# Lukas Manufacturing is currently producing a tape holderExample of the Break-even Point - Analysis of Alternatives

### Problem Data

It is necessary to find the alternative that generates **the highest profit** using **the break-even analysis**:

- Alternative 1
Fixed Costs (F): 20000

Variable Cost per Unit (V): 0.75

Selling Price per Unit (P): 2

Expected unit sales (U): 40000

- Alternative 2
Fixed Costs (F): 25000

Variable Cost per Unit (V): 0.25

Selling Price per Unit (P): 2

Expected unit sales (U): 50000

- Description
**Lukas Manufacturing is currently producing a tape holder**Lukas Manufacturing is currently producing a tape holder that has a variable cost of $0.75 per unit and a selling price of $2.00 per unit. Fixed costs are $20,000 a year. Current volume is 40,000 units a year. The firm can produce a better product by adding a new piece of equipment to the process line. This equipment represents an increase of $5,000 per year in fixed costs. The variable cost would decrease to $0.25 per unit. The volume for the new and improved product should rise to 50,000 units a year. (a) Should the company invest in the new equipment? (b) At what volume does the equipment choice change? (c) At a volume of 15,000 units, which process should be used?

## Solution

The following are the calculations and detailed graphs to obtain the **best alternative** according to the data provided:

### Alternative 1:

**a) Break-even point in units:**

To calculate the break-even point in units for alternative 1 (BEP_{U}) we will use the following formula:

According to the results, the company must sell **16000 units** to break even (no profit or loss).

**b) Break-even point in dollars:**

To calculate the break-even point in dollars (BEP_{$}), we will use the following formula:

The company must earn **$32000** to break even (no profit or loss).

**c) Profits Earned:**

To calculate the profit obtained when 40000 units are sold, we will do the following:

As profits have a positive, this means that the company makes a profit of **$30000**.

**Note:** You can zoom the chart using the scroll wheel and move the view by dragging it with the mouse.

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