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Chapter 3: Problem 22

The Express Banquet has two restaurants that are open 24 -hours a day. Fixed costs for the two restaurants together total \(\$ 459,000\) per year. Service varies from a cup of coffee to full meals. The average sales check per customer is \(\$ 8.50 .\) The average cost of food and other variable costs for each customer is \(\$ 3.40 .\) The income tax rate is \(30 \% .\) Target net income is \(\$ 107,100\). 1\. Compute the revenues needed to earn the target net income. 2\. How many customers are needed to break even? To earn net income of \(\$ 107,100 ?\) 3\. Compute net income if the number of customers is 170,000 .

Short Answer

Expert verified
The revenues needed are $1,020,000. 90,000 customers are needed to break even, 120,000 for the target income. Net income for 170,000 customers is $285,600.

Step by step solution

01

Calculate Contribution Margin Per Customer

Firstly, find the contribution margin per customer by subtracting the variable cost per customer from the sales check per customer. This is calculated as follows:\[ \text{Contribution Margin per Customer} = \text{Average Sales per Customer} - \text{Average Variable Cost per Customer} \]\[ = 8.50 - 3.40 = 5.10 \]
02

Determine Break-Even Point in Customers

To find out how many customers are needed to cover fixed costs, adjust for the contribution margin. The formula to calculate the break-even point in terms of customers is:\[ \text{Break-even Customers} = \frac{\text{Total Fixed Costs}}{\text{Contribution Margin per Customer}} \]Substituting the values, we get:\[ \text{Break-even Customers} = \frac{459,000}{5.10} \approx 90,000 \]This means at least 90,000 customers are needed to break even.
03

Calculate Required Revenue for Target Net Income

To calculate the required revenues for the target net income, first calculate the total required contribution, and then determine required revenue. Using the formula:\[ \text{Total Required Contribution} = \text{Total Fixed Costs} + \frac{\text{Target Net Income}}{1 - \text{Tax Rate}} \]\[ \text{Total Required Contribution} = 459,000 + \frac{107,100}{0.70} = 612,000 \]Now, the required revenue is:\[ \text{Revenue} = \frac{\text{Total Required Contribution}}{\text{Contribution Margin Ratio}} \]Where the Contribution Margin Ratio is given by:\[ \text{Contribution Margin Ratio} = \frac{\text{Contribution Margin per Customer}}{\text{Average Sales per Customer}} = \frac{5.10}{8.50} \approx 0.6 \]Substituting the values, we calculate the required revenue:\[ \text{Required Revenue} = \frac{612,000}{0.6} = 1,020,000 \]
04

Determine Number of Customers for Target Net Income

Once you have the total required contribution, you can determine the number of customers needed to achieve the target net income. Using the formula:\[ \text{Number of Customers for Target} = \frac{\text{Total Required Contribution}}{\text{Contribution Margin per Customer}} \]Substituting the values, we find:\[ \text{Number of Customers for Target} = \frac{612,000}{5.10} \approx 120,000 \]This means around 120,000 customers are needed.
05

Compute Net Income for Given Customers

For a given number of customers (170,000), calculate the net income as follows. First, determine the total contribution:\[ \text{Total Contribution} = \text{Number of Customers} \times \text{Contribution Margin per Customer} \]\[ \text{Total Contribution} = 170,000 \times 5.10 = 867,000 \]Subtract the fixed costs to get profit before tax:\[ \text{Profit Before Tax} = 867,000 - 459,000 = 408,000 \]Finally, apply the tax rate to find net income:\[ \text{Net Income} = \text{Profit Before Tax} \times (1 - \text{Tax Rate}) \] \[ \text{Net Income} = 408,000 \times 0.70 = 285,600 \]

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Key Concepts

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

Contribution Margin
The contribution margin represents the portion of sales revenue that exceeds total variable costs. It is a useful metric for understanding how much of each dollar earned contributes to covering fixed costs and generating profit. In this example:
  • Average Sales per Customer: $8.50
  • Average Variable Cost per Customer: $3.40
  • Contribution Margin per Customer: $8.50 - $3.40 = $5.10
This contribution margin of $5.10 indicates how much each customer contributes towards fixed costs and profit after accounting for variable expenses. It's a crucial factor in determining things like break-even and target revenues needed for specific profit goals.
Fixed Costs
Fixed costs are those expenses that do not change with the number of customers served. Whether you have one customer or one thousand customers, fixed costs remain constant. For Express Banquet, the fixed costs are:
  • Total Fixed Costs: $459,000 per year
These fixed costs must be covered by the contribution margin generated by each customer before any profit can be realized. Understanding fixed costs is essential because it allows businesses to calculate their break-even point and plan for profitability.
Variable Costs
Variable costs, unlike fixed costs, fluctuate based on the number of customers. They include the costs of things like food and other expenses that vary depending on customer activity. For Express Banquet:
  • Average Variable Cost per Customer: $3.40
This means that for each additional customer, the business incurs an extra $3.40 in costs. By keeping track of variable costs, businesses can determine the contribution margin and make informed financial decisions. Efficiency in controlling variable costs can directly impact the overall profitability of the operation.
Target Net Income
Achieving a target net income involves calculating the sales needed to not only cover fixed and variable costs but also to reach the desired level of profit after taxes. For the given exercise, the target net income is:
  • Target Net Income: $107,100
To compute the revenues needed, consider both fixed costs and desired profit corrected for taxes. Since the income tax rate is 30%, the pre-tax profit needs to be higher to achieve this target post-tax income. Businesses must calculate:
  • Total Contribution Needed = Fixed Costs + (Target Net Income)/(1-Tax Rate)
  • Revenues Required = Total Contribution Needed / Contribution Margin Ratio
Understanding the target net income allows businesses to set sales goals and create strategies to achieve their financial objectives.

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Most popular questions from this chapter

Hoot Washington is the newly elected leader of the Republican Party. Media Publishers is negotiating to publish Hoot's Manifesto, a new book that promises to be an instant best-seller. The fixed costs of producing and marketing the book will be \(\$ 500,000\). The variable costs of producing and marketing will be \(\$ 4.00\) per copy sold. These costs are before any payments to Hoot. Hoot negotiates an up-front payment of \(\$ 3\) million, plus a \(15 \%\) royalty rate on the net sales price of each book. The net sales price is the listed bookstore price of \(\$ 30,\) minus the margin paid to the bookstore to sell the book. The normal bookstore margin of \(30 \%\) of the listed bookstore price is expected to apply. 1\. Prepare a PV graph for Media Publishers. 2\. How many copies must Media Publishers sell to (a) break even and (b) earn a target operating income of \(\$ 2\) million? 3\. Examine the sensitivity of the breakeven point to the following changes: a. Decreasing the normal bookstore margin to \(20 \%\) of the listed bookstore price of \(\$ 30\) b. Increasing the listed bookstore price to \(\$ 40\) while keeping the bookstore margin at \(30 \%\) c. Comment on the results.

The Super Donut owns and operates six doughnut outlets in and round Kansas City. You are given the following corporate budget data for next year: $$\begin{array}{ll}\text { Revenues } & \$ 10,000,000 \\ \text { Fixed costs } & \$ 1,800,000 \\\\\text { Variable costs } & \$ 8,000,000\end{array}$$ Variable costs change with respect to the number of doughnuts sold. Compute the budgeted operating income for each of the following deviations from the original budget data. (Consider each case independently.) 1\. \(A\) 10 \(\%\) increase in contribution margin, holding revenues constant 2\. \(A\) 10 \(\%\) decrease in contribution margin, holding revenues constant 3\. \(A 5 \%\) increase in fixed costs 4\. A \(5 \%\) decrease in fixed costs 5\. An \(8 \%\) increase in units sold 6\. \(\mathrm{An} 8 \%\) decrease in units sold 7\. \(A \cdot 10 \%\) increase in fixed costs and a \(10 \%\) increase in units sold 8\. \(A 5 \%\) increase in fixed costs and a \(5 \%\) decrease in variable costs.

The Ronowski Company has three product lines of belts \(-A, B,\) and \(C-\) with contribution margins of \(\$ 3, \$ 2,\) and \(\$ 1,\) respectively. The president foresees sales of 200,000 units in the coming period, consisting of 20,000 units of \(\mathrm{A}, 100,000\) units of \(\mathrm{B},\) and 80,000 units of \(\mathrm{C}\). The company's fixed costs for the period are \(\$ 255,000\) 1\. What is the company's breakeven point in units, assuming that the given sales mix is maintained? 2\. If the sales mix is maintained, what is the total contribution margin when 200,000 units are sold? What is the operating income? 3\. What would operating income be if 20,000 units of \(A, 80,000\) units of \(B\), and 100,000 units of \(C\) were sold? What is the new breakeven point in units if these relationships persist in the next period?

Stylewise Printing Company currently leases its only copy machine for \(\$ 1,000\) a month. The company is considering replacing this leasing agreement with a new contract that is entirely commission based. Under the new agreement Stylewise would pay a commission for its printing at a rate of \(\$ 10\) for every 500 pages printed. The company currently charges \(\$ 0.15\) per page to its customers. The paper used in printing costs the company \(\$ .03\) per page and other variable costs, including hourly labor amount to \(\$ .04\) per page. 1\. What is the company's breakeven point under the current leasing agreement? What is it under the new commission based agreement? 2\. For what range of sales levels will Stylewise prefer (a) the fixed lease agreement (b) the commission agreement? 3\. Do this question only if you have covered the chapter appendix in your class. Stylewise estimates that the company is equally likely to sell 20,\(000 ; 40,000 ; 60,000 ; 80,000 ;\) or 100,000 pages of print. Using infor mation from the original problem, prepare a table that shows the expected profit at each sales level under the fixed leasing agreement and under the commission based agreement. What is the expected value of each agreement? Which agreement should Stylewise choose?

Garrett Manufacturing sold 410,000 units of its product for \(\$ 68\) per unit in 2011 Variable cost per unit is \(\$ 60\) and total fixed costs are \(\$ 1,640,000\). 1\. Calculate (a) contribution margin and (b) operating income. 2\. Garrett's current manufacturing process is labor intensive. Kate Schoenen, Garrett's production manager, has proposed investing in state-of-the-art manufacturing equipment, which will increase the annual fixed costs to \(\$ 5,330,000\). The variable costs are expected to decrease to \(\$ 54\) per unit. Garrett expects to maintain the same sales volume and selling price next year. How would acceptance of Schoenen's proposal affect your answers to (a) and (b) in requirement 1?
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