Question Tag: Break-Even Point

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  • 1 Marks

MI – May 2016 – L1 – SA – Q11 – Cost-Volume-Profit Analysis

Calculate the number of units required to break even given the fixed costs, sales price, and marginal cost.

A company manufactures a single product with a sales price of N1,000 and a marginal cost of N650. If the fixed cost is N685,300 per annum, then the number of units required to Break Even is:

A. 1,950
B. 1,955
C. 1,958
D. 1,985
E. 1,988

Answer: C

Explanation:
The break-even point in units is calculated using the formula:

Break-Even Point = Fixed Costs/ (Sales Price−Marginal Cost)

Substitute the given values:

Break-Even Point = ≈1,958 units

Therefore, the number of units required to break even is 1,958.

  • 1 Marks

MI – May 2015 – L1 – SA – Q3 – Cost-Volume-Profit (CVP) Analysis

Calculate the variable cost per unit based on the given dat

The variable cost per unit is
A. N8.00
B. N7.50
C. N6.25
D. N5.50
E. N5.00

Answer:
A. N8.00

Explanation:
The variable cost is calculated by subtracting the fixed cost (N6,000) from the total cost for 6,000 units, and dividing by the number of units.

  • 15 Marks

MA – Nov 2017 – L2 – Q5 – Standard Costing and Variance Analysis

Calculate standard selling price, variances, break-even point, and margin of safety for a company using standard marginal costing.

Zealow Ltd has just introduced a new standard marginal costing system to assist in the planning and control of the production activities for the single product which the company manufactures, “The Stand.” The system became operational on 1 March 2017.

The Management Accountant has consulted with the Senior Engineer and they have agreed on the following standard specifications to manufacture one unit of the product known as “The Stand”:

  • Direct materials: 4kg @ GH¢1.75 per kg
  • Direct labour: 2 hours @ GH¢10 per hour
  • Variable overhead: 2 hours @ GH¢8.25 per hour

The Marketing Director has advised that in Zealow Ltd’s industry, the budgeted selling price is normally calculated to achieve a mark-up of 30% on cost.

The budgeted level of production and sales activity has been agreed with both production managers and sales staff at 24,000 units per month.

The actual results for the month of March 2017 are as follows:

  • Sales: 22,000 units yielding a total revenue of GH¢1,276,000
  • Production: 23,000 units
  • Direct Materials: 90,000 kgs at a cost of GH¢162,000
  • Direct labour: 48,000 hours at a cost of GH¢576,000
  • Variable overhead: GH¢350,000

Required:

a) Calculate the standard selling price of one unit of “The Stand” and prepare a summary budgeted profit statement for Zealow Ltd for the month of March 2017.
b) Calculate the relevant variances for March 2017 under the headings of sales, materials, labour, and overheads.
c) Zealow Ltd uses a standard marginal costing system and therefore fixed costs have been ignored in the calculations shown above. Assuming that the fixed costs for the company are estimated to be GH¢1,879,200 per annum, calculate the monthly sales in both units and value that will be required to break-even and estimate the margin of safety, based on the current budget levels.

a) Standard selling price and budgeted profit statement for March 2017:

Standard Selling Price Calculation:

Component Calculation Amount (GH¢)
Direct materials 4kg @ GH¢1.75 per kg 7.00
Direct labour 2 hours @ GH¢10 per hour 20.00
Variable overhead 2 hours @ GH¢8.25 per hour 16.50
Standard marginal cost 43.50
Standard contribution (Mark-up) 30% on GH¢43.50 13.05
Standard selling price 56.55

Budgeted Profit Statement for March 2017:

Description Calculation Amount (GH¢)
Sales (24,000 units @ GH¢56.55) 24,000 x 56.55 1,357,200
Direct materials 24,000 units @ GH¢7.00 168,000
Direct labour 24,000 units @ GH¢20.00 480,000
Variable overhead 24,000 units @ GH¢16.50 396,000
Total Costs 1,044,000
Budgeted Profit Sales – Total Costs 313,200

(2 marks)

b) Relevant variances for March 2017:

Sales Variances:

Variance Type Calculation Amount (GH¢)
Sales Price Variance (GH¢1,276,000 – 22,000 x GH¢56.55) 31,900 (Favourable)
Sales Volume Variance (24,000 – 22,000) x GH¢13.05 26,100 (Adverse)

Material Variances:

Variance Type Calculation Amount (GH¢)
Material Price Variance (GH¢162,000 – 90,000 x GH¢1.75) 4,500 (Adverse)
Material Usage Variance (23,000 x 4 – 90,000) x GH¢1.75 3,500 (Favourable)

Labour Variances:

Variance Type Calculation Amount (GH¢)
Labour Rate Variance (GH¢576,000 – 48,000 x GH¢10) 96,000 (Adverse)
Labour Efficiency Variance (23,000 x 2 – 48,000) x GH¢10 20,000 (Adverse)

Overhead Variances:

Variance Type Calculation Amount (GH¢)
Overhead Expenditure Variance (48,000 x GH¢8.25 – GH¢350,000) 46,000 (Favourable)
Overhead Efficiency Variance (23,000 x 2 – 48,000) x GH¢8.25 16,500 (Adverse)

(10 marks)

c) Break-even point and margin of safety:

Description Calculation Amount
Contribution per unit GH¢13.05 GH¢13.05
Contribution to sales ratio GH¢13.05 / GH¢56.55 0.2307
Break-even point (units) GH¢1,879,200 / GH¢13.05 12,000 units
Break-even point (sales value) 12,000 units x GH¢56.55 GH¢678,600
Margin of safety (24,000 – 12,000) / 24,000 50% or 12,000 units

(3 marks)

(Total: 15 marks)

  • 20 Marks

MA – Nov 2020 – L2 – Q5 – High/Low Analysis, Cost-Volume-Profit (CVP) Analysis

Determine maintenance costs using the high-low method, and calculate break-even point, required sales for target profit, and margin of safety for Quickspray Ltd.

Quickspray Ltd offers professional car spraying services at Suame Magazine. The company is planning its activities for the month of June 2018 for its saloon car spraying section. The company charges a service fee of GH¢1,000 and incurs fixed cost (excluding fixed maintenance cost) and variable cost per unit (excluding variable maintenance cost) of GH¢35,000 and GH¢644.39 respectively for spraying a saloon car.

The following data also relates to Quickspray Ltd on the maintenance hours of its key machine, revenue, and profit for the six months ended April 2018:

Month Maintenance Hours Revenue (GH¢) Profit (GH¢)
November 2017 1,200 19,000 700
December 2017 1,425 24,000 1,425
January 2018 1,410 20,100 650
February 2018 1,400 20,000 1,000
March 2018 1,175 18,000 (125)
April 2018 1,275 19,000 175

Total fixed cost increases by GH¢1,120 when maintenance hours go beyond 1,400.

Required:

a) Determine the total maintenance cost of production, using the high-low method if:

i) Maintenance hours for May are budgeted to be 1,520.
ii) Maintenance hours for June are budgeted to be 1,075.

b) Calculate for the month of May the:

i) Break-even point in units and value.
ii) Sales level required to make an after-tax profit of GH¢21,150, assuming Quickspray Ltd is in the 25% tax bracket.
iii) Margin of safety if the target after-tax profit of GH¢21,150 is achieved.

a) Determination of Total Maintenance Cost Using High-Low Method:

i) High-Low Method Calculation:

  • Variable Cost per Unit:

Variable Cost per Unit=Highest Cost−Lowest CostHighest Activity Level−Lowest Activity Level\text{Variable Cost per Unit} = \frac{\text{Highest Cost} – \text{Lowest Cost}}{\text{Highest Activity Level} – \text{Lowest Activity Level}} Variable Cost per Hour=(22,575−18,125)(1,425−1,175)=4,450250=GH¢13.32 per hour\text{Variable Cost per Hour} = \frac{(22,575 – 18,125)}{(1,425 – 1,175)} = \frac{4,450}{250} = GH¢13.32 \text{ per hour}

  • Total Fixed Cost (Activity exceeds 1,400 hours):

Total Fixed Cost=Total Cost at Maximum Activity Level−(Variable Cost per Hour×Maximum Activity Level)\text{Total Fixed Cost} = \text{Total Cost at Maximum Activity Level} – (\text{Variable Cost per Hour} \times \text{Maximum Activity Level}) Total Fixed Cost=GH¢22,575−(GH¢13.32×1,425)=GH¢22,575−GH¢18,981=GH¢3,594\text{Total Fixed Cost} = GH¢22,575 – (GH¢13.32 \times 1,425) = GH¢22,575 – GH¢18,981 = GH¢3,594

  • Total Fixed Cost (Activity below 1,400 hours):

Total Fixed Cost=GH¢3,594−GH¢1,120=GH¢2,474\text{Total Fixed Cost} = GH¢3,594 – GH¢1,120 = GH¢2,474

ii) Maintenance Cost Calculation:

  • For May 2018 (1,520 hours):

Maintenance Cost=Fixed Cost+(Variable Cost per Hour×Maintenance Hours)\text{Maintenance Cost} = \text{Fixed Cost} + (\text{Variable Cost per Hour} \times \text{Maintenance Hours}) Maintenance Cost=GH¢3,594+(GH¢13.32×1,520)=GH¢3,594+GH¢20,246.40=GH¢23,840.40\text{Maintenance Cost} = GH¢3,594 + (GH¢13.32 \times 1,520) = GH¢3,594 + GH¢20,246.40 = GH¢23,840.40

  • For June 2018 (1,075 hours):

Maintenance Cost=GH¢2,474+(GH¢13.32×1,075)=GH¢2,474+GH¢14,319=GH¢16,793\text{Maintenance Cost} = GH¢2,474 + (GH¢13.32 \times 1,075) = GH¢2,474 + GH¢14,319 = GH¢16,793

b) Calculations for May:

i) Break-Even Point:

  • Break-Even Point in Units:

BEP (Units)=Total Fixed CostContribution per Unit\text{BEP (Units)} = \frac{\text{Total Fixed Cost}}{\text{Contribution per Unit}} BEP (Units)=GH¢35,000+GH¢3,594GH¢1,000−(GH¢644.39+GH¢13.32)=GH¢38,594GH¢342.29≈113 cars\text{BEP (Units)} = \frac{GH¢35,000 + GH¢3,594}{GH¢1,000 – (GH¢644.39 + GH¢13.32)} = \frac{GH¢38,594}{GH¢342.29} \approx 113 \text{ cars}

  • Break-Even Point in Sales Value:

BEP (Sales Value)=BEP (Units)×Selling Price per Unit\text{BEP (Sales Value)} = \text{BEP (Units)} \times \text{Selling Price per Unit} BEP (Sales Value)=113×GH¢1,000=GH¢113,000\text{BEP (Sales Value)} = 113 \times GH¢1,000 = GH¢113,000

ii) Sales Level for After-Tax Profit of GH¢21,150:

  • Required Sales Level:

Required Sales Level=Total Fixed Cost+ProfitContribution Margin Ratio\text{Required Sales Level} = \frac{\text{Total Fixed Cost} + \text{Profit}}{\text{Contribution Margin Ratio}} Required Sales Level=GH¢38,594+GH¢21,150/(1−0.25)0.34229=GH¢38,594+GH¢28,2000.34229=GH¢195,138.63\text{Required Sales Level} = \frac{GH¢38,594 + GH¢21,150/(1 – 0.25)}{0.34229} = \frac{GH¢38,594 + GH¢28,200}{0.34229} = GH¢195,138.63

iii) Margin of Safety:

  • Margin of Safety Calculation:

Margin of Safety (%)=Budgeted Sales Level−Break-Even SalesBudgeted Sales Level×100\text{Margin of Safety (\%)} = \frac{\text{Budgeted Sales Level} – \text{Break-Even Sales}}{\text{Budgeted Sales Level}} \times 100 Margin of Safety (%)=GH¢195,138.63−GH¢113,000GH¢195,138.63×100=42.10%\text{Margin of Safety (\%)} = \frac{GH¢195,138.63 – GH¢113,000}{GH¢195,138.63} \times 100 = 42.10\%

  • 15 Marks

MA – May 2019 – L2 – Q4 – Cost-volume-profit (CVP) analysis

Evaluate different options to improve profitability and perform CVP analysis including break-even and margin of safety calculations.

Boasiako Ltd manufactures high-quality coffee biscuits that are sold to hotels and restaurants in Koforidua. Two months ago, it had prepared a budget for the forthcoming financial year.

Details of the budget are presented below:
Sales GH¢6,000,000
Less:
Direct materials GH¢2,080,000
Direct labour GH¢1,160,000
Variable overheads GH¢840,000
Fixed overheads GH¢972,600
Total costs GH¢5,052,600
Profit GH¢947,400

The budget above has been prepared on the assumption that sales will be 800,000 packets of biscuits. However, due to changing economic conditions, the sales forecast for the year is now 720,000 packets of biscuits. It is expected that the selling price per unit, direct costs per unit, and variable overhead cost per unit will not change from those budgeted. It is also expected that fixed overheads will be the same as those budgeted.

Management is now considering a number of options to improve profitability for the forthcoming financial year:

Option 1:
Decrease the selling price by 20%. It is anticipated that this would increase sales volume by 25% on the forecast sales for the current year.

Option 2:
Decrease all variable costs by 10% and decrease fixed costs by 10%. This is not expected to have any impact on the sales level.

Option 3:
Decrease the selling price by 10% and decrease fixed costs by 5%. This is expected to increase sales volume by 25% on the forecast sales for the current year.

Required:
a) Calculate the expected profit for the current year (forecast sales). (2 marks)
b) Based on the forecast activity for the year, calculate:
i) The breakeven point in packets of biscuits.
ii) The margin of safety in percentage terms.
iii) The sales revenue required to earn a profit of GH¢1,440,000. (6 marks)
c) Evaluate the profitability of the three options and recommend the option that Boasiako Ltd should adopt. (7 marks)

a) Expected Profit for the Current Year (Forecast Sales):

Per Unit (GH¢) Total (GH¢)
Sales 7.50 5,400,000
Less: Variable Costs
Direct materials 2.60 1,872,000
Direct labour 1.45 1,044,000
Variable overheads 1.05 756,000
Total Variable Costs 5.10 3,672,000
Contribution 2.40 1,728,000
Less: Fixed Overheads 972,600
Profit 755,400

(2 marks)

b) CVP Analysis:

i) Breakeven Point (BEP) in Packets of Biscuits:
BEP (in units) = Total Fixed Costs / Contribution per unit
= GH¢972,600 / GH¢2.40
= 405,250 packets

ii) Margin of Safety in Percentage Terms:
Margin of Safety (%) = (Actual Sales – BEP Sales) / Actual Sales * 100
= (720,000 – 405,250) / 720,000 * 100
= 43.7%

iii) Sales Revenue Required to Earn a Profit of GH¢1,440,000:
Required Sales Revenue = (Total Fixed Costs + Target Profit) / Contribution to Sales Ratio
= (GH¢972,600 + GH¢1,440,000) / 0.32
= GH¢7,539,375

(6 marks evenly spread using ticks)

c) Evaluation of Profitability of the Three Options:

Option 1 (SP -20%, Volume +25%) Option 2 (VC -10%, FC -10%) Option 3 (SP -10%, FC -5%, Volume +25%) Current Situation
Units 900,000 720,000 900,000 720,000
Sales 5,400,000 5,400,000 6,075,000 5,400,000
Less: Variable Costs
Direct materials 4,590,000 3,304,800 4,590,000 3,672,000
Contribution 810,000 2,095,200 1,485,000 1,728,000
Less: Fixed Costs 972,600 875,340 923,970 972,600
Profit (162,600) 1,219,860 561,030 755,400

Recommendation:
The company should consider adopting Option 2 as it provides the highest profit among the options, with a profit of GH¢1,219,860.

  • 13 Marks

MA – May 2016 – L2 – Q2b – Cost-Volume-Profit (CVP) Analysis, Relevant Cost and Revenue

Calculate break-even points, operating leverage, and expected income for two rent options for a bakery.

Anima Ventures wants to start a new bakery at Bodwease in Ashanti Region. She plans to rent a storeroom for her operations under the following terms and conditions:

Option 1 Option 2
Fixed Rent Charge GH¢5,000 GH¢3,000
Variable Rent – 10% of selling price of each loaf

The following data are also relevant for her business:

  • Selling Price: GH¢5.00
  • Material Cost (Flour): GH¢0.80
  • Material Cost (Margarine): GH¢0.70
  • Labour Cost: GH¢0.50

Required:

i) Determine the break-even point in units under each option.
(2 marks)

ii) Calculate the degree of operating leverage (DOL) for the two options if 10,000 loaves of bread are to be sold in the current year.
(4 marks)

iii) What would be the expected operating income if sales increase by 25% next year?
(4 marks)

iv) Which of the two options would you recommend to Anima Ventures and why?
(3 marks)

i) Break-Even Point in Units:

  • Option 1:
    Contribution per unit = GH¢5.00 – (GH¢0.80 + GH¢0.70 + GH¢0.50) = GH¢3.00
    Break-Even Point = Fixed Cost / Contribution per unit
    = GH¢5,000 / GH¢3.00 = 1,667 loaves of bread
  • Option 2:
    Contribution per unit = GH¢5.00 – (GH¢0.80 + GH¢0.70 + GH¢0.50 + 10% of GH¢5.00)
    = GH¢5.00 – GH¢2.50 = GH¢2.50
    Break-Even Point = Fixed Cost / Contribution per unit
    = GH¢3,000 / GH¢2.50 = 1,200 loaves of bread

ii) Degree of Operating Leverage (DOL):

  • Option 1:
    Total Contribution for 10,000 units = 10,000 x GH¢3.00 = GH¢30,000
    Operating Profit = GH¢30,000 – GH¢5,000 = GH¢25,000
    DOL = Total Contribution / Operating Profit
    = GH¢30,000 / GH¢25,000 = 1.20
  • Option 2:
    Total Contribution for 10,000 units = 10,000 x GH¢2.50 = GH¢25,000
    Operating Profit = GH¢25,000 – GH¢3,000 = GH¢22,000
    DOL = Total Contribution / Operating Profit
    = GH¢25,000 / GH¢22,000 = 1.14

iii) Expected Operating Income if Sales Increase by 25%:

  • Option 1:
    Percentage change in Operating Income = DOL x % change in Sales
    = 1.20 x 25% = 30.00%
    Expected Operating Income = GH¢25,000 + (30.00% x GH¢25,000) = GH¢32,500
  • Option 2:
    Percentage change in Operating Income = DOL x % change in Sales
    = 1.14 x 25% = 28.50%
    Expected Operating Income = GH¢22,000 + (28.50% x GH¢22,000) = GH¢28,270

iv) Recommendation: Option 1 is recommended as it has a higher Degree of Operating Leverage (1.20 vs. 1.14), indicating higher returns for any given level of sales. Additionally, since the expected sales exceed the break-even point, Option 1 provides a greater opportunity for profit if sales increase beyond the expected levels.

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