Break-even analysis：練習問題

A manufacturing firm currently operates with a fixed cost of \(\text{\pounds}120,000\) and produces \(8,000\) units. At this level, it is exactly breaking even. The selling price is \(\text{\pounds}40\) per unit. The firm is considering an expansion that will increase capacity to \(12,000\) units, but this will result in a stepped fixed cost, increasing total fixed costs by \(20\%\). Simultaneously, a new production process will reduce variable costs per unit by \(\text{\pounds}5\).

Calculate the new break-even point in units following these changes.

A boutique bakery has a maximum capacity of 5,000 units per month. Currently, they produce 3,000 units. The following cost and price data applies:
- Selling price per unit: \(\text{\pounds}4.50\)
- Variable cost per unit: \(\text{\pounds}1.50\)
- Total Fixed Costs: \(\text{\pounds}6,000\) per month

The bakery is considering a stepped fixed cost scenario where hiring an extra supervisor to reach full capacity will increase total fixed costs by 25%. Evaluate the impact on the break-even point if they decide to increase production to 5,000 units.

Define the term break-even point and state the formula used to calculate it in terms of units.

A business has fixed costs of \(\text{\pounds}12,000\), a selling price of \(\text{\pounds}50\) per unit, and variable costs of \(\text{\pounds}30\) per unit. Calculate the margin of safety in units if the current level of actual sales is 800 units.

A high-volume logistics firm operates with fixed costs of \(\text{\pounds}450,000\) and a unit contribution of \(\text{\pounds}15\). Due to a new regulatory requirement, the firm must hire an additional compliance officer once output exceeds \(40,000\) units, which creates a stepped fixed cost of \(\text{\pounds}60,000\).

Calculate the target level of profit if the firm produces and sells \(50,000\) units.

A manufacturer of high-end sports equipment is analyzing its cost structure for a new production line. The following financial data has been provided:
- Target Level of Profit: \(\text{\pounds}50,000\)
- Selling Price per unit: \(\text{\pounds}250\)
- Variable Cost per unit: \(\text{\pounds}150\)
- Fixed Costs (up to 1,000 units): \(\text{\pounds}40,000\)

The business is considering an expansion. If production exceeds 1,000 units, the business will experience a stepped fixed cost, increasing total fixed costs by \(\text{\pounds}15,000\) to cover additional warehouse leasing.

(a) Calculate the break-even point in units for the current production capacity (under 1,000 units).
(b) Calculate the number of units required to achieve the target level of profit, taking into account the stepped fixed cost if applicable.
(c) Evaluate the impact on the margin of safety if the business currently produces 900 units but decides to increase production to 1,200 units to meet the profit target.