https://file.aiquickdraw.com/mathbot/file/17294763261206ooby5z4.jpg

Let's go through each part of the problem step by step:

### Given Data:
- **Sales** = $902,000
- **Fixed Costs** = $510,000
- **Total Variable Costs** = $204,030
- **Total Costs** = $714,030
- **Net Income** = $187,970

### (a) Contribution Margin and Contribution Rate
The **contribution margin** represents the amount of sales revenue remaining after covering variable costs. It is calculated as:

\[
\text{Contribution Margin} = \text{Sales} - \text{Total Variable Costs}
\]

\[
\text{Contribution Margin} = 902,000 - 204,030 = 697,970
\]

The **contribution rate** (or contribution margin ratio) is the percentage of sales that contributes to covering fixed costs and generating profit. It is calculated as:

\[
\text{Contribution Rate} = \frac{\text{Contribution Margin}}{\text{Sales}} \times 100
\]

\[
\text{Contribution Rate} = \frac{697,970}{902,000} \times 100 \approx 77.4\%
\]

### (b) Break-Even Sales
The **break-even point** in sales is the level at which total revenue equals total costs (no profit or loss). It is calculated as:

\[
\text{Break-Even Sales} = \frac{\text{Fixed Costs}}{\text{Contribution Rate}}
\]

Substituting the values:

\[
\text{Break-Even Sales} = \frac{510,000}{0.774} \approx 658,523.14
\]

### (c) Break-Even Sales with Additional Costs
If the business spends an additional $22,000 to upgrade its processes, the new fixed cost becomes:

\[
\text{New Fixed Costs} = 510,000 + 22,000 = 532,000
\]

The break-even sales are recalculated using the same formula:

\[
\text{Break-Even Sales} = \frac{\text{New Fixed Costs}}{\text{Contribution Rate}} = \frac{532,000}{0.774} \approx 687,476.68
\]

### (d) Effect of 3% More Sales on Net Income
If sales increase by 3%, the new sales amount will be:

\[
\text{New Sales} = 902,000 \times (1 + 0.03) = 902,000 \times 1.03 = 929,060
\]

The new contribution margin is:

\[
\text{New Contribution Margin} = \text{New Sales} - \text{Total Variable Costs}
\]

Since the variable cost will also increase proportionally with sales, we calculate the new variable cost:

\[
\text{New Variable Costs} = 204,030 \times 1.03 = 210,151
\]

\[
\text{New Contribution Margin} = 929,060 - 210,151 = 718,909
\]

The new net income is:

\[
\text{New Net Income} = \text{New Contribution Margin} - \text{Fixed Costs} = 718,909 - 510,000 = 208,909
\]

---

Would you like a further breakdown of any part of this solution? Here are 5 related questions for practice:

1. What happens to the break-even point if the variable cost increases by 10%?
2. How does the contribution margin change if sales decrease by 5%?
3. If fixed costs decrease by $50,000, what would be the new break-even point?
4. What would the profit be if sales increased by 5%, and variable costs stayed the same?
5. How much would net income change if both fixed costs and sales increased by 5%?

**Tip**: The contribution margin is a crucial indicator for analyzing how much revenue remains to cover fixed costs and generate profit. Keep an eye on it in cost analysis.

Projected financial results for the university's cafeteria for next year are shown. Answer each of the following independent questions: (a) How much is the contribution margin and the contribution rate? (b) How much does the business need to sell to break even? (c) If the business was to spend $22,000 to upgrade their processes, how much does the business need to sell to break even? (d) If 3% more meals were sold, what would be the resulting net income?

Learn how to calculate the contribution margin, break-even sales, and the impact of upgrades on a university cafeteria's financial results. This problem covers cost accounting concepts including contribution margin and break-even analysis.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation