Problem 14 - Accounting

Question

The Junior League of Tampa, Florida, collected recipes from members and published a cookbook entitled Life of the Party. The book will sell for \(22 per copy. The chairwoman of the cookbook development committee estimated that the league needed to sell 16,000 books to break even on its \)140,000 investment. What is the variable cost per unit assumed in the Junior League’s analysis? Round to the nearest cent.

Step-by-Step Solution

Answer

The variable cost per unit is $13.25.

Step 1: Understand Break-Even Point Equation

The break-even point occurs when total revenue equals total cost. We know the total investment (fixed cost) is \(140,000\). The revenue for selling one unit is \(22\). If we let \(c\) represent the variable cost per unit, then the break-even equation is:\[\text{Total Revenue} = \text{Total Fixed Cost} + \text{Total Variable Cost}\]For 16,000 books, this can be written as:\[\16000 \times 22 = 140000 + 16000 \times c\]

Step 2: Substitute and Simplify the Equation

Substitute the known values into the equation:\[\352,000 = 140,000 + 16000c\]

Step 3: Isolate the Variable Cost per Unit

Rearrange the equation to solve for \(c\):\[352,000 - 140,000 = 16000c\]\[212,000 = 16000c\]

Step 4: Solve for c

Divide both sides by 16,000 to get the variable cost per unit:\[c = \frac{212,000}{16000}\]Now compute the division:\[c = 13.25\]

Step 5: Conclusion

The variable cost per unit, rounded to the nearest cent, is \(13.25\).

Key Concepts

Variable Cost

The term "variable cost" refers to expenses that change directly with the level of production. In the context of the Junior League's cookbook project, variable costs include costs tied directly to each book produced. This could involve expenses such as printing, binding, and materials. As production increases, so do these costs.

• Variable costs are crucial for understanding how each additional unit affects overall expenses.
• Key in calculations such as the break-even analysis, they help determine pricing and profit margins.

Knowing the variable cost per book allows businesses to set prices that cover these costs and contribute toward fixed expenses.

Fixed Cost

Fixed costs remain constant regardless of how many units are produced. For the Junior League, this amounted to a $140,000 initial investment.

• These costs can include expenses like the initial setup, equipment, facilities, or other overheads not impacted by the production volume.
• Unlike variable costs, fixed costs must be absorbed into the price of units produced to recover the initial expenditure over time.

Understanding fixed costs helps ensure that production efforts are financially viable and helps in planning for the recovery of initial investments.

Revenue Equation

The revenue equation is vital in determining how sales translate into financial success. The equation typically is:
\[ ext{Total Revenue} = ext{Selling Price per Unit} \times ext{Number of Units Sold}\]
In this exercise, with each cookbook selling for $22, understanding the revenue equation helps assess how many units must sell to cover both fixed and variable costs.

• It's used to forecast the results of sales strategies and price setting.
• By calculating revenue and breaking it down to cost components, businesses fully understand their financial landscape.

Accounting Education

Incorporating break-even analysis into accounting education provides practical skills for financial planning and analysis. This exercise exemplifies how accounting students and practitioners bridge theoretical knowledge with real-world application.

• Break-even analysis highlights the importance of separating costs into fixed and variable categories.
• It prepares students to perform financial evaluations essential in business decision-making, from pricing strategies to cost management.

Understanding these concepts allows students to evaluate financial conditions accurately and improve their strategic planning abilities in any business context.