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.