## Break-even analysis - numerical questions

#### Question 1

A company makes a product with a selling price of $20 per unit and variable costs of $12 per unit. The fixed costs for the period are $40,000. What is the required output level to make a target profit of $10,000?

#### Question 2

A company has fixed costs of $300,000 and produces one product with a selling price of $72.00 and a variable cost of $42.00 per unit. The maximum factory capacity is 20,000 units and it anticipates selling 15,000 units. Construct a break-even chart showing the break-even point and the margin of safety at present. Fully label your diagram.

How much profit will they make:

- at the present level of operation?
- if sales increase to the maximum that the factory can supply?

#### Question 3

The following information relates to a company, which produces a single product.

Direct labour per unit | $ 22 |
---|---|

Direct materials per unit | $ 12 |

Variable overheads per unit | $ 6 |

Fixed costs | $ 400,000 |

Selling price per unit | $ 60 |

- Define the term 'break-even'.
- Explain why break-even analysis is of reduced value to a multi-product firm?
- Use the figures above to construct a break-even chart showing the minimum number of units that must be sold for the company to break even. Fully label your diagram.
- Analyse the factors that any business should take into consideration before using break-even analysis as a basis for decision making.

#### Question 4

The Sherston Brick Company manufactures a standard stone block for the building industry. The production capacity for the year is 100,000 standard blocks. The selling price per block is $1.60, variable costs are $0.60 per brick and fixed costs are $60,000 per annum.

** Determine**:

- The break-even point in terms of sales revenue and output.
- The margin of safety if sales amount to 90,000 bricks in the year.

The market for blocks becomes much more competitive, and SBC reduces its price to $1.50 per brick. Sales still decline to 80,000 bricks, whilst costs rise relentlessly. Variable costs rise to $0.66 per brick and rises in business taxes and other contributions increase fixed costs to $80,000 per annum.

- Is the firm still profitable?

#### Question 5

Windy Sails Limited has prepared the following cost analysis for 6 months of trading.

Sales (sets) | 1,800 |
---|---|

Price | $850 per set |

Materials costs | $150 per set |

Labour costs | $150 per set |

Other variable costs | $150 per set |

Overheads | $600,000 for 6 months operation |

- Draw the break-even chart for the company for the 6-month period.
- Determine the break-even quantity, and confirm this by calculation.
- Identify the firm's margin of safety for the period.
- Calculate the profit made during the period?
- Evaluate the use of break-even analysis to a company within its decision-making procedures.

*Fully label your diagram*.

#### Question 6

Provision plc makes luxury hampers for sale in a chain of high-class department stores. The following financial information is available:

Wholesale price | $80 per hamper |
---|---|

Labour and material costs | $15 per hamper |

Bought-in components | $25 per hamper |

Overheads | $800,000 per year |

Current output and sales are set at 30,000 hampers per year, though the firm has the capacity to produce 50,000 hampers per year.

- Calculate the break-even quantity for the firm.
- Draw and fully label the break-even chart for the business.
- Identify the margin of safety.
- Calculate the level of profit the firm is making.

Sales go well, but the buyer puts pressure on Provision to reduce its prices. In the following financial year Provision expects sales to reach 40,000, but at a price of $75 per hamper. Labour and materials costs, and bought-in items are expected to rise in price by 15%, but Provision is planning to cut its fixed costs by 10%.

- Calculate how these changes will affect Provision's break-even quantity, margin of safety and profitability.

#### Question 7

Woodturn Ltd. makes a television table that sells for $50 per unit. It has variable costs of $30 per unit and incurs fixed costs of $100,000 per period. Construct the break-even chart for this operation and determine the sales value that the firm will have to reach if it is to make $20,000 profit per period.

*Fully label your diagram*.

#### Question 8

Bremend Ltd manufactures a computer stand. It has fixed costs of $500,000 and each stand sells for $120, with a variable cost of $70 per unit. The factory has a maximum capacity of 20,000 units and it anticipates selling 15,000 units each period. Construct the break-even chart for the business, showing the break-even point, and the margin of safety.

*Fully label your diagram*.

#### Question 9

Sibon plc manufactures soft toys for the European market. The costs incurred by the firm are as follows:

$ | |
---|---|

Materials (per toy) | 5 |

Wages (per toy) | 4 |

Packaging (per toy) | 3 |

Rent of premises | 5,000 |

Machinery hire | 3,000 |

Marketing and administration | 1,000 |

The soft toys sell for an average price of $16. Current capacity of Sibon plc is 3000 toys per year.

#### Required

- Calculate the following:
- Contribution per toy sold
- Break-even in units of output
- Break-even level of sales revenue

- Construct a break-even chart showing the break-even level of output and margin of safety.

*Fully label the chart*.

#### Question 10

John Pitman runs a small business specialising in delivering organic fruit and vegetables to the local area. He buys from local farms and packages these together in boxes and delivers them locally. Each box is sold for $12. He has the following costs

Direct wages are $9 per hour (30 minutes per box on average)

Fruit and vegetables are $4 per box

Other fixed costs incurred each year are as follows:

$ | |
---|---|

Rent of delivery van | 4,500 |

Rent of premises | 10,500 |

Advertising | 2,000 |

- Calculate the marginal cost of producing one box of vegetables.
- State the formula for break-even in boxes (units)
- Calculate the break-even point in boxes (unit)
- Examine the factors that influence the setting of the price of a box of fruit and vegetables.