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Financial Breakeven Niko has purchased a brand new machine to produce its High Flight line of shoes. The machine has an economic life of five years. The depreciation schedule for the machine is straight-line with no salvage value. The machine costs \(\$ 390,000\). The sales price per pair of shoes is \(\$ 60\), while the variable cost is \(\$ 14\). \(\$ 185,000\) of fixed costs per year are attributed to the machine. Assume that the corporate tax rate is 34 percent and the appropriate discount rate is 8 percent. What is the financial break- even point? INTERMEDIATE (Questions 11-25)

Short Answer

Expert verified
The financial breakeven point for Niko's High Flight line of shoes is approximately 8720 pairs of shoes. This is the number of shoes that Niko must sell in order to cover the fixed costs, variable costs, and taxes.

Step by step solution

01

Calculate yearly depreciation

The machine has an economic life of 5 years and is depreciated on a straight-line method with no salvage value. To find the yearly depreciation, we divide the total cost of the machine by its economic life: Yearly depreciation = Total cost of the machine / Economic life Yearly depreciation = \(\$390,000) / (5\text{ years}\) Yearly depreciation = \(\$78,000\)
02

Calculate annual fixed costs

Fixed costs include the yearly depreciation and other fixed costs attributed to the machine: Annual fixed costs = Yearly depreciation + Other fixed costs Annual fixed costs = \(\$78,000) + \(\$185,000\) Annual fixed costs = \(\$263,000\)
03

Calculate annual variable costs

We're given that the variable cost per pair of shoes is \$14. Let 'x' be the number of shoes produced/sold. The total annual variable cost can be represented as: Annual variable costs = Variable cost per pair of shoes * x Annual variable costs = \(\$14 * x\)
04

Calculate sales revenue and operating profit

Sales revenue is the money received from selling the shoes at $60 per pair. The operating profit is calculated by subtracting total costs (fixed costs + variable costs) from the sales revenue: Operating profit = Sales revenue - (Annual fixed costs + Annual variable costs) Operating profit (x) = (\(\$60 * x\)) - (\(\$263,000) + \(\$14 * x\))
05

Calculate breakeven point before taxes

The breakeven point before taxes is when the operating profit is zero, as it means that the company has covered all its costs: Operating profit (x) = 0 \(\$60 * x\) - (\(\$263,000) + \(\$14 * x\)) = 0
06

Solve for x

Now solve the equation for x to find the breakeven point: \(\$60 * x - \$14 * x = \(\$263,000) \(46 * x = \(\$263,000\) x = \(\$263,000) / (46) x ≈ 5714.13 ≈ 5715 pairs of shoes
07

Calculate financial breakeven point

Considering that the corporate tax rate is 34%, the financial breakeven point will be higher than the breakeven point before taxes. Let 'y' be the financial breakeven point: \(y * (60 - 14) * (1 - 0.34) = 263,000\) \(y * 46 * 0.66 = 263,000\) y ≈ 8719.42 ≈ 8720 pairs of shoes So, the financial breakeven point for Niko's High Flight line of shoes is around 8720 pairs of shoes.

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Key Concepts

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

Straight-Line Depreciation
Straight-line depreciation is a method of allocating the cost of an asset equally over its useful life. It is calculated by taking the purchase price of the asset minus any salvage value and dividing that by the number of years of its expected life. For example, Niko's machine costs \(\$390,000\) and has a lifespan of 5 years with no salvage value, making the yearly depreciation \(\$78,000\):
\[\text{Yearly Depreciation} = \frac{\text{Total Cost}}{\text{Life Expectancy}} = \frac{\$390,000}{5}\]
This depreciation expense is recorded on the income statement annually and reflects the cost of using the asset for that year. In financial reporting, depreciation is essential as it spreads out the expense of an asset over its useful life, providing a more accurate picture of a company's profitability over time.
Fixed and Variable Costs
Understanding the types of costs a business incurs is crucial for breakeven analysis. Fixed costs are expenses that do not vary with the amount of goods or services produced, such as rent, salaries, and equipment depreciation. Niko's fixed costs include the yearly depreciation of the machine, \(\$78,000\), and other operation-related costs amounting to \(\$185,000\), totaling \(\$263,000\).
On the other hand, variable costs change with production volume. In Niko's case, the variable cost is \(\$14\) per pair of shoes. As production increases, variable costs go up proportionally. The relationship between fixed, variable costs, and production output plays a fundamental role in determining the breakeven point.
Operating Profit Calculation
Operating profit, sometimes referred to as operating income, is calculated by subtracting all the necessary operating expenses, including fixed and variable costs, from the sales revenue. It represents the profit earned from a firm's core business operations. For Niko, if 'x' signifies the number of shoes produced and sold, the operating profit can be defined as:
\[\text{Operating Profit} = (\text{Sales Price per Unit} \times x) - (\text{Annual Fixed Costs} + (\text{Variable Cost per Unit} \times x))\]
It indicates how efficiently a company is managing its resources to generate earnings before the deduction of interest and taxes. A positive operating profit is an indicator of a potentially viable business, while operating losses can signal that a company needs to reassess its financial or operational strategies.
Breakeven Analysis
Breakeven analysis is a critical financial calculation to determine when a business or a new product will be profitable. It identifies the point at which total revenue equals total costs, meaning that the business has neither made a profit nor incurred a loss. This is known as the breakeven point (BEP). For Niko, the breakeven point before taxes is found by setting the operating profit to zero and solving for 'x':
\[\$60 \times x - (\$263,000 + \$14 \times x) = 0\]Upon calculating, it yields approximately 5715 pairs of shoes. However, the financial breakeven point, which considers taxes, is higher:
\[\text{Financial BEP} = \frac{\text{Total Fixed Costs}}{(\text{Sales Price per Unit} - \text{Variable Cost per Unit}) \times (1 - \text{Tax Rate})}\]
For Niko, with a tax rate of 34%, the financial breakeven is around 8720 pairs of shoes. Breakeven analysis is essential for financial planning, helping to make informed decisions about pricing, budgeting, and strategy formulation.

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Most popular questions from this chapter

Option to Wait Your company is deciding whether to invest in a new machine. The new machine will increase cash flow by \(\$ 340,000\) per year. You believe the technology used in the machine has a 10 -year life; in other words, no matter when you purchase the machine, it will be obsolete 10 years from today. The machine is currently priced at \(\$ 1,800,000\). The cost of the machine will decline by \(\$ 130,000\) per year until it reaches \(\$ 1,150,000\), where it will remain. If your required return is 12 percent, should you purchase the machine? If so, when should you purchase it?

Scenario Analysis Consider a project to supply Detroit with 55,000 tons of machine screws annually for automobile production. You will need an initial \(\$ 1,700,000\) investment in threading equipment to get the project started; the project will last for five years. The accounting department estimates that annual fixed costs will be \(\$ 520,000\) and that variable costs should be \(\$ 220\) per ton; accounting will depreciate the initial fixed asset investment straight-line to zero over the five-year project life. It also estimates a salvage value of \(\$ 300,000\) after dismantling costs. The marketing department estimates that the automakers will let the contract at a selling price of \(\$ \mathbf{2 4 5}\) per ton. The engineering department estimates you will need an initial net working capital investment of \(\$ 600,000\). You require a 13 percent return and face a marginal tax rate of 38 percent on this project. 1\. What is the estimated OCF for this project? The NPV? Should you pursue this project? 2\. Suppose you believe that the accounting department's initial cost and salvage value projections are accurate only to within \pm 15 percent; the marketing department's price estimate is accurate only to within \pm 10 percent; and the engineering department's net working capital estimate is accurate only to within \pm 5 percent. What is your worst-case scenario for this project? Your best-case scenario? Do you still want to pursue the project?

Abandonment Value We are examining a new project. We expect to sell 9,000 units per year at \(\$ 50\) net cash flow apiece for the next 10 years. In other words, the annual operating cash flow is projected to be \(\$ 50 \times 9,000=\$ 450,000\). The relevant discount rate is 16 percent, and the initial investment required is \(\$ 1,900,000\). 1\. What is the base-case NPV? 2\. After the first year, the project can be dismantled and sold for \(\$ \mathbf{1 , 3 0 0 , 0 0 0}\). If expected sales are revised based on the first year's performance, when would it make sense to abandon the investment? In other words, at what level of expected sales would it make sense to abandon the project? 3\. Explain how the \(\$ 1,300,000\) abandonment value can be viewed as the opportunity cost of keeping the project in one year.

Abandonment Decisions M.V.P. Games, Inc., has hired you to perform a feasibility study of a new video game that requires a \(\$ 5\) million initial investment. M.V.P. expects a total annual operating cash flow of \(\$ 880,000\) for the next 10 years. The relevant discount rate is 10 percent. Cash flows occur at year-end. 1\. What is the NPV of the new video game? 2\. After one year, the estimate of remaining annual cash flows will be revised either upward to \(\$ 1.75\) million or downward to \(\$ 290,000\). Each revision has an equal probability of occurring. At that time, the video game project can be sold for \(\$ 1,300,000\). What is the revised NPV given that the firm can abandon the project after one year?

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?

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