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Chapter 21: Problem 14

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?

Short Answer

Expert verified
The variable cost per unit is $16.

Step by step solution

01

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.
02

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: \(Total \ Revenue = 25 \times 10,000\).
03

Calculate Total Revenue

Calculate the total revenue from selling 10,000 books: \[Total \ Revenue = 25 \times 10,000 = 250,000.\]
04

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, \(250,000 = 90,000 + (Variable \ Cost \ per \ Unit \times 10,000)\).
05

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 \( \frac{160,000}{10,000} = 16.00.\)

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

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.

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Most popular questions from this chapter

For the coming year, Paladin Inc. anticipates fixed costs of \(\$ 120,000\), a unit variable cost of \(\$ 60\), and a unit selling price of \(\$ 90\). The maximum sales within the relevant range are \(\$ 900,000\). a. Construct a cost-volume-profit chart. b. Estimate the break-even sales (dollars) by using the cost-volume-profit chart constructed in part (a). c. What is the main advantage of presenting the cost-volume-profit analysis in graphic form rather than equation form?

a. If Fama Company, with a break-even point at \(\$ 360,000\) of sales, has actual sales of \(\$ 480,000\), what is the margin of safety expressed (1) in dollars and (2) as a percentage of sales? b. If the margin of safety for Watkins Company was \(25 \%\), fixed costs were \(\$ 1,200,000\), and variable costs were \(75 \%\) of sales, what was the amount of actual sales (dollars)?

For the current year ending March 31 , Jwork Company expects fixed costs of \(\$ 440,000\), a unit variable cost of \(\$ 50\), and a unit selling price of \(\$ 75\). a. Compute the anticipated break-even sales (units). b. Compute the sales (units) required to realize income from operations of \(\$ 90,000\).

Currently, the unit selling price of a product is \(\$ 280\), the unit variable cost is \(\$ 230\), and the total fixed costs are \(\$ 525,000\). A proposal is being evaluated to increase the unit selling price to \(\$ 300\). a. Compute the current break-even sales (units). b. Compute the anticipated break-even sales (units), assuming that the unit selling price is increased and all costs remain constant.

Intuit Inc. develops and sells software products for the personal finance market, including popular titles such as Quicken and TurboTax \(^{\circledast}\). Classify each of the following costs and expenses for this company as either variable or fixed to the number of units produced and sold: a. Shipping expenses b. Property taxes on general offices c. Straight-line depreciation of computer equipment d. Salaries of human resources personnel e. President's salary f. Advertising g. Sales commissions h. CDs i. Packaging costs j. Salaries of software developers k. Wages of telephone order assistants 1\. User's guides
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