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Mod Inc. sells parts for $300 each. Fixed costs are $7,500 per year and variable costs are $175 per unit. If the initial investment is $22,500 and is expected to last for 15 years and the firm pays 30% taxes, what is the accounting and economic break-even level of sales respectively?

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Final answer:

The accounting break-even level of sales for Mod Inc. is 60 units, ignoring taxes and considering its $7,500 yearly fixed costs and $175 variable costs per unit.

Step-by-step explanation:

To answer the question posed by the student regarding Mod Inc.'s break-even level of sales, we will look at both the accounting and economic break-even points. The accounting break-even point is when a company's total sales are equal to its total expenses, excluding the opportunity cost of capital. The economic break-even point includes these opportunity costs and compares returns to what could have been earned if the investment was made elsewhere.

First, let's calculate the accounting break-even point using the given data: The parts sell for $300 each, variable costs are $175 per unit, and fixed costs are $7,500 per year. The formula for the accounting break-even point in units is:

Accounting Break-Even Units = Fixed Costs / (Sales Price per Unit - Variable Cost per Unit)

Inserting the figures we get:

Accounting Break-Even Units = $7,500 / ($300 - $175) = $7,500 / $125 = 60 units

So, Mod Inc. must sell 60 units to reach its accounting break-even point.

Now, to find the economic break-even point, we must consider the initial investment and its opportunity costs. If the initial investment is $22,500 and is expected to last for 15 years, we can calculate an annual opportunity cost using a simple straight-line depreciation (not including any interest rate). We'll neglect taxes for this calculation as taxes are paid after profits are calculated:

Economic Break-Even Units = (Fixed Costs + Annual Depreciation) / (Sales Price per Unit - Variable Cost per Unit)

Where Annual Depreciation = Initial Investment / Investment's Lifespan. Using the data, this gives us:

Annual Depreciation = $22,500 / 15 years = $1,500 per year

So, the economic break-even point is:

Economic Break-Even Units = ($7,500 + $1,500) / ($300 - $175) = $9,000 / $125 = 72 units

Therefore, Mod Inc. must sell 72 units each year to reach its economic break-even point.

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