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Break-Even Analysis Your buddy comes to you with a sure-fire way to make some quick money and help pay off your student loans. His idea is to sell T-shirts with the words "I get" on them. "You get it?" He says, "You see all those bumper stickers and T-shirts that say 'got milk' or 'got surf.' So this says, 'I get.' It's funny! All we have to do is buy a used silk screen press for \(\$ 3,200\) and we are in business!" Assume there are no fixed costs, and you depreciate the \(\$ 3,200\) in the first period. Taxes are 30 percent. 1\. What is the accounting break-even point if each shirt costs \(\$ 7\) to make and you can sell them for \(\$ 10\) apiece? Now assume one year has passed and you have sold 5,000 shirts! You find out that the Dairy Farmers of America have copyrighted the "got milk" slogan and are requiring you to pay \(\$ 12,000\) to continue operations. You expect this craze will last for another three years and that your discount rate is 12 percent. 2\. What is the financial break-even point for your enterprise now?

Step by step solution

01

Calculate Fixed Costs

The fixed costs include the initial investment in the silk screen press, which is \(\$3,200\). Since there are no other fixed costs mentioned in the exercise, the total fixed costs are \(\$3,200\).

02

Calculate Variable Costs

The variable costs include the cost to make each shirt, which is \(\$7\) per shirt.

03

Calculate Contribution Margin per Shirt

To calculate the contribution margin per shirt, subtract the variable costs from the selling price of each shirt: \(Contribution\_Margin\_per\_Shirt = Selling\_Price - Variable\_Costs\) \(Contribution\_Margin\_per\_Shirt = \$10 - \$7 = \$3\)

04

Calculate Accounting Break-Even Point

The accounting break-even point is reached when the total contribution margin from selling shirts equals the fixed costs. Divide the fixed costs by the contribution margin per shirt to determine the number of shirts necessary to break even: \(Break\_Even\_Point\_in\_Units = \frac{Fixed\_Costs}{Contribution\_Margin\_per\_Shirt}\) \(Break\_Even\_Point\_in\_Units = \frac{\$3,200}{\$3} = 1,066.67\) Since it's not possible to sell a fraction of a shirt, the accounting break-even point is 1,067 shirts. #Part 2: Financial Break-Even Point# Now we need to find the financial break-even point, considering the additional \(\$12,000\) payment over the next three years and a discount rate of 12%. We will find the present value of the payment and calculate the new fixed costs. Then, we'll calculate the new break-even point.

05

Calculate Present Value of Copyright Payment

To calculate the present value of the copyright payment, use the discount rate, the payment amount, and the number of years over which the payment must be made: \(Present\_Value = \frac{Payment\_Amount}{(1 + Discount\_Rate)^{Number\_of\_Years}}\) \(Present\_Value = \frac{\$12,000}{(1 + 0.12)^{3}} = \$8,411.70\)

06

Calculate New Fixed Costs

Add the present value of the copyright payment to the initial fixed costs to find the new fixed costs: \(New\_Fixed\_Costs = Initial\_Fixed\_Costs + Present\_Value\_of\_Copyright\_Payment\) \(New\_Fixed\_Costs = \$3,200 + \$8,411.70 = \$11,611.70\)

07

Calculate Financial Break-Even Point

Since the variable costs and contribution margin per shirt remain the same, use the new fixed costs to find the financial break-even point: \(Financial\_Break\_Even\_Point\_in\_Units = \frac{New\_Fixed\_Costs}{Contribution\_Margin\_per\_Shirt}\) \(Financial\_Break\_Even\_Point\_in\_Units = \frac{\$11,611.70}{\$3} = 3,870.57\) Since it's not possible to sell a fraction of a shirt, the financial break-even point is 3,871 shirts.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Fixed Costs

Fixed costs are expenses that do not change with the level of goods or services produced. Whether you sell one shirt or a thousand, these costs remain the same. In the exercise with the T-shirts, the main fixed cost was the silk screen press, priced at $3,200. This cost was incurred upfront and doesn't fluctuate with the number of shirts sold.

When planning for a business, knowing your fixed costs is crucial as they form the baseline expense that must be covered by sales. Over the long run, understanding fixed costs helps in setting the right pricing and estimating the volume of sales necessary to avoid losses.

Common fixed costs include:

• Rent and utilities
• Salaries
• Depreciation of assets
• Insurance premiums

Monitoring and managing fixed costs effectively is vital for maintaining a healthy financial position in a business.

Variable Costs

Variable costs, unlike fixed costs, change with the level of production. In the T-shirt example, each shirt produced costs $7, making it the variable cost.

These costs scale with the number of units made or sold, meaning the more shirts you sell, the higher the variable costs. This aspect makes them easier to manage in the short term as they align with business activity.

Here are some typical variable costs:

• Costs of raw materials
• Direct labor costs
• Sales commissions
• Packaging and shipping expenses

It's important to track and optimize variable costs to enhance profitability. Efficient supply chain management and negotiating with suppliers can help reduce these expenses.

Contribution Margin

The contribution margin is a vital metric that represents the difference between the selling price per unit and the variable cost per unit. It indicates how much revenue from each unit sale contributes to covering fixed costs and generating profit.

For the "I get" T-shirt scenario, the selling price per shirt was \(10, while the variable cost per shirt was \)7, resulting in a contribution margin of $3 per shirt. To calculate this, you simply use the formula:

\[Contribution\ Margin\ =\ Selling\ Price\ -\ Variable\ Cost\]
Understanding contribution margin is essential for assessing the profitability of a product. A higher margin means that more of each sale can go towards covering fixed costs and increasing profits.

Financial Break-Even Point

The financial break-even point is the sales level at which a business covers all its costs, including both fixed and variable, thus achieving neither profit nor loss. It is crucial for financial planning as it tells you the minimum sales needed to sustain the business.

In the T-shirt business example, the accounting break-even initially required selling 1,067 shirts to cover the initial \(3,200 fixed cost. However, with the new obligation of a \)12,000 payment and using a discount rate, new calculations adjusted the financial break-even point to 3,871 shirts.

The concept involves covering fixed costs with the contribution from each sale, using the formula:

\[Financial\ Break-Even\ =\ \frac{New\ Fixed\ Costs}{Contribution\ Margin\ per\ Unit}\]
Achieving this point ensures that the business can operate without incurring losses, making it a foundational concept in financial management.