somewhat due to decreased production and sales—and vice versa. (e) Quite often costs increase sharply at certain points in production and sales levels and then level out until a certain greater stage of production and/or sales is reached, at which time the phenomenon is repeated as production and/or sales are again increased. (f) Performance must be constantly compared to the break-even analysis in order to determine whether the conditions that existed at the time of the calculations have held true, and whether any changes have been considered.8) (a) With sales price per unit and total fixed cost remaining constant, the break-even point moves up rapidly as unit variable cost is increased; at the same time, the break-even point moves down as unit variable cost is decreased. (b) A decrease in fixed

cost lowers the breakeven point. An increase in fixed cost moves the break-even point higher.9) The break-even chart gives information in terms of total cost and revenue; the unit profit graph is in terms of unit costs and revenue.10) The margin of safety is a selected sales figure less break-even sales. The margin of safety is a cushion against sales decreases. The greater the margin, the greater the cushion against suffering a loss.11) Cost-volume-profit relationship is the relationship of profit to sales volume. This relationship is important to management because management tries at all times to keep volume, cost, price, and product mix in a ratio that will achieve a desired level of profit.12) Price and sale are inversely related. If cost does not change with a reduction in price, it may lead to

loss even with increase in sales volume. So this theory is not applicable in practice. 13) a cost-volume profit analysis by products is of value because it shows the contribution of each product to the contribution margin.14) The P/V analysis graph analysis can be used to illustrate graphically a product’s contribution to the total profit. Starting at the fixed cost line, each product’s contribution margin is plotted until the profit figure is reached. The profit path of each product is then plotted, beginning with the product having the highest C/M ratio.15) (1) Aiding budgetary control, (2) Improving and balancing sales (3) Analyzing volume change impact (4) Analyzing sales price and cost change impact (5) negotiating wages (6) Analyzing product mix (7) Assessing further capitalization and expansion decisions (8) Analyzing margin of safety.

EXERCISES

E-1

1) Breakeven in Dollars = Fixed Cost / Contribution Margin RatioBreakeven in Dollars = $ 6000/ 0.6 = $ 10,000Working C/M Ratio = Sale price -- Variable Cost / Sale price = (5500units × $2) -- (5500units × 0.8) / (5500units × $2) = 11000 -- 4400 / 11000 = 0.6

2) Breakeven point in units = B.E.P in Dollars / Unit Sale price = $ 10,000 /2 = 5,000 units

E-2

1) C/M = Sale price -- Variable Cost = $ 7,640,000 -- $ 4,736,800 = $ 2,903200

2) C/M Ratio = C/M / Sale price = $ 2,903200 / $ 7,640,000 = 0.38

3) Breakeven in Dollars = Fixed Cost / C/M Ratio = $ 24, 51,000/0.38 = $ 64, 50,000

E-3

1) Breakeven sale in Dollars = Fixed Cost / C/M Ratio = $ 42909 / 0.33 = $ 13000WorkingFixed Cost = 2000 + 2290 = $ 4290C/M Ratio = (18000×2.50) -- (18000×1.675)/ (18000×2.50) = 45000 -- 30150 / 45000 = 0.33

2) Breakeven in units = B.E.S in Dollars/unit sale price =$ 13000 / 2.50 = 5200 units

3) Profit = (Sales × C/M Ratio) -- Fixed cost $8250 = (Sales × 0.33) -- $ 4290Let Sales = x,$8250 = (X × 0.33) -- $ 4290$ 8250 + $ 4290 = 0.33X = ($8250 + $4280)/ 0.33 X = Sales = $ 38000

E-4

1) Breakeven in units = Fixed Cost / (unit sale price) -- (unit variable cost) =$ 26000 / (45) -- ($3) =26000/2 = 13000 units

2) Breakeven in Dollars = B.E in units × unit sale price = 13,000 × 5 = $ 65000

3) No of units = Sales / Sale price per unit = $ 90,000/$5

= 18000 units

4) Profit = (Sales × C/M Ratio) -- Fixed Cost $ 10,000 = (X × 0.4) -- 26000$ 10,000 + $ 26000 = 0.4XX = 36000/0.4 = $90,000WorkingContribution Margin Ratio = Sale Price -- Variable Cost / Sale price = (20,000units×$5) -- (20,000units×3)/ (20,000units×$5) = (100,000 -- 60,000)/100,000 = 0.4

E-5

1) Margin of safety = (Estimated sales) -- (Breakeven sales) = 2000,000 -- 1500,000 = $ 500,000

2) M/S Ratio = (Estimated Sales) -- (Breakeven Sales)/(Estimated Sales) = 500,000/20, 00,000 = 0.25

E-6

1) Breakeven Sales = Fixed Cost / C/M Ratio = $9300 / 0.62 = $ 15000

2) Actual Sales = Breakeven Sales / (100 -- M/S Ratio) =15,000/ (100 -- 25/100) = 15,000/.75 = $ 20,000

3) Profit = (Sales × C/M Ratio) -- Fixed Cost = ($20,000 × 0.62) – 9,300 = $ 3100

E-7

1) Breakeven Sales = Fixed Cost / C/M Ratio = $ 30, 0000/0.60 = $ 50,000

2) Profit = (Sales × C/M Ratio) -- 30,000 = $ 7500 (Working for actual sales)Actual Sales = Breakeven Sales / (100 -- M/S Ratio/100) = $ 50,000/ (100 -- 20/100) =50,000/0.8 = $ 62500

3) Contribution Margin Ratio = C/M / Sales (Actual)0.60 = C/M / 6, 2500C/M = 6, 2500 × 0.60 = $ 37500

E-8

(CHIP A) (CHIP B)

Units = 100,000 Units = 200,000

Sale price per unit = $4 Sale price per unit = $3

Total sales = (100,000×4) =$400,000 Total Sales= (200,000×3)

=$600,000

Total Variable Cost= (400,000×70/100) Total Variable Coast=

($600,000×80%)

=$280,000 = $ 480,000

Operating profit = $ 140,000

Sale price = $ 400,000 (chip A) + 600,000 (chip B)

= 10, 00,000

Variable Cost = $ 280,000 (chip A) + $ 480,000 (chip B)

= $ 760,000

C/M Ratio = Sale price -- Variable cost / Sale price

= (10, 00,000 -- 760,000) / 10, 00,000

= 240,000/10, 00,000

= 0.24

Profit = (Sales × C/M Ratio) -- Fixed cost

Let, Fixed cost = x

$ 140,000 + ($10, 00,000 × 0.24) -- X

X = 240,000 -- 140,000

Fixed cost = $ 100,000

E-9

Unit cost = Fixed cost + Variable cost(x) / Units given(x)

Unit cost = 1008 + 742 (0.90) / 350 (0.90)

= 1676 / 315

= $ 5.32 / units

E-10

1) Break even in units = Fixed cost / (Unit sale price) -- (Unit variable cost)

= $ 2990 / (100 -- 54)

= 2990 /46

= 65 units

Working

Fixed cost = 990 + 1000 + 1000

= $ 2990

Unit variable cost = Total variable cost / No. of units sold

= (1500 + 1400 + 1000 + 1000 + 500) / 100

= 5400 /100

= $ 54 / units

2) Present operating profit = $ 1,610

Additional sales units = 25C/M per unit (100 – 54) = x 46 1,150

New operating profit $ 2,760

3) Breakeven point in Dollars = (2990+690) / 0.46

= 3680 /0.46 = $ 8000

E-11 Tables Chairs

Sales price per unit ...................................................... $60 $30Variable cost per unit ................................................... 35 20Contribution margin per unit....................................... $ 25 $10

Break Even in Dollars = Fixed cost = $675,000 __ Total C/M ratio {25 + (10x2)} / {60 + (30x2)

= 675,000 = $180,000 45/120

Break even in units = Fixed Cost = $675,000__ = 15,000 units Total C/M 25 + (2x10)

E-12

Product Sale price Variable cost Sale mix

Per unit per unit

L 20 12 2

M 15 10 3

Product L Product MSales price per unit $20 $15Variable cost per unit 12 10Unit contribution margin $ 8 $ 5Sales mix × 2 × 3Contribution margin $16 + $15 = $31

(1) Break even in units = Fixed Cost = $372,000 = 12,000 units Total C/M $31

12,000 × 2 units of L = 24,000 units of L12,000 × 3 units of M = 36,000 units of M

24,000 × $20 = $ 480,000 sales of L36,000 × $15 = $ 540,000 sales of M

Break-even sales = 480,000 + 540,000 = $1,020,000

(2) Fixed cost + Profit = 372,000 + 93,000 C/M 31

= 15,000 units to achieve profit at $93,000

15,000 × 2 = 30,000 units of L15,000 × 3 = 45,000 units of M30,000 × $20 = $ 600,000 sales of L45,000 × $15 = $ 675,000 sales of M

Sales to achieve profit = 600,000 + 675,000 = $1,275,000

E-13Expected sales (a) Low sale increase (b) high sale increase

50,000 units 52,000 units 80,000 unitsPer unit total per unit total per unit total

Sales $10 $500,000 $9 $468,000 $9 $720,000Total variable costs 6 300,000 5.9 306,800 5.9 472,000

C/M $4 $200,000 $ 3.10 $161,200 $3.10 $248,000

Increase in Fixed CostManufacturing+ non manufacturing $6,000 (5,000 + 1,000)

Contribution to other fixed cost And to income before incomeTax $200,000 $161,200 $242,000

E-14

1) Breakeven is that point where: Total sales = Total cost so as to arrive at profit = 0 Therefore total sales in this case = $ 455,000Sale price charged = Total sales / No. of units = $ 455,000 /70000 = $ 6.5 / units

1) Fixed cost __________ = ($80,000 + $60,000)

Price per unit – v.c per unit – profit per unit $8 – $4.50 – (10% × $8)

= 51,852 units

2) Fixed cost __________ = ($100,000 + $60,000) Price per unit – v.c per unit – profit per unit $8 – $4.50 – (15% × $8)

= 69,565 units

E-15 See book page 613, and get help from class teacher.

PRPBLEMS

P-1

Capital LaborIntensive Intensive

Sales price $30 $30Variable costs:Materials $5 $5.60Direct labor 6 7.20Variable factory overhead 3 4.80Variable marketing expenses 2 16 2 19.60 Contribution margin per unit $14

$10.40

1) (a) Capital-intensive manufacturing method; Break even unit

Fixed factory overhead $2,440,000Fixed marketing expenses 500,000Total fixed cost $2,940,000

Total Fixed cost= 29,40,000 = 210,000 Units C/M 14

(b) Labor-intensive manufacturing method; break even units

Fixed factory overhead $1,320,000Fixed marketing expenses 500,000Total fixed cost $1,820,000

Total Fixed cost= 218,20,000 = 175,000 Units C/M 10.40

2) Kimbrell Company would be indifferent between the two alternative manufacturing methods at the volume of sales for which total cost was equal under both alternatives. Let X equal the quantity of units of product manufactured and sold.

($16 × X) + $2,940,000 = ($19.80 × X) + $1,820,000$2,940,000 – $1,820,000 = ($19.60 × X) – ($16 × X)$1,120,000 = $ 3.60 × X311,111 = XTotal cost will be the same for both manufacturing methods at 311,111 units of sales.

P-2

1) Break Even in units = $468,000/$25 -- $19.8 = 90,000 units2) Sales in units for profit $156,000 after tax

= $468,000 + ($156,000/0.60) = $728,000= 140,000 units$5.20 $5.20

3) Break even in units with increase in labor cost by 8%

= $468,000_________ = $468,000= 97,500 units $25 – {$19.80 + ($5 x 8%)] $4.80

4) Unit sale price to maintain same C/M ratio if direct labor cost increase 8%

$5.20 = 0.208 original C/M ratio $ 25

Let new sale price per unit = X

0.208= X – [$19.80 + ($5 x 8%) X

Solve for X

New sale price per unit = $25.51

P-3 1) Break even sale = $25,600__________ = $25,600 = $25,600 = $80,000

1-- $187,000/$275,000 1 – 0.68 0.32

orSales $275,000Variable cost 187,000

C/M $ 88,000

C/M ratio = $88,000/$275,000 = 0.32 or 32%

2) Chesterton Inc.

Projected statement of gross profitFor the year 19B

$Sales [$275,000 + (15,000 x 2.45) 311,750Cost of goods sold:Materials (115,000 x 0.78) $89,700Labor (115,000 x 0.60) 69,000Variable F.O.H (115,000 x 0.43) 49,450Fixed F.O.H ($25,600 + $5,000) 30,600 238,750

Gross Profit $ 73,000

3) Break even sales = $30,600 ____ = $30,600__ = $30,600

1 -- $208,150/$311,750 1 – 0.6677 0.3323 = $92,085

Or Sales $311,750Variable cost 208,150

C/M $103,600

C/M ratio = $103,600/$311,750 = 0.3323 or 33.23%

P-4

1) Break even units at sales price per unit $38.50:

Variable costs:Direct materials $ 60,000Direct labor 40,000Variable factory overhead 20,000Variable marketing and administrative expenses 10,000 Total variable costs $130,000

$30,000 + $15,000 = $45,000 = 3,600 units $38.50 -- $26* $12.50

*$130,000 ÷ 5,000 units = $26 variable cost per unit

2) Units that must be sold to produce an $18,000 profit, at a $40 per unit sales price.

= $45,000 + $18,000 = $63,000 = 4,500 units $40 -- $26 $14

3) The price Castleton must charge at a 5,000-unit sales level, in order to producea profit equal to 20% of sales:

Let x = sales price per unit

5,000x = 5,000($26) + $45,000 + 5,000 (.2x)

4,000x = $175,000

x = $43.75 sales price per unit

P-5

1) Fixed cost and variable cost per sale dollar:

April and May

$59,990 -- $56,000 = $3,990 = $0.57 variable cost per sale dollar$77,000 -- $70,000 $7,000

May and June

$64,550 -- $59,990 = $4,560 = 0.57 variable cost per sales dollar$85,000 -- $77,000 $8,000

Fixed Cost = $64,550 – ($85,000 x 0.57) = $64,550 -- $48,450 = $16,100

2) C/M ratio= 1 – 0.57 = 0.43 or 43%

3) Break Even point = $16,100/0.43 = $37,442

4) July Profit if sale are $79,000

P = (S x C/M) – FCP = ($79,000 x 0.43) -- $16,100P = $17,870

5) August sales if the month’s loss is $1,050

= $16,100 -- $1,050/0.43 = $15,050/0.43 = $35,000

P-6

1) Break even units - whistles = $2,000/$1 -- $0.60 = $2,000/$0.40

= 5,000 units

2) Break even dollars – bells = $5,600___ = $5,600 = $8,000 1 -- $3,000/$10,000 1 – 0.3

3) Whistles BellsSale price per unit $1 $1.250Variable cost per unit 0.60 0.375

Unit C/M $0.40 $0.875Units x 4 x 3

Total C/M $1.60 $2.625

Composite unit C/M = $1.60 + $2.625 = $4.225

4) Break even – whistles = $7,600/$4.225 x 4 = 7,196 units

Break even – Bells = $7,600/$4.225 x 3 = 5,397 units\

5) Whistles Bells totalSale price per unit $1 $1.250$2.250Variable cost per unit 0.60 0.375 0.975

Unit C/M $0.40 $0.875 $1.275

Composite C/M ratio = $1.275/$2.250 = 0.57

6) Break Even point = $7,600/0.57 = $13,333

P-7

1) Sales mix in units is 1:2 i.e Tape recorders = 70,000 units then electronic calculators will be 70,000 x 2 = 140,000

Let x = number of tape recorders at break even and 2x = number of electronic calculators at break even

At Break Even point:

Sales = Fixed cost + Variable cost

15x + 2($22.50x) = $13,20,000 + $8x + 2($9.50x)

Solve for x = 40,000 tape recorders

2x = 80,000 electronic calculators

Fixed cost = $280,000 + 10,40,000 = $13,20,000

2) S = VC(S) + FC + _ P(S____

1 -- T

S = 0.46(S) + 13,77,000 + 0.09(S) 1 – 0.55

S = 0.46(S) + 13,77,000 + 0.2(S)

Solve for S = $40,50,000

Working:

VC = Variable cost % Tape Recorders Electronic Calculators Per unit % Per Unit %

Sales $15 100% $20 100%Variable costs:Materials 3.60 3.60Labor 2.20 3.30F.O.H 2 2___

Total variable costs $ 7.80 52% $8.90 44.5%C/M $ 7.20 48% $11.10 55.5%

Composite VC %

(0.20 x Tape recorder VC rate) + (0.80 x Calculator VC rate) = 0.20(0.52) + 0.80(0.445) = 0.46 or 46%

FC = Fixed Costs:F.OH $280,000Marketing and admin 10,40,000Additional advertising 57,000

Total $ 13,77,000

3) Let X = number of tape recorders at break even 3X = number of electronic calculators at break even

We know that:

Sales = VC + FC at break even

Then

$15X + 3($20X) = $7.80X + 3($8.90X) + $13,77,000

Solve for X = 34,000 units of tape recorders

And 3X = 102,000 units of electronic calculators

P-8

1) Break even in units = 100,000 x ($0.25 + $0.65) = 45,000 units $5 – ($1 + $2)

2) (a) Operating Income Direct Costing:

Sales (110,000 x $5) $550,000Variable C.G.S (110,000 x $1) 110,000

Gross C/M $440,000Variable marketing cost (110,000 x $2) 220,000

C/M $220,000Less: Fixed CostsManufacturing $25,000Marketing 65,000 90,000

Operating income $130,000

(b) Operating Income Absorption Costing:

Sales (110,000 x $5) $550,000Cost of goods sold (110,000 x $1.25) $137,500Fixed F.O.H over applied [(100,000 – 120,000) x $0.25] 5,000 Adjusted cost of goods sold $132,500

Gross profit $417,500Marketing expenses (110,000x2)+(100,000x.65) 285,000

Operating Income $132,500

3) Let X = price per unit to charge on special order

10,000X = 10,000 ($1+$2) + $5,000Solve for X = $3.50

4) Let X = Required number of units to generate 10% profit of C/M

X = $104,400 + 0.1($2.90)X$2.90

Solve for X = 40,000 units

Working:

Sale price ($5 + 20%) $6Variable manufacturing cost per unit ($1+10%) $1.10Variable marketing cost per unit 2__

$3.10C/M per unit $2.90

P-9 skipped

P-10 (1) (2) (3)

8% price cut 15% price cut & 20% volume & 40% volume

19A Increase Increase Units 937,500 11,25,000 13,12,500Sale price per unit $5 ` $4.60 $4.25Total sales $46,87,500 $51,75,000 $55,78,125Variable cost per unit $2.40 $2.40 $2.40Total variable cost $22,50,000 $27,00,000 $31,50,000

C/M $24,37,500 $24,75,000 $24,28,125Fixed cost $20,00,000 $20,00,000 $20,00,000

Operating income $437,500 $475,000 $428,125 __

P-11 skipped

P-12(1) (a) (b)

XV-7 BD-4Sale price per unit $4__ $3__Variable cost:Manufacturing $2 $1.5Marketing 1__ 1__

Total variable cost $3__ $2.5C/M $1 $0.5

$160,000/$1 = 160,000 units$160,000/$0.5 = 320,000 units160,000 x $4 $640,000 sales320,000 x $3 $960,000 sales

(2) (a) (b)XV-7 BD-4

C/M per unit $1 $0.5100,000/0.75 133,333 units100,000/0.20 500,000 units

C/M increase = C/M x units $133,333 $250,000