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Feb 20, 2024

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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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3. A US company has revenue of $5.5 million and total costs of $7.5 million, which are or can be broken down into total fixed cost of $3 million and total variable cost of $4.5 million. The net loss on the firm’s income statement is reported as $2,000,000 (ignoring tax implications). In prior periods, the firm had reported profits on its operations. a. What decision should the firm make regarding operations over the short term? b. What decision should the firm make regarding operations over the long term? c. Assume the same business scenario except that revenue is now $5.0 million, and total costs of $7.5 million, which are or can be broken down into total fixed cost of $3 million and total variable cost of $4.5 million, which creates a net loss of $2.5 million. What decision should the firm make regarding operations in this case? a. In the short term, the company should take immediate steps to address its current financial situation. It is clear from the company's $2 million net loss that its revenue is insufficient to meet all of its expenses. To minimize these losses, the company should explore options like reducing variable costs and boosting revenue. This could involve measures such as renegotiating contracts with suppliers to secure better terms, enhancing operational efficiency to reduce costs, and, if feasible, increasing prices for its products or services. The key decision in the short term is to implement actions that can curtail the losses and steer the company toward profitability. b. Looking at the long term, the firm should embark on a more comprehensive analysis of its overall business operations. If the losses persist, it's imperative to question the sustainability of the existing business model. Strategic alternatives should be explored, which might encompass restructuring the organization, diversifying into new product lines or markets, or reassessing the balance between fixed and variable costs. In addition, the company needs to evaluate its competitive position and the dynamics of the market it operates within. This is the stage where fundamental changes to the business strategy

come into consideration, aiming to rectify the ongoing losses and pave the way for long- term sustainability. c. The scenario gets much worse when revenue stays at $5.0 million while total costs stay at $7.5 million, leaving a net loss of $2.5 million. The firm is now incurring a more significant loss relative to its revenue. In this scenario, the company should be deeply concerned about its long-term viability. The same principles apply: efforts should be made to reduce variable costs, boost revenue, and consider substantial long-term strategic adjustments. It may be necessary to make more substantial changes to the business model, including potential downsizing or exiting unprofitable product lines or markets. The key decision in this case is to take immediate and substantial action to address the escalating losses and secure the company's sustainability. References Froeb, L. M., McCann, B. T., Ward, M. R., & Shor. (2017). Managerial Economics . Cengage Learning. Girardin, M. (2023, March 17). How to calculate Net Present Value (NPV) . Forage. https://www.theforage.com/blog/skills/npv

Activity2

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