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Selected Exercises in preparation of Question 3 on BA
6601 (Section 9) Compressive Exam
Question 1
The Atkins Company manufactures and sells one product. The sales price, $30 per unit, remains constant regardless of
volume. Last years sales were 15,000 units and operating profits (Profit before tax) were $200,000. Fixed costs depend
on production levels, as the following table showed. Variable cost per unit are 40 percent higher for level 2 (day and
night shift) than for level 1 (day shift only). This is because additional labour costs result primarily from higher wages
required to employ workers for the night shift.
Annual production range (in units) Annual total fixed costs
Level 1 (Day shift) 0 - 20,000 $ 100,000
Level 2 (Day and night shifts) 20,001 - 36,000 (Max capacity) $ 164,000
Atkins expects last years cost structure and selling price not to change in this year. The company is able to sells all unit it
produces.
Required :
1. Compute the contribution margin per unit for last year for day and night shift.
2. Compute the break-even points in units for last year for each of the two production level.
3. Compute the volume in units that will maximise operating profits.
Question 2
The leaded Bottoms Company manufactures kewpie dolls for carnivals and sells them for $2 per kewpie. The variable
costs of manufacturing and selling are $1.00 and $0.25 per kewpie, respectively. The fixed costs are based upon the
following ranges of activity.
Range of Activity Fixed costs
0 - 40,000 kewpies $ 35,000
40,001 - 75,000 kewpies 50,000
75,001 - 125,000 kewpies (maximum capacity) 70,000
During this year Leaded Bottoms produced and sold 45,000 kewpies.
Required :
1. Determine the net income for Lead Bottoms for this year.
2. How many additional units (above the 45,000) would Leaded Bottoms need to sell in order to break- even if the additional units will be sold for only $1.90 ?
3. How many additional units (above the 45,000) would Leaded Bottoms need to sell in order to generate a profit of $6,000 if the additional units will be sold for only $1.90 ?
4. What is the maximum profit that could be earned by Leaded Bottom [disregard (2) and (3)]?
5. Leaded Bottoms wants to produce and sell 85,000 units but does not want to incur any additional fixed costs. The company production supervisor decided to pay double time for labour in order to produce the 10,000 kewpies above the second range of activity. If the labour costs are three-fourths of the variable manufacturing costs, determine the profit that the company should earn.
6. For the next year , it is proposed to add another product line (product Y) whose selling price
would be $ 3 per unit with a variable cost ratio of 60 percent. Total fixed costs for production of
both product X and Y are not subjected to step fixed cost scheme but it is collectively
estimated at $100,000. The sales mix of X : Y would be 7 : 3. The company is subjected to an
income tax level of 30 percent. At what level of sales (in dollar) next year would the company
achieve target profit after tax amount of $14,000 ?
Question 3
Bell Bang Company furnishes the following income statement :
Bell Bang Company
Income Statement
For the first half of the year ended 30 June 20xx
Sales $ 200,000
Less : Cost of goods sold :
Direct materials 30,000
Direct labor 35,000
Factory overhead (of which $22,000 is fixed expense) 37,000 102,000
Gross profit 98,000
Less : Operating expense :
Salaries expense 13,000
Commission expense 20,000
Depreciation expense 5,000
Advertising expense 10,000 48,000
Income before tax 50,000
Less : Income tax expense 20,000
Net income 30,000
Required : Answer which following questions independently
1. Reconstruct the above income statement into contribution margin income statement.
2. For the first half of the year ended 30 June 20xx, compute :
2.1 Contribution margin ratio
2.2 Break-even point in dollars.
2.3 Margin of safety ratio
3. Compute the expected sales volume for the second half of the year ended 31 December 20xx if Bell Bang had projected a loss of $10,000 for the second half of the year, assuming that sale price and fixed expenses remain unchanged.
4. How much additional sales from (3) would Bell Bang need to make in order to break-even if the variable cost of the additional sales is decreased by 20%.
5. How much sales should Bell Bang make for the whole year ending 31 December to generate a net profit after tax of $120,000?
6. If the sales commission in next year are discontinued in exchange for additional annual salaries of $25,000. How much sales would have to make for the next whole year to generate a net profit after tax of $120,000.
Question 4
Mayberry owns and operates a BEAUTIFUL CUT company, a small salon. The only service that is offered is haircuts at a price of $8 a clip. Tip is also another source of the company which average about 15% of the price. The number of hairdressers (in addition to Mayberry) that Mayberry employs depends on the number of estimated haircuts for the year. As long as Mayberry expects fewer than 4,000 cuts in a year, he will operate the shop by himself. In case he estimated the number of haircuts will exceed 4,000 cuts, he will hire additional hairdressers (employees) to meet following yearly demands :
Number of additional employees Expected number of haircuts for year
1 4,001 - 8,000
2 8,001 - 15,000
All hairdressers including Mayberry shares all work equally. For example, if the numbers of haircuts is 12,000 cuts,
Mayberry will hire 2 additional employees and thereby each hairdresser (including Mayberry) will work for 12,000 3 = 4,000 haircuts.
The compensations that Mayberry pay to his individual employee are as follows :
1) Salary amount of $5,000 per year,
2) Commission at the rate of 25% of the price. Payment of commission is made to the employees for his or her services provided to customers.
3) Tip, which average about 15% of the price. Payment of tip is made to the employees for his or her services provided to customers.
As being the owner of the company, Mayberry takes no salary, commission and tip for his work. The other costs of operating the company are $6,000 per year and $2 per haircut.
Required :
1. If the number of haircuts was less than 4,000, determine the number of haircuts that enable the company to reach break-even point.
2. If the number of haircuts is expected to increase to 9,000, what will be the profit (loss) for the company (Mayberrys income)?
Question 5
Marston Corporation manufactures pharmaceutical products that are sold through a net work of independent sales
agents located in the United States and Canada. The agents are currently paid an 18% commission on sales. Marston
used this percentage in preparing the following budgeted income statement for the fiscal year ending 30 June 20xx :
(In thousands)
Sales 26,000
Cost of goods sold :
Variable 11,700
Fixed 2,870 14,570
Gross margin 11,430
Marketing & administrative expenses :
Sales commissions 4,680
Fixed marketing expenses 750
Fixed administrative expenses 1,850 7,280
Operating income 4,150
Interest expenses 650
Net income before taxes 3,500
Income taxes 1,400
Net income 2,100
Since preparing this budgeted income statement, Marston has learned that its agents are demanding an increase in the
commission rate to 23% for the upcoming year. As a result, Marstons president has decided to investigate the
possibility of hiring it own sales staff in place of the network of sales agents and has asked Tom Ross, Marstons
controller, to gather information on the cost associated with this alternative.
Ross estimates that Marston will have to hire eight salespeople to cover the current market area. The annual payroll
cost of each of these employees will average $80,000, including fringe benefit costs. Travel and entertainment cost are
expected to total $600,000 for the year, and the annual cost of sales manager and sales secretary will be $150,000.
In addition to their salary, the eight salespeople will each earn commissions at the rate of 10% on the first $2 million in
sales and 15% on all sales over $2 million. Ross expects that all eight salespeople will exceed the $2 million and that
sales will be at the level originally projected ($26,000,000). Ross believes that Marston should also increase its
marketing budget by $500,000.
Required :
1) Calculate Marston Corporations breakeven point in sales dollars for the fiscal year ending 30 June 20xx if the company hires its own sales force and increase its marketing costs.
2) If Marston Corporation continues to sell through its network of sales agent and pays the higher
commission rate, determine how many percent increase of dollar sales for the fiscal year ending 30 June
20xx would be to generate the same net income as projected in the budgeted income statement
presented above.
Solution to Cost Volume Profit Question
Question 1
1) Day shift
30(15,000) - 15,000VC - 100,000 = 200,000
VC = 10
CMU = P - VC = 30 - 10 = 20
Night shift
VC = 140% 10 = 14
CMU = 30 - 14 = 16
2) Break-even point of production level 1
S - (10/30)S - 100,000 = 0
S = 150,000
Q = 150,000/30 = 5,000
Break-even point of production level 2
Let X = number of units in excess of 20,000 units
30(20,000 + x) [(10)(20,000) + 14x] - 164,000 = 0
x = 19,000
Q + x = 20,000 + 19,000 = 39,000
3)
Q = 20,000 Q = 36,000
Sales 600,000 1,080,000
Total variable expenses 200,000 424,000
Total contribution margin 400,000 656,000
Total fixed expenses 100,000 164,000
Operating profits 300,000 492,000
The volume that will maximise operating profits = 36,000 units
Question 2
1) 2(45,000) - 1.25(45,000) - 50,000 = -16,250
2) Let x = additional units above 45,000 units
[(245,000) +( 1.90x)] [1.25(45,000 + x)] - 50,000 = 0
x = 25,000
Q + x = 45,000 + 25,000 = 70,000 70,000 units is valid for 50,000 fixed expenses
The additional units (above 45,000) would lead bottoms need to sell in order to break even is 25,000 units
3) Let x = additional units above 45,000 units
[(245,000) +( 1.90x)] [1.25(45,000 + x)] - 50,000 = 6,000
x = 34,231
Q + x = 45,000 + 34,231 = 79,231 79,231 units is invalid for 50,000 fixed expenses try at 70,000 fixed
Expenses [(245,000) + (1.90x)] [1.25(45,000 + x)] - 70,000 = 6,000
x = 65,000
Q = 45,000 + 65,000 = 110,000 110,000 units is valid for 70,000 fixed expenses
Therefore, the additional unit (above 45,000) would lead bottoms need to sell in order to generate profit of 6,000 are
65,000 units
4)
Q = 40,000 Q = 75,000 Q = 125,000
Sales 80,000 150,000 250,000
Total variable expenses 50,000 93,750 156,250
Total contribution margin 30,000 56,250 93,750
Total fixed expenses 35,000 50,000 70,000
Operating profits (5,000) 6,250 23,750
5)
Sales (85,000@2) 170,000
Total variable expenses [(75,[email protected] + 10,000@[1.25+(1*3/4)] 113,750
Total contribution margin 56,250
Total fixed expenses 50,000
Operating profits 6,250
6)
Product X P = 2, VC per unit = 1.25
Product Y P = 3, VC per unit = 3*60% = 1.8
TFC for both products = 100,000
Sales mix X : Y = 7 : 3
Tax rate = 30%
Let Q = the number of composite units sold (X and Y in bundle)
[[(2 1.25)(7/10) + (3 1.8)(3/10)]Q 100,000](1 0.3) = 14,000
Q = 135,594 units
units of product X sold = 135,594(7/10) = 94,916 sales in dollar = (94,916)(2) = 189,832
unit of product Y sold = 135,594(3/10) = 40,678 sales in dollar = (40,678)(3) = 122,034
Total sales = 311,866
Question 3
1)
Bell Bang Company
Income Statement
For the first half of the year ended 30 June 20xx
Sales 200,000
Less : Variable expenses :
Direct materials 30,000
Direct labor 35,000
Variable overhead 15,000
Commission expense 20,000 100,000
Total contribution margin 100,000
Less : Fixed expenses :
Fixed overhead 22,000
Salaries expense 13,000
Depreciation expense 5,000
Advertising expense 10,000 50,000
Income before tax 50,000
Less : Income tax 40% 20,000
Net income 30,000
2) Contribution margin ratio = 100,000 / 200,000 = 0.50
Break-even point in dollar : S - 0.50S - 50,000 = 0
S = 100,000
Margin of safety ratio = (200,000 - 100,000) / 200,000 = 0.50
3) S - 0.50S - 50,000 = -10,000
S = 80,000
4) Let x = additional sales
(80,000 + x) - (40,000 + 0.40x) - 50,000 = 0
x = 16,667
5) Tax rate = 20,000 / 50,000 = 0.4
[S - 0.50S - (50,0002)] (1-0.40) = 120,000
S = 600,000
6) [S - 0.40S - 125,000] (1-0.40) = 120,000
S = 541,667
Question 4
1) S [2/(8 + (8*0.15)]S - 6,000 = 0
S = 7,666.67
Q = 7666.67 / (8 + (8*0.15)) = 834
2)
Hair cut revenue (9,000@8) 72,000
Tip [3,000@(8*0.15)] 3,600
Total revenue 75,600
Variable expenses :
Commission (6,000@2) 12,000
Other operating expense (9,000@2) 18,000 30,000
Total contribution margin 45,600
Fixed expenses :
Salaries (2@5,000) 10,000
Other operating expense 6,000 16,000
Operating profits 29,600
Question 5
Current situation : Sales = 26,000,000
: Total variable expenses = 11,700,000 + 4,680,000 = 16,380,000
: Total fixed expense = 2,870,000 + 750,000 + 1,850,000 + 650,000 = 6,120,000
: Tax rate = 1,400,000 / 3,500,000 = 0.40
New situation ( Increasing commission) : Sales = 26,000,000
: Total variable expense = 11,700,000 + [(23%/18%)*4,680,000]
= 17,680,000
: Total fixed expense = 2,870,000 + 750,000 + 1,850,000 + 650,000
= 6,120,000
: Tax rate = 0.40 (unchanged)
New situation : (Arranging own sale force)
Sales = 26,000,000
Variable expense :
Sales dollar Variable cost ratio (based on sales at 2,600,000)
0 - 2,000,000 [11,700,000 + (26,000,000*10%)]/ 26,000,000 = 0.55
2,000,000 and over [11,700,000 + (26,000,000*15%)]/ 26,000,000 = 0.60
Total fixed expense = 2,870,000 + (750,000 + 500,000) + 1,850,000 + 650,000 + 640,000 + 600,000 + 150,000
= 8,010,000
1) Let S = Sales dollars above $ 2,000,000
(2,000,000 + S) [0.55(2,000,000) + 0.6S] - 8,010,000 = 0
S = 17,775,000
Total sales at breakeven point = 2,000,000 + 17,775,000 = 19,775,000
2) S (17,680,000 / 26,000,000)S - 6,120,000 = 3,500,000
S = 30,062,500
Therefore sales have to increase by (30,062,500 26,000,000)/26,000,000 = 15.625%