Question Tag: Break-even Analysis

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  • 20 Marks

MI – May 2016 – L1 – SB – Q3 – Cost-Volume-Profit (CVP) Analysis

Perform various CVP calculations including break-even point, profit, margin of safety, and contribution for a product.

HEALTH-GRACE limited produces one standard product called Bambino Syrup which sells at ₦20.00 per bottle. The trading results for the six months ended June 30, 2015 were as follows:

Month Sales (Units) Profit / Loss (₦)
January 120,000 80,000
February 140,000 120,000
March 60,000 (40,000)
April 96,000 32,000
May 104,000 24,000
June 72,000 16,000

From the above information, you are required to calculate the following:

a. Break-even point in units and Naira value. (2 Marks)
b. Fixed cost. (2 Marks)
c. Variable cost per unit. (8 Marks)
d. Profit volume ratio. (2 Marks)
e. Contribution, assuming 70,000 bottles are sold. (2 Marks)
f. Margin of safety assuming 90,000 bottles are sold. (1 Mark)
g. The number of bottles to be sold to generate a profit after tax of ₦70,000 assuming the tax rate is 30%. (3 Marks)

a. Break-even point in units = Total fixed cost / contribution per unit = N160,000/ (20 – 18) = 80,000 units
Break-even point in value = Total fixed cost / contribution Margin Ratio = N160,000/ (2 / 20) = N1,600,000

b. Fixed cost: Fixed Cost = ₦1,600,000

c. Variable cost per unit:

Using High and Low Methods

Variable cost per unit = N18

d. Profit volume ratio: Profit / Volume Ratio = 2 / 20 x 100 = 10%

e. Contribution, assuming 70,000 bottles are sold: 70,000 x N2 = N140,000

f. Margin of safety assuming 90,000 bottles are sold: 90,000 – BEP in units = 90,000 – 80,000 = 10,000 units

g. The number of bottles to be sold to generate a profit after tax of ₦70,000 assuming the tax rate is 30%:

Sales in units = (Total fixed cost + target profit) / contribution per unit

Target profit = N70,000 / 30% = N233,333
Sales in units = (N160,000 + N233,333)/2 = 196,667 bottles

 

 

 

  • 10 Marks

QT – May 2017 – L1 – Q1c – Basic Mathematics

Analyze the profit function to find the break-even point and number of boxes to make a profit.

A paper-producing company has determined that its profit from selling x hundred boxes of envelopes is given by the expression:

Required:

i) Determine the number of boxes the company must sell to break even.
(5 marks)

ii) Determine the number of boxes the company must sell to make money.
(5 marks)

  • 10 Marks

MA – May 2017 – L2 – Q1a – Introduction to capital budgeting,

Calculate the break-even rate for a taxi service investment considering a 5% annual cash flow increase over five years.

Kwame, after his National Service and with no hope of securing a job in the formal sector, has decided to run a taxi service. The following forecast has been made for the operation of a service between Abisim and Sunyani:

  1. Revenue totaling GH¢300 a week for 52 weeks in a year. This is net of fuel and other variable costs.
  2. Tyres: four pieces for a year at GH¢120 per unit.
  3. Maintenance and servicing: GH¢120 per month.
  4. Salaries: GH¢3,000 per year.
  5. Insurance: GH¢350 per year.

The net cash flow will increase at 5% per annum for the next five years due to inflation. The cost of the vehicle is estimated at GH¢28,000. The project appears quite profitable based on the NPV criteria using the Government policy rate of 26%. However, the banks are offering rates far higher than the policy rate.

Required:

You are to calculate the break-even rate for the project.

(10 marks)

The guiding rate is the internal rate of return (IRR). Any borrowing rate greater than that will render the venture unprofitable.

Calculation of cash flow:

Item Amount (GH¢)
Receipt (300×52) 15,600.00
Less:
Tyres 480.00
Maintenance (120×12) 1,440.00
Salaries 3,000.00
Insurance 350.00
Net Cash Flow 10,330.00

Calculation of NPV at different rates:

Year Cash Flow (GH¢) DF (26%) DCF (GH¢) DF (30%) DCF (GH¢)
0 (28,000.00) 1.00 (28,000) 1.00 (28,000)
1 10,330 0.794 8,202.02 0.769 7,943.77
2 10,846.5 0.630 6,833.30 0.592 6,421.13
3 11,388.83 0.500 5,694.41 0.455 5,181.92
4 11,958.27 0.397 4,747.43 0.350 4,185.40
5 12,556.18 0.315 3,955.20 0.269 3,377.61
NPV 1,432.36 (890.17)

IRR Calculation:

IRR = 26% + (1432.36 ÷ 2322.53) × 4
IRR = 26% + 2.47% = 28.47%

  • 12 Marks

MA – Nov 2016 – L2 – Q5a – Discounted cash flow

Calculate the NPV break-even point under different cost of capital scenarios and determine the project's duration based on given cash inflows.

DDB Limited has decided to set up a factory to process groundnuts into oil. The feasibility studies cost them GH¢35,000. The consultants have advised that the initial outlay will be GH¢250,000; however, they were unable to estimate the cash inflow due to the uncertain economic environment.

Required:
Using NPV as an appraisal technique, you are required to calculate:

i) The constant cash inflow needed to break even if the cost of capital is 15% and the project is to last for 10 years.

(4 marks)

ii) By how much should the cash inflow increase to break even if the cost of capital is increased to 20%. (4 marks)

iii) If the cash inflow is GH¢45,000, for how long should the project run to break even if the cost of capital is 15%.

(4 marks)

i) Constant Cash Inflow Needed to Break Even at 15% Cost of Capital:

  • Initial outlay: GH¢250,000
  • Annuity factor (15% for 10 years): 5.019
  • Break-even cash inflow (CF) = GH¢250,000 / 5.019 = GH¢49,810.72

(Total: 4 marks)

ii) Cash Inflow Increase Needed to Break Even at 20% Cost of Capital:

  • Initial outlay: GH¢250,000
  • Annuity factor (20% for 10 years): 4.192
  • Break-even cash inflow (CF) = GH¢250,000 / 4.192 = GH¢59,637.40
  • Increase in cash inflow = GH¢59,637.40 – GH¢49,810.72 = GH¢9,826.68
  • Percentage increase = (GH¢9,826.68 / GH¢49,810.72) × 100 = 19.7%

(Total: 4 marks)

iii) Duration Needed to Break Even at 15% Cost of Capital with GH¢45,000 Cash Inflow:

  • Initial outlay: GH¢250,000
  • Given cash inflow: GH¢45,000
  • Required annuity factor (AF) = GH¢250,000 / GH¢45,000 = 5.556
  • This annuity factor lies between years 12 (5.421) and 13 (5.583)
  • Interpolating between year 12 and year 13:
    • (0.135 / 0.162) × 12 = 0.833 year
    • Therefore, the project should run for 12 years and 10 months to break even.

(Total: 4 marks)

  • 20 Marks

IMAC – July 2023 – L1 – Q1 – Cost-Volume-Profit (CVP) Analysis | Process Costing

Prepare the Process Account for Omicron vaccine production and calculate the break-even point and required units to achieve target profit before and after tax

a) Adom Ltd manufactures Omicron vaccine for the treatment of COVID-19 in Africa. The manufacturing process uses two raw materials (M & W) which are mixed in the proportions (2:3). Materials are priced: M = GH¢10 per kg and W = GH¢3.2 per kg. Normal weight loss of 5% of material input is expected during the process, and material losses recorded in the manufacturing process have no saleable value. At the end of production, 18,260 kg of Omicron vaccine were manufactured from 19,320 kg of raw materials. Conversion costs in the period were GH¢57,316. There was no work in process at the beginning or end of the period.

Required:
Prepare the Process Account of the Omicron vaccine for the period. (10 marks)

b) Manna Industries sold 150,000 units of its product at GH¢20 per unit. Variable costs are GH¢15 per unit (manufacturing cost of GH¢12 and selling expenses of GH¢3). Fixed costs are incurred uniformly throughout the year and amount to GH¢972,000, that is, manufacturing costs of GH¢600,000 and selling expenses of GH¢372,000.

Required:
i) Calculate the break-even point in units and Ghana cedis. (4 marks)
ii) Calculate the number of units that must be sold to earn an income of GH¢75,000 before income tax. (2 marks)
iii) Calculate the number of units that must be sold to earn an after-tax profit of GH¢100,000 if the income tax rate is 40%. (4 marks)

 

  • 20 Marks

IMAC – NOV 2020 – L1 – Q1 – Cost-Volume-Profit (CVP) Analysis

Explain break-even point and margin of safety; calculate CVP metrics for Kack Ltd.

a) Explain the terms break-even point and margin of safety as used in cost-volume-profit (CVP) analysis in short term decision making. (4 marks)

b) Kack Ltd is a company which uses cost-volume-profit analysis for planning and control decisions. You have been given the following information for the just ended operational period:

Description Amount (GH¢)
Total revenue 3,600,000
Total cost 3,510,000
Variable cost 2,700,000

Required:
i) Variable cost/sales ratio. (1 mark)
ii) Contribution/sales (C/S) ratio. (2 marks)
iii) Break-even sales (in value). (2 marks)
iv) Margin of safety (in value). (1 mark)
v) Margin of safety (in percentage). (1 mark)
vi) The sales value which would yield a profit of GH¢270,000 assuming the C/S ratio and fixed costs remain unchanged. (3 marks)
vii) The sales value which would yield a profit of 15% of that sales value assuming the C/S ratio and the fixed costs remain unchanged. (3 marks)
viii) The break-even sales value if total fixed costs are reduced by GH¢180,000 while the selling price is reduced by 10%, assuming no changes in variable costs ratio. (3 marks)

a) Break-even Point (BEP): The level of sales at which total revenue equals total costs, resulting in no profit or loss. It is the point where the company covers all its fixed and variable costs.
Margin of Safety (MoS): The difference between actual or budgeted sales and the break-even sales level. It represents the extent to which sales can drop before the company incurs losses.

b)

Description Calculation Result (GH¢)
Sales 3,600,000
Total costs 3,510,000
Variable costs 2,700,000
Fixed costs 3,510,000 – 2,700,000 810,000

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