Question

if a business had a capacity of $10,000,000 of sales, actual sales of $6,000,000, break-even sales of $4,200,000, fixed costs of $1,800,000, and variable costs of 60% of sales, what is the margin of safety expressed as a percentage of sales?
%

Explanation:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"blank_filling_formatter",
"explain_then_answer",
"tutor",
"mastery_adaptive_brevity"
],
"needs_drawing": false,
"concepts_used": [
"Margin of Safety"
],
"new_concepts": [],
"current_concepts": [
"Margin of Safety",
"Break-Even Analysis"
]
}
</pre_analysis>

<reasoning>

Identify the given values

Using the Margin of Safety knowledge point
\[

$$\begin{aligned} &\text{Actual Sales} = \$6,000,000 \\ &\text{Break-Even Sales} = \$4,200,000 \end{aligned}$$

\]

Calculate the margin of safety in dollars

Using the Margin of Safety knowledge point
\[

$$\begin{aligned} \text{Margin of Safety (Dollars)} &= \text{Actual Sales} - \text{Break-Even Sales} \\ &= \$6,000,000 - \$4,200,000 \\ &= \$1,800,000 \end{aligned}$$

\]

Calculate the margin of safety percentage

Using the Margin of Safety knowledge point
\[

$$\begin{aligned} \text{Margin of Safety Percentage} &= \frac{\text{Margin of Safety (Dollars)}}{\text{Actual Sales}} \times 100\% \\ &= \frac{\$1,800,000}{\$6,000,000} \times 100\% \\ &= 30\% \end{aligned}$$

\]
</reasoning>

<answer>
If a business had a capacity of \$10,000,000 of sales, actual sales of \$6,000,000, break-even sales of \$4,200,000, fixed costs of \$1,800,000, and variable costs of 60% of sales, what is the margin of safety expressed as a percentage of sales?
<blank>30</blank>%
</answer>

<post_analysis>
{
"subject": "Business",
"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Business",
"Accounting",
"Margin of Safety"
]
}
</post_analysis>

Answer:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"blank_filling_formatter",
"explain_then_answer",
"tutor",
"mastery_adaptive_brevity"
],
"needs_drawing": false,
"concepts_used": [
"Margin of Safety"
],
"new_concepts": [],
"current_concepts": [
"Margin of Safety",
"Break-Even Analysis"
]
}
</pre_analysis>

<reasoning>

Identify the given values

Using the Margin of Safety knowledge point
\[

$$\begin{aligned} &\text{Actual Sales} = \$6,000,000 \\ &\text{Break-Even Sales} = \$4,200,000 \end{aligned}$$

\]

Calculate the margin of safety in dollars

Using the Margin of Safety knowledge point
\[

$$\begin{aligned} \text{Margin of Safety (Dollars)} &= \text{Actual Sales} - \text{Break-Even Sales} \\ &= \$6,000,000 - \$4,200,000 \\ &= \$1,800,000 \end{aligned}$$

\]

Calculate the margin of safety percentage

Using the Margin of Safety knowledge point
\[

$$\begin{aligned} \text{Margin of Safety Percentage} &= \frac{\text{Margin of Safety (Dollars)}}{\text{Actual Sales}} \times 100\% \\ &= \frac{\$1,800,000}{\$6,000,000} \times 100\% \\ &= 30\% \end{aligned}$$

\]
</reasoning>

<answer>
If a business had a capacity of \$10,000,000 of sales, actual sales of \$6,000,000, break-even sales of \$4,200,000, fixed costs of \$1,800,000, and variable costs of 60% of sales, what is the margin of safety expressed as a percentage of sales?
<blank>30</blank>%
</answer>

<post_analysis>
{
"subject": "Business",
"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Business",
"Accounting",
"Margin of Safety"
]
}
</post_analysis>