Minden Company Introduced A New Product Last Year

Minden Company Introduced A New Product Last Year For Which It Is Tryi

Minden Company introduced a new product last year for which it is trying to find an optimal selling price. Marketing studies suggest that the company can increase sales by 5,000 units for each $2 reduction in the selling price. The company’s present selling price is $93 per unit, and variable expenses are $63 per unit. Fixed expenses are $835,800 per year. The present annual sales volume (at the $93 selling price) is 25,800 units.

1. What is the present yearly net operating income or loss?

2. What is the present break-even point in unit sales and in dollar sales?

3. Assuming that the marketing studies are correct, what is the maximum annual profit that the company can earn? At how many units and at what selling price per unit would the company generate this profit?

4. What would be the break-even point in unit sales and in dollar sales using the selling price you determined in (3) above (e.g., the selling price at the level of maximum profits)?

Paper For Above instruction

Introduction

The determination of optimal pricing and sales strategies is crucial for companies seeking to maximize profits, especially when introducing new products. Minden Company's recent efforts to identify the most profitable selling price for its new product involve an analysis of current sales data, cost structures, and marketing forecasts. This paper examines the current financial position, identifies the break-even point, and explores the potential for profit maximization based on regression insights from marketing studies, ultimately suggesting an optimal price point and sales volume for maximum profitability.

Current Financial Position

The initial step involves calculating Minden Company’s present net operating income or loss using current sales data. The company's present selling price per unit is $93, with variable expenses of $63 per unit, fixed expenses totaling $835,800 annually, and current sales volume at 25,800 units. To determine the net operating income, we need to compute the contribution margin and then subtract fixed expenses.

Contribution margin per unit = Selling price per unit – Variable expenses per unit = $93 – $63 = $30

Total contribution margin at current sales volume = 25,800 units × $30 = $774,000

Net operating income = Total contribution margin – Fixed expenses = $774,000 – $835,800 = -$61,800

This indicates that Minden Company is currently operating at a loss of $61,800 annually.

Break-Even Analysis

The break-even point occurs when total contribution margin equals fixed expenses. To find this point in units:

Break-even units = Fixed expenses / Contribution margin per unit = $835,800 / $30 ≈ 27,860 units

To find the dollar sales at break-even:

Break-even sales in dollars = Break-even units × Selling price per unit = 27,860 × $93 ≈ $2,592,180

Thus, Minden Company must sell approximately 27,860 units or generate $2,592,180 in sales to break even.

Profit Maximization Based on Marketing Study

Marketing studies suggest that for every $2 decrease in the selling price, sales increase by 5,000 units. This relation can be expressed mathematically as a linear demand function:

New sales volume = 25,800 + 5,000 × (Price reduction / $2)

Let x be the number of $2 price reductions. Then, the new selling price P can be written as:

P = $93 – 2x

Correspondingly, new sales volume S(x) is:

S(x) = 25,800 + 5,000x

We now evaluate the profit function, which is:

Profit(x) = (P – variable expense) × S(x) – Fixed expenses

Substituting P and S(x):

Profit(x) = [$93 – 2x – $63] × [25,800 + 5,000x] – $835,800

Simplifying:

Profit(x) = [$30 – 2x] × [25,800 + 5,000x] – $835,800

This quadratic expression expands to:

Profit(x) = $30(25,800 + 5,000x) – 2x(25,800 + 5,000x) – $835,800

= 774,000 + 150,000x – 2x(25,800 + 5,000x) – 835,800

Further expanding:

= 774,000 + 150,000x – 2x×25,800 – 2x×5,000x – 835,800

= 774,000 + 150,000x – 51,600x – 10,000x² – 835,800

Combine like terms:

Profit(x) = (774,000 – 835,800) + (150,000x – 51,600x) – 10,000x²

= -61,800 + 98,400x – 10,000x²

Maximum Profit and Corresponding Price and Units

To find the maximum profit, differentiate the profit function with respect to x and set it to zero:

dProfit/dx = 98,400 – 20,000x = 0

Solving for x:

x = 98,400 / 20,000 = 4.92 ≈ 5

Since x must be an integer, the maximum profit occurs at x = 5.

Calculate the corresponding selling price:

P = $93 – 2(5) = $93 – $10 = $83

Calculate the sales volume at x=5:

S(5) = 25,800 + 5,000 × 5 = 25,800 + 25,000 = 50,800 units

The maximum profit occurs when the selling price is approximately $83, and sales reach about 50,800 units annually.

Break-Even Point at the New Price

Using the same demand function, at the optimal price of $83, the sales volume is 50,800 units. To find the new contribution margin per unit:

Contribution margin per unit = $83 – $63 = $20

Break-even units at this price point:

Break-even units = Fixed expenses / Contribution margin per unit = $835,800 / $20 = 41,790 units

Corresponding dollar sales in this case:

Dollar sales = 41,790 × $83 ≈ $3,473,370

This lower price increases the sales volume needed to break even, but the company can reach maximum profits with higher contribution margins at the new optimal price point.

Conclusion

The analysis indicates that Minden Company is currently operating at a loss but can achieve maximum profitability by strategically reducing the selling price to approximately $83. This price reduction aligns with increased sales volume, resulting in maximized profit margins. Furthermore, the refined pricing and sales volume projections provide a practical framework for the company's sales and marketing strategies, illustrating the importance of linear demand modeling and cost analysis in optimizing product profitability.

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