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1. You own a plant that produces 10,000 copiers per year. Your fixed costs are $50,000 per year. The marginal cost per copier is a constant $5. What is your break-even price? What would be your break-even price if you were to sell 70% more copiers?
To calculate the break-even price using the formula you provided, you first need to determine the
contribution margin and then apply it to find the break-even price. The contribution margin is the
amount left over from the selling price after covering the variable costs.
Given:
Fixed Costs = $50,000 per year
Marginal Cost per Copier = $5
Number of Copiers Produced = 10,000
First, calculate the total variable cost:
Total Variable Cost = Marginal Cost per Copier × Number of Copiers Produced Total Variable Cost = $5 × 10,000 = $50,000
Now, calculate the contribution margin:
Contribution Margin = Selling Price per Copier - Marginal Cost per Copier (Froeb et al., 2017)
The selling price per copier must cover both variable and fixed costs:
Selling Price per Copier = (Fixed Costs + Total Variable Cost) / Number of Copiers Produced Selling Price per Copier = ($50,000 + $50,000) / 10,000 Selling Price per Copier = $100,000 / 10,000 Selling Price per Copier = $10
Now that we have the selling price per copier, we can use it to calculate the break-even price using the formula:
Break-Even Price ($) = Fixed Costs ÷ Contribution Margin (Froeb et al., 2017)
Break-Even Price = $50,000 ÷ ($10 - $5) = $50,000 ÷ $5 = $10,000
So, your break-even price is $10,000.
If you were to sell 70% more copiers, you can calculate the new break-even price using the same
formula, but with the updated number of copiers produced (10,000 + 0.70 * 10,000 = 17,000):
Total Variable Cost = Marginal Cost per Copier × Number of Copiers Produced Total Variable Cost = $5 × 17,000 = $85,000
Now, calculate the contribution margin:
Contribution Margin = Selling Price per Copier - Marginal Cost per Copier
The selling price per copier must cover both variable and fixed costs:
Selling Price per Copier = (Fixed Costs + Total Variable Cost) / Number of Copiers Produced Selling Price per Copier = ($50,000 + $85,000) / 17,000 Selling Price per Copier = $135,000 / 17,000 Selling Price per Copier = $ 7.94
Now that we have the selling price per copier, we can use it to calculate the break-even price using the formula:
Break-Even Price ($) = Fixed Costs ÷ Contribution Margin Break-Even Price = $50,000 ÷ ($7.94 - $5) = $50,000 ÷ $5 = $17,006
So, your new break-even price is $17,006.
2. Suppose you make an initial investment of $70,000 that will return $20,000/year for four years (assume the $20,000 is received each year at the end of the year). Is this a profitable investment if the discount rate is 15%?
To calculate the Net Present Value (NPV) for the investment with the updated cash flows, we can use the formula:
NPV = Σ (Cash Flow / (1 + r) ^t) - Initial Investment (Girardin, 2023)
Where:
Initial Investment = $70,000
Cash Flow Year 1 = $20,000
Cash Flow Year 2 = $20,000
Cash Flow Year 3 = $20,000
Cash Flow Year 4 = $20,000
r = Discount rate (opportunity cost of capital), which is 15%
t = Time period (Year 1 to Year 4)
Now, let's calculate the NPV:
NPV = ($20,000 / (1 + 0.15) ^1) + ($20,000 / (1 + 0.15) ^2) + ($20,000/ (1 + 0.15) ^3) + ($20,000 / (1 + 0.15) ^4) - $70,000
NPV = ($17,391.3) + ($15,122.87) + ($13,150.32) + ($11,435) - $70,000
NPV = $ 57,099.49 - $ 70,000
NPV= -$ 12,900.51 The NPV is negative, which means that at a 15% discount rate, this investment is not profitable. The investment would result in a loss of $12,900.51 when considering the time value of money.
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