MA1 2007-2008

MANAGEMENT ACCOUNTING

MODULE 4

COST-VOLUME-PROFIT ANALYSIS – KEY FORMULAS Operating income (before tax):

SPx – VCx – FC = P

Contribution margin:

SP-VC=CM

Contribution margin ratio:

CM SP

Breakeven in units:

FC =x CM

Breakeven in sales dollars:

FC =Y CM ratio

Unit sales to reach target before tax operating income:

FC + P =x CM

Unit sales to reach target after tax operating income:

PAT FC + (1-T) CM

Sales dollars to reach target before tax operating income:

FC + P =Y CM ratio

=CM ratio

=x

Cost-volume-profit analysis variables P

Before tax profits (operating income)

PAT

After tax profits (after tax operating income)

SP

Selling price per unit

VC

Variable cost per unit

FC

Fixed costs

x

Number of units

CM

Contribution margin (SP-VC)

CM ratio

CM/SP

Y

Total sales dollars

T

Tax rate

-1-

ma1_mod4_handout1.doc

MA1 2007-2008

MANAGEMENT ACCOUNTING

MODULE 4

PART 6 Slides 70 – 72: Question 4 December 1992 Omego Enterprises Ltd., has estimated the following costs for producing and selling 8,000 units of their product. Direct materials Direct labour Variable overhead Fixed overhead Variable selling and administrative expenses Fixed selling and administrative expenses

$ 32,000 40,000 20,000 30,000 24,000 33,000

Omego’s income tax rate is 30%.

REQUIRED: (a) Given that the selling price of one unit is $35.00, how many units would Omego have to sell in order to break even? (b) At a selling price of $37.50 per unit, how many units would Omego have to sell in order to produce a profit of $22,000 before taxes?

(c) If 7,500 units were produced and sold, what price would Omego have to charge in order to produce a profit of $28,000 after taxes? (d) If 9,000 units were produced and sold, what price would Omego have to charge in order to produce a before-tax profit equal to 30% of sales?

-2-

ma1_mod4_handout1.doc

MA1 2007-2008

MANAGEMENT ACCOUNTING

MODULE 4

Question 4 December 1992 Solution (a)

Variable costs Direct materials Direct labour Variable overhead Variable selling

Total 32,000/8,000 40,000/8,000 20,000/8,000 24,000/8,000

SP(X) - VC(X) - FC 35(X) - 14.50(X) - 63,000 20.50(X) X

= 0 = 0 = 63,000 = 3,073.17

Per unit = 4.00 = 5.00 = 2.50 = 3.00 14.50

=

3,073 units or 3,074 units

Some texts/exams suggest this solution would be 3,073 units. But, by selling 3,073 units or less you will not break even. SO, tell the marker why you are rounding up.

(b)

37.50(X) 23(X)

-

14.50(X)

-

63,000

= 22,000 = 85,000 = 3,695.65 or 3,696 units

X

(c)

[ 7,500(SP) 7,500(SP) 7,500(SP) Selling Price

(d)

9,000(SP) 9,000(SP) 6,300(SP) Selling Price

7,500(14.50) 108,750

-

-

9,000(14.50) 130,500

63,000 ] 63,000

-

-3-

63,000 63,000

= 28,000 /(1-.3) = 40,000 = 211,750 = $28.23 = .30(9,000SP) = 2,700(SP) = 193,500 = $30.71

ma1_mod4_handout1.doc

MA1 2007-2008

MANAGEMENT ACCOUNTING

MODULE 4

PART 6 Slides 73-74: Question 5 December 2005 Warton Ltd. is considering replacing an existing machine with a new and faster machine that will produce a more reliable product (that is, better tolerances). The switch to a new machine resulting in a superior product is expected to allow Warton to increase its sales price for the product. The switch will increase fixed costs, but not the variable costs. The cost and revenue estimates are as follows: Cost Item Monthly fixed costs Variable cost per unit Sales price per unit

Old Machine $120,000 14 18

New Machine $250,000 14 20

Required a. Determine the break-even point in units for the two machines. b. Determine the sales level in units at which the new machine will achieve a 10% target profit-tosales ratio (ignore taxes). c. Determine the sales level at which profits will be the same for either the old or new machine. d. Which machine represents a lower risk if demand is uncertain? Explain.

Solution a)

Old machine: BEP units New machine: BEP units

(b)

20(X)

6X 4X X

(c)

4(X) 2X X

-

(d)

If demand is uncertain, the old machine represents less risk because of its lower fixed costs. In this case, it is not the variable cost per unit that is reduced by the new machine but rather the selling price per unit which has increased.

14(X)

120,000

–

= =

120,000/(18 – 14) 250,000/(20 – 14)

250,000 250,000

= = =

= = = =

= =

30,000 units 41,667 units

.10(20X) 2X 250,000 62,500 units

6(X) - 250,000 130,000 65,000 units

However, the effect is the same — the contribution margin per unit is increased with the new machine at the “Cost” of higher fixed costs. This is an example of operating leverage. For every unit short of the break-even point, the new machine results in a greater loss per unit, and for every unit past the break-even point, the new machine results in a greater profit per unit. Also notice that the break-even point is higher with the new machine than the old machine.

-4-

ma1_mod4_handout1.doc

MA1 2007-2008

MANAGEMENT ACCOUNTING

MODULE 4

PART 7 Slides 76 – 78: Question 3 March 1994 The company you work for as a managerial accountant engages independent agents to sell the company’s products. These agents are currently being paid a commission of 15% based on sales price but are asking for an increase to 20% of sales made during the coming year. You had already prepared the following pro-forma income statement for the company based on the 15% commission. Dry Rot Corporation Pro-forma Income Statement For the year ending April 30, 1995 Sales Cost of goods sold (all variable) Gross profit Selling and administrative: Variable (commission only) Fixed Income before taxes Income tax expense (25%) Net income

$ 1,000,000 600,000 400,000 $ 150,000 10,000

160,000 240,000 60,000 $ 180,000

Management wants to examine the possibility of employing the company’s own sales people. They believe they will need a sales manager at an annual salary of $60,000 and three salespeople at an annual salary of $30,000 each plus a commission of 5% of sales. All other fixed costs as well as the variable cost percentages would remain the same as in the above pro-forma statement. REQUIRED a. Based on the pro-forma income statement you have already prepared, what is the breakeven point in sales dollars for Dry Rot for the year ending April 30, 1995? b. If Dry Rot employs its own salespeople, what would be the breakeven point in sales dollars for the year ending April 30, 1995? c. What would be the volume of sales dollars required for the year ending April 30, 1995 to yield the same net income as projected in the pro-forma income statement if Dry Rot continues to use the independent sales agents and agrees to their demand for a 20% sales commission? d. Compute the estimated sales volume in sales dollars that would generate an identical net income for the year ending April 30, 1995 regardless of whether Dry Rot employs its own salespeople or continues to use the independent sales agents and pays them a 20% commission.

-5-

ma1_mod4_handout1.doc

MA1 2007-2008

MANAGEMENT ACCOUNTING

MODULE 4

Question 3 March 1994 Solution a)

BEP ($)

=

FC/CM ratio =

10,000/.25 =

$40,000

To determine the CM ratio, you must determine the contribution margin first. Sales = Var. COGS = Commissions Contribution margin b)

1,000,000 ( 600,000) ( 150,000) 250,000

CM ratio = 250,000/1,000,000 = .25

Var. COGS = Commissions =

60% Fixed costs = sales manager 5% 3 sales people 65% admin costs Contribution margin ratio = 100 – 65 = 35% BEP ($)

=

160,000/.35

=

= 60,000 = 90,000 = 10,000 160,000

457,142.86 = $457,143

c)

Sales dollars = (FC + NIBT)/CM ratio = (10,000 + 240,000)/.20 = $1,250,000

d)

X = sales volume in dollars where you’d be indifferent AGENTS = OWN sales people X -.80X + 10,000 = X - .65X + 160,000 .2X + 10,000 = .35X + 160,000 .15X = 150,000 X = $1,000,000

-6-

ma1_mod4_handout1.doc

MA1 2007-2008

MANAGEMENT ACCOUNTING

MODULE 4

PART 7 Slides 79 – 80: Question 3 March 2005 (14 marks) Timeworks Inc. produces two lines of clocks — standard and deluxe. Cost and revenue data are shown below: Standard $ 30

Deluxe $ 50

9 7 3 2 $9

15 10 5 2 $ 18

Percentage of total unit sales 70% Total contribution margin $504,000 Fixed manufacturing costs (total for both lines of clocks combined) Administrative Net income

30% $432,000

Selling price (per clock) Variable costs (per clock) Direct materials Direct labour Overhead Selling Contribution margin (per clock)

Total expected sales in units (both lines of clocks combined) Capacity (both lines of clocks combined)

$ 936,000 400,000 325,000 $ 211,000 80,000 100,000

Required The following three cases are independent, but are based on the above information in the question. 6

a.

The company is considering steps to increase sales, particularly of the deluxe model. It is considering increasing advertising by $200,000 and increasing the sales commission on the deluxe clock by $2 per clock. Management believes that these steps will increase total sales to 95,000 clocks and increase the proportion of deluxe models sold to 40%. Calculate the new net income if both changes were implemented and the resulting sales were as predicted.

6

b.

The management of Timeworks is considering purchasing new equipment that will reduce direct materials and direct labour costs by 20% for both products. The new equipment would increase fixed manufacturing costs by $175,000, reflecting the amortization on the new equipment. Calculate the total sales volume that must be achieved in order for the purchase of the new equipment to have a positive effect on net income. Assume the mix of sales would be unaffected.

2

c.

A wholly-owned subsidiary of Timeworks purchases standard clocks for use in its own production process. Sales to the subsidiary do not incur selling expenses. What is the minimum price that Timeworks should charge the subsidiary for each of its standard clocks, assuming that Timeworks has sufficient capacity to supply both the outside demand and the needs of the subsidiary.

-7-

ma1_mod4_handout1.doc

MA1 2007-2008

MANAGEMENT ACCOUNTING

MODULE 4

Question 3 March 2005 Solution 6

a.

Standard model Contribution margin per clock $9.00 New sales level 95,000 × 0.6 = 57,000 clocks New total contribution margin from the standard model (57,000 × $9) = Deluxe model New contribution margin per clock $18 – $2 = $16.00 New sales level 95,000 × 0.4 = 38,000 clocks New total contribution from the deluxe model (38,000 × $16) = Total contribution margin Less fixed costs ($400,000 + $325,000 + $200,000) = New net income

6

b.

$ 513,000

608,000 1,121,000 925,000 $ 196,000

The indifference point for the purchase of the new equipment will be the sales volume at which the net income with the new equipment equals the net income with the old equipment. Let the sales volume equal X: .70X(12.2) + .30X(23) - (400,000 + 325,000 + 175,000) 8.54X + 6.9X X X

= 211,000 = 1,111,000 = 71,955.95855 = 71,956 rounded

Calculations: Standard: 30 – (7.2 + 5.6 + 3 + 2) = 12.2 Deluxe: 50 – (12 + 8 + 5 + 2) = 23 If the total sales volume will be 71,956 units or more in the 70/30 mix, the net income with the new equipment will be greater than the net income with the old equipment. 2

c.

The minimum price that Timeworks should charge to its wholly-owned subsidiary is simply the variable costs of production: $9.00 + $7.00 + $3.00 = $19.00.

-8-

ma1_mod4_handout1.doc

MA1 2007-2008

MANAGEMENT ACCOUNTING

MODULE 4

PART 8 Slides 81-82: Question 4 June 2007

Jazz Dance Shoes makes 3 different types of shoes: ballroom shoes, tap shoes, and ballet shoes. Production data for the month of March indicates the following costs: Tap Shoes 6,000 pairs

Ballet Shoes 3,000 pairs

$ 30,000 $ 60,000 $ 6,000 $ 72,000

$ 24,000 $ 54,000 $ 5,400 $ 90,000

$ 21,000 $ 33,000 $ 3,300 $ 33,000

Fixed costs: Fixed factory overhead $ 200,000 Fixed selling and administration costs $ 50,000 Unit selling prices $ 120

$ 600,000 $ 50,000 $ 150

$ 350,000 $ 50,000 $ 110

Units produced and sold

Ballroom Shoes 6,000 pairs

Costs for the month of March: Direct labour Direct materials Variable overhead Variable selling and administration

Required a. Using the weighted-average contribution margin method, calculate the break-even point for the company as a whole. Show your calculations. State your answer in pairs of shoes of each type. b. How many pairs of each type of shoe would have to be sold to achieve a target after-tax profit of $1,000,000, assuming the corporate tax rate was 40%? c. What is the margin of safety in part (b)? State it in terms of each type of shoe sold.

-9-

ma1_mod4_handout1.doc

MA1 2007-2008

MANAGEMENT ACCOUNTING

MODULE 4

Question 4 June 2007 Solution

a. Add the costs and revenues for the production of all 3 shoes together. Units (in pairs)

Ballroom Shoes Tap Shoes Ballet Shoes 6,000 6,000 3,000

Revenue Total variable costs Contribution margin

$ 720,000 168,000

$ 900,000 173,400

Fixed costs

$ 250,000 $ 650,000

Total 15,000

Per unit

$ 330,000 $ 1,950,000 90,300 431,700 $ 1,518,300 $101.22 $ 400,000 $ 1,300,000

Weighted-average break-even point: X = 1,300,000 / 101.22 = 12,844 pairs, of which 6,000 / 15,000 × 12,844 = 5,138 pairs are ballroom shoes, 5,138 pairs are tap shoes, and [12,844 – (5,138 × 2)] = 2,568 pairs are ballet shoes. b. Profit before tax = $1,000,000 / 0.6 = $1,666,667 Weighted-average number of pairs: X = (1,300,000 + 1,666,667) / 101.22 = 29,310 pairs, of which 6,000 / 15,000 × 29,310 = 11,724 pairs are ballroom shoes, 11,724 pairs are tap shoes, and 5,862 pairs are ballet shoes. c. Margin of safety is: 29,310 – 12,844 = 16,466 pairs of shoes, of which 6,586 are ballroom shoes, 6,586 are tap shoes, and 3,293 are ballet shoes.

-10-

ma1_mod4_handout1.doc

MA1 2007-2008

MANAGEMENT ACCOUNTING

MODULE 4

PART 9 Slides 84-86: Multiple Choice Questions - Module 4 Q1.

ABC Manufacturing produces and sells Xenon. During the year 2000, Xenon had sales of $500,000, a contribution margin of 20%, and a margin of safety of $200,000. What is Xenon’s fixed cost? 1) 2) 3) 4)

$ 60,000 $100,000 $120,000 $200,000

USE the formulas you have learned based on the information given in the question. Total sales - breakeven sales = Margin of Safety 500,000 X = 200,000

December 1999 exam: answer 1)

Q2.

Breakeven sales Variable costs (80%) Contribution margin Fixed costs Net income

= = = = =

300,000 (240,000) 60,000 (60,000) 0

Upsilon Co., a manufacturer of widgets, had the following data for 2000: Sales Sales price Variable costs Fixed costs

2,400 units $40 per unit $14 per unit $19,500

If the company wishes to increase its total dollar contribution by 40% in 2001, all other factors remaining constant, by how much will it need to increase its sales? 1) 2) 3) 4)

$ 17,160 $ 24,960 $ 26,400 $ 38,400

If CM increases 40%, then sales must increase 40%. Sales will increase: (2,400 x $40) x 40% = 38,400

June 2000 exam: answer 4) Q3.

Monthly transportation costs at RFP Ltd. were $18,000 for 16,000 kg transported in July and $22,500 for 22,000 kg transported in August. If the company plans to transport 18,000 kg in September, what is the expected shipping cost? 1) $18,500 2) $19,500 3) $20,400 4) $24,000

Use the high low method Cost = (22,500 – 18,000)=4,500 Weight = (22,000 – 16,000) = 6,000 4,500/6,000=.75 per kg FC = 22,500 - .75(22,000) = 6,000 Shipping cost = 6,000 + .75(18,000) = 19,500

March 2005 exam: answer 2)

-11-

ma1_mod4_handout1.doc

MA1 2007-2008

MANAGEMENT ACCOUNTING

MODULE 4

PART 9 Slides 84-86: Multiple Choice Questions (continued) Q4.

Which of the following statements concerning the high-low method of mixed cost analysis is true? 1) The high-low method of mixed cost analysis provides the best fit for all of the data. 2) The high-low method of mixed cost analysis always shows the fixed cost component of mixed costs to be zero. 3) The high-low method of mixed cost analysis can be influenced by extreme values or outliers. 4) The cost formula resulting from the high-low method of mixed cost analysis is based on least squares. December 2000 exam: answer 3)

Q5.

Chang Company has 2 divisions, True and West. The company’s overall contribution margin ratio is 40% when combined sales in the 2 divisions total $900,000. If variable costs are $200,000 in Division True, and if Division West’s contribution margin ratio is 20%, what must be the sales in Division West? 1) 2

$ 200,000 $ 340,000

True Sales

3) 4)

$ 425,000 $ 700,000

(VC) CM

December 2000 exam: answer 3)

200,000

(340,000) .20X

2

Total 900,000 ( 540,000)

1

Calculations: JUST fill in what you need. 1 2

900,000 x 60%

= 540,000

540,000 - 200,000

= 340,000

X - 340,000 .80X X Q6.

West X

= = =

.20X 340,000 425,000

Dabbler Co. has two divisions, A and B. Dabbler’s overall contribution margin is 30%, and combined sales in the two divisions total $500,000. If variable expenses in Division A are $300,000 and Division A’s contribution margin ratio is 25%, then what are sales in Division B? 1)

$ 50,000

2) 3) 4)

$ 100,000 $ 150,000 $ 200,000

Div A Sales (VC) CM

1

400,000 100% 300,000 ( 75%) 25%

March 2005 exam: answer 2)

Div B X

2

Total 500,000

Calculations: JUST fill in what you need. 1

75%(Sales of Div A) Sales of Div A

= 300,000 = 400,000

2

Total Sales – Div A Sales = Div B Sales Div B Sales = 500,000 – 400,000 = 100,000

-12-

ma1_mod4_handout1.doc

MA1 2007-2008

MANAGEMENT ACCOUNTING

MODULE 4

PART 9 Slides 84-86: Multiple Choice Questions (continued) Q7. Salxom Ltd. had the following results for the year: Sales Less: Variable costs Contribution margin Less: Fixed costs Net operating income

$ 45,000 27,000 18,000 12,000 $ 6,000

The average selling price for the units sold was $15 per unit. If sales decrease by 500 units, by how much will fixed expenses have to be reduced to maintain the current net operating income of $6,000? 1) 2) 3) 4)

$ 2,000 $ 3,000 $ 3,600 $ 5,000

March 2002 exam: answer 2)

First we need to determine how many units were sold originally. $45,000/15 = 3,000 units. Reduction of 500 units means sales of 2,500 units VC = 27,000/3,000 = $9 per unit CM = 6 per unit CM - FC = Net income 6(2,500) - FC = 6,000 Fixed costs = 9,000 THEREFORE, the reduction in FC = 3,000

Q8. Dally Co. has a break-even point of 4,000 units. At that break-even point, variable costs are $4,000 and fixed costs are $2,000. What is the contribution margin of the 401st unit sold? 1) 2) 3) 4)

$ 0.50 $ 1.00 $ 1.50 $ 2.00

It is the same as for all other units! So what is the CM? BEP (units)

=

4,000

=

March 2002 exam: answer 1) 4,000(SP – 1.00) SP – 1.00 SP

Fixed Costs CM per unit 2,000 SP – 1.00 = 2,000 = .50 = 1.50

Contribution margin per unit = SP – VC = 1.50 – 1.00 = .50 Q9. Seamless Gutter Co. sells 10-metre sections of gutter for $12.00. Unit variable costs per section are $8.80. Fixed costs total $4,800. How many sections must be sold to earn an after-tax income of $4,000 if the tax rate is 40%? [FC + (after tax inc/(1-tax rate))]/CM 1) 3,000 sections [$4,800 + (4,000/(1-.4))]/($12-$8.80) 2) 3,300 sections . 3) 3,583 sections 4) 3,800 sections = 3,583.33 March 2002 exam: answer 3)

-13-

ma1_mod4_handout1.doc

MA1 2007-2008

MANAGEMENT ACCOUNTING

MODULE 4

PART 10 Slides 88-89: Multiple Choice Questions Q10.

Gorge Mfg. produces two products, X and Y. The following information is presented for both products: X Y Selling price per unit $9 $6 Variable cost per unit 7 3 Total fixed costs are $117,000. What will the breakeven point be for Gorge in units of X and Y if the ratio of sales is expected to be 3X:1Y? 1) 2) 3) 4)

X = 13,000 units: Y = 13,000 units X = 26,000 units: Y = 78,000 units X = 39,000 units: Y = 13,000 units X = 78,000 units: Y = 26,000 units

June 2003 exam: answer 3) Q11.

X = number of units of Y to breakeven 3X = number of units of X to breakeven 3X ($2) + X ($3) - 117,000 = 0 9X = 117,000 X ( # units of Y ) = 13,000 units 3X ( # units of X ) = 39,000 units

June 2002 exam: Parts (a) and (b) refer to the following information: Belton Company operated at normal capacity during the current year, producing 50,000 units of its single product. Sales totalled 40,000 units at an average price of $20 per unit. Variable manufacturing costs were $8 per unit, and variable marketing costs were $4 per unit sold. Fixed costs were incurred uniformly throughout the year and amounted to $188,000 for manufacturing and $64,000 for marketing. There was no year-end work in process inventory.

(a) What is Belton’s break-even point in sales dollars for the current year? 1) 2) 3) 4)

$ 420,000 $ 470,000 $ 630,000 $ 732,000

SP = VC = CM BEP $

answer 3)

20 (12) 8

100% ( 60) 40%

= Fixed Costs / CM ratio = 252,000 / 40% = 630,000

(b) If Belton’s variable manufacturing costs unexpectedly increase by 10%, what is the new unit selling price that would yield the same contribution margin ratio as before the cost increase (rounded to the nearest cent)? 1) 2) 3) 4)

$ 20.00 $ 20.67 $ 21.00 $ 21.33

Only the variable manufacturing costs increase. New VC = (8 x 1.10) + 4.00 = 12.80 SP (12.80) CM

answer 4)

=

100% 60% 40%

New selling price: 60% (SP) = 12.80 SP = $ 21.33

-14-

ma1_mod4_handout1.doc

MA1 2007-2008

MANAGEMENT ACCOUNTING

MODULE 4

PART 10 Slides 88-89: Multiple Choice Questions (continued) Q12.

Ceta Ltd. manufactures top-quality lacrosse sticks. The selling price per stick is $160 and the variable cost per stick is $95. The sales volume of $1,552,000 is necessary to produce a net income of $201,500 before taxes. What are Ceta’s total fixed costs? 1) 2) 3) 4)

$201,500 $429,000 $535,000 $635,500

June 2003 exam: answer 2) Q13.

SP(X) - VC(X) - FC 1,552,000 - 95(9,700) - FC 1,552,000 - 921,500 - FC Fixed Costs

NIBT 201,500 201,500 429,000

To calculate the number of units: 1,552,000/160 = 9,700

If fixed expenses were to double and contribution margin ratio per unit were to double, what would the effect be on the break-even point? 1) 2) 3) 4)

The break-even point would be reduced to half. USE NUMBERS – don’t guess! The break-even point would not change. BEP = FC/Contrib margin per unit The break-even point would double. = 10,000/(20 – 10) The break-even point would quadruple. = 1,000 units

December 2004 exam: answer 2) Q14.

= = = =

Double it…. BEP = 20,000/(40 – 20) = 1,000 units

June 2004 exam: Parts (a) and (b) refer to the following information: The following data is for the Liu Company, a manufacturer of ball-point pens: Income tax rate 40% Selling price per unit $2.75 Variable cost per unit $2.20 Total fixed costs $115,000

(a) How many units must Liu Co. sell to earn an after-tax income of $30,000? 1) 2) 3) 4)

30,000 units 55,000 units 155,000 units 300,000 units

[FC + (after tax inc/(1-tax rate))]/CM [115,000 + (30,000/(1-.4))]/(2.75-2.2) . = 300,000 units

answer: 4) (b) If total fixed costs doubled and contribution margin per unit was cut in half, what would happen to the break-even point? 1) 2) 3) 4)

It would decrease by half. It would double. It would triple. It would quadruple.

Fixed Costs CM/unit BEP

answer: 4)

-15-

Now 100 10

Change 200 5

100/10 = 10

200/5 = 40

ma1_mod4_handout1.doc