A cement manufacturer has supplied the following data:
Tons of cement produced and sold 220,000
Sales revenue $924,000
Variable manufacturing expense $297,000
Fixed manufacturing expense $280,000
Variable selling and admin expense $165,000
Fixed selling and admin expense $82,000
Net operating income $100,000
a. Calculate the company’s unit contribution margin
b. Calculate the company’s unit contribution ratio
c. If the company increases its unit sales volume by 5% without increasing its fixed expenses, what would the company’s net operating income be?
The Correct Answer and Explanation is :
To analyze the cement manufacturer’s financial performance, we’ll calculate the following:
a. Unit Contribution Margin
The unit contribution margin represents the amount each unit sold contributes to covering fixed costs and generating profit. It’s calculated as:
[
\text{Unit Contribution Margin} = \frac{\text{Sales Revenue} – \text{Total Variable Expenses}}{\text{Total Units Sold}}
]
Given:
- Sales Revenue = $924,000
- Variable Manufacturing Expense = $297,000
- Variable Selling and Administrative Expense = $165,000
- Total Units Sold = 220,000
First, determine the total variable expenses:
[
\text{Total Variable Expenses} = \text{Variable Manufacturing Expense} + \text{Variable Selling and Administrative Expense} = \$297,000 + \$165,000 = \$462,000
]
Next, calculate the total contribution margin:
[
\text{Total Contribution Margin} = \text{Sales Revenue} – \text{Total Variable Expenses} = \$924,000 – \$462,000 = \$462,000
]
Now, compute the unit contribution margin:
[
\text{Unit Contribution Margin} = \frac{\$462,000}{220,000 \text{ units}} = \$2.10 \text{ per unit}
]
b. Contribution Margin Ratio
The contribution margin ratio indicates the percentage of each sales dollar available to cover fixed costs and contribute to profit. It’s calculated as:
[
\text{Contribution Margin Ratio} = \frac{\text{Total Contribution Margin}}{\text{Sales Revenue}} \times 100
]
Using the previously calculated total contribution margin:
[
\text{Contribution Margin Ratio} = \frac{\$462,000}{\$924,000} \times 100 = 50\%
]
c. Impact of a 5% Increase in Sales Volume on Net Operating Income
If the company increases its sales volume by 5% without increasing fixed expenses, the new net operating income can be estimated as follows:
- Calculate the increase in units sold:
[
\text{Additional Units} = 220,000 \times 0.05 = 11,000 \text{ units}
]
- Determine the additional contribution margin from these units:
[
\text{Additional Contribution Margin} = \text{Additional Units} \times \text{Unit Contribution Margin} = 11,000 \times \$2.10 = \$23,100
]
- Add the additional contribution margin to the existing net operating income:
[
\text{New Net Operating Income} = \$100,000 + \$23,100 = \$123,100
]
Explanation
The unit contribution margin of $2.10 indicates that each ton of cement sold contributes $2.10 towards covering fixed costs and generating profit. The contribution margin ratio of 50% reveals that half of the sales revenue is available to cover fixed expenses and profit, while the other half covers variable costs.
When sales volume increases by 5%, the company sells an additional 11,000 tons. Each of these additional units contributes $2.10, leading to an extra $23,100 in contribution margin. Since fixed costs remain unchanged, this entire amount boosts the net operating income, increasing it from $100,000 to $123,100.
This analysis underscores the importance of the contribution margin in decision-making. A higher contribution margin per unit means that each sale adds more to covering fixed costs and profit, enhancing the company’s profitability. Understanding these metrics enables management to make informed decisions about pricing, cost control, and sales strategies to optimize financial performance.