Problem 14 - Accounting

Question

The Dash Club of Tampa, Florida, collected recipes from members and published a cookbook entitled Life of the Party. The book will sell for \(\$ 25\) per copy. The chairwoman of the cookbook development committee estimated that the club needed to sell 10,000 books to break even on its \(\$ 90,000\) investment. What is the variable cost per unit assumed in the Dash Club's analysis?

Step-by-Step Solution

Answer

The variable cost per unit is $16.

Step 1: Understanding the Break-Even Point

The break-even point is where total revenue equals total costs (fixed plus variable). In this case, they need to sell 10,000 books to cover an investment of $90,000. This investment represents the fixed costs.

Step 2: Setting Up the Equation

To find the variable cost per unit, we can set up the equation for total revenue which is equal to the total cost. The total revenue from selling books is given by the sale price multiplied by the number of books sold: \(Total \ Revenue = 25 \times 10,000\).

Step 3: Calculate Total Revenue

Calculate the total revenue from selling 10,000 books: \[Total \ Revenue = 25 \times 10,000 = 250,000.\]

Step 4: Find Total Cost Equation

The total cost includes both the fixed and variable costs. The equation for total cost is: \(Total \ Cost = Fixed \ Costs + Variable \ Costs\). Thus, \(250,000 = 90,000 + (Variable \ Cost \ per \ Unit \times 10,000)\).

Step 5: Solve for the Variable Cost per Unit

Rearrange the equation to solve for the variable cost per unit: \(250,000 - 90,000 = Variable \ Cost \ per \ Unit \times 10,000\). Simplify: \(160,000 = Variable \ Cost \ per \ Unit \times 10,000\), which gives the variable cost per unit as \( \frac{160,000}{10,000} = 16.00.\)

Key Concepts

Fixed Costs

Fixed costs are expenses that do not change regardless of how many units of a product are sold. In the case of Dash Club's cookbook project, the fixed cost is the initial investment of $90,000. These costs could cover expenses such as design, editing, and marketing. The important thing about fixed costs is that they remain constant over time or production levels. For instance, whether the Dash Club sells one book or 10,000 books, the $90,000 investment remains the same. Understanding fixed costs is crucial because they directly impact the break-even point, which is the number of units needed to sell to cover all costs.

Variable Costs

Variable costs differ from fixed costs because they change directly with the production volume. In this exercise, the variable cost per unit is what we calculate: \( rac{160,000}{10,000} = 16 \) per book. These costs might include paper, printing, and shipping.

• If the Dash Club produces more books, the total variable costs increase.
• If they produce fewer books, the total variable costs decrease.

Calculating the correct variable cost per unit helps businesses set a viable selling price and determine accurate profit margins. The combination of variable and fixed costs allows companies to understand their total expenses and break-even point effectively.

Total Revenue

Total revenue is the complete amount of money earned from sales, calculated by multiplying the number of units sold by the sale price per unit. For the Dash Club, selling 10,000 books at $25 each results in a total revenue of \[ 25 \times 10,000 = 250,000 \]. This revenue must cover both the fixed and variable costs to achieve a break-even point. If the total revenue exceeds the total costs, the business makes a profit.

• Achieving a higher total revenue than the break-even point results in financial gain.
• If total revenue is less, the Dash Club will incur a loss.

Having a firm grip on revenue expectations helps businesses plan for different scenarios and make informed decisions about pricing and production levels.