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Sagot :
Certainly! Let's break down the solution step by step to determine the financial impact of discontinuing the Beta product line.
### Step 1: Calculate the Contribution Margin per Unit of Beta
The contribution margin per unit is calculated as the selling price minus all variable costs per unit.
[tex]\[ \text{Contribution Margin per Unit} = \text{Selling Price} - (\text{Direct Materials} + \text{Direct Labor} + \text{Variable Manufacturing Overhead} + \text{Variable Selling Expenses}) \][/tex]
Given the data:
- Selling Price of Beta: \[tex]$85 - Direct Materials: \$[/tex]6
- Direct Labor: \[tex]$12 - Variable Manufacturing Overhead: \$[/tex]20
- Variable Selling Expenses: \[tex]$19 Calculate the contribution margin per unit: \[ \text{Contribution Margin per Unit} = 85 - (6 + 12 + 20 + 19) = 85 - 57 = 28 \] So, the contribution margin per unit of Beta is \$[/tex]28.
### Step 2: Calculate the Total Contribution Margin Lost from Discontinuing Beta
Next, determine the total contribution margin lost if Beta is discontinued. Multiply the contribution margin per unit by the number of units sold annually.
Given:
- Units Sold of Beta: 91,000
[tex]\[ \text{Total Contribution Margin Lost} = \text{Contribution Margin per Unit} \times \text{Units Sold} \][/tex]
[tex]\[ \text{Total Contribution Margin Lost} = 28 \times 91,000 = 2,548,000 \][/tex]
So, the total contribution margin lost is \[tex]$2,548,000. ### Step 3: Calculate Traceable Fixed Manufacturing Overhead Saved The traceable fixed manufacturing overhead is avoidable if the Beta product line is discontinued. Multiply the fixed overhead per unit by the number of units sold. Given: - Traceable Fixed Manufacturing Overhead of Beta: \$[/tex]6
- Units Sold of Beta: 91,000
[tex]\[ \text{Fixed Manufacturing Overhead Saved} = \text{Traceable Fixed Manufacturing Overhead per Unit} \times \text{Units Sold} \][/tex]
[tex]\[ \text{Fixed Manufacturing Overhead Saved} = 6 \times 91,000 = 546,000 \][/tex]
So, the traceable fixed manufacturing overhead saved is \[tex]$546,000. ### Step 4: Determine the Financial Impact Finally, calculate the overall financial impact of discontinuing the Beta product line. Subtract the fixed manufacturing overhead saved from the total contribution margin lost. \[ \text{Financial Impact} = -\text{Total Contribution Margin Lost} + \text{Fixed Manufacturing Overhead Saved} \] \[ \text{Financial Impact} = -2,548,000 + 546,000 = -2,002,000 \] So, the financial impact (disadvantage) of discontinuing the Beta product line is \$[/tex]-2,002,000 or a \[tex]$(2,002,000) disadvantage. Therefore, discontinuing the Beta product line would result in a financial disadvantage of \$[/tex](2,002,000).
### Step 1: Calculate the Contribution Margin per Unit of Beta
The contribution margin per unit is calculated as the selling price minus all variable costs per unit.
[tex]\[ \text{Contribution Margin per Unit} = \text{Selling Price} - (\text{Direct Materials} + \text{Direct Labor} + \text{Variable Manufacturing Overhead} + \text{Variable Selling Expenses}) \][/tex]
Given the data:
- Selling Price of Beta: \[tex]$85 - Direct Materials: \$[/tex]6
- Direct Labor: \[tex]$12 - Variable Manufacturing Overhead: \$[/tex]20
- Variable Selling Expenses: \[tex]$19 Calculate the contribution margin per unit: \[ \text{Contribution Margin per Unit} = 85 - (6 + 12 + 20 + 19) = 85 - 57 = 28 \] So, the contribution margin per unit of Beta is \$[/tex]28.
### Step 2: Calculate the Total Contribution Margin Lost from Discontinuing Beta
Next, determine the total contribution margin lost if Beta is discontinued. Multiply the contribution margin per unit by the number of units sold annually.
Given:
- Units Sold of Beta: 91,000
[tex]\[ \text{Total Contribution Margin Lost} = \text{Contribution Margin per Unit} \times \text{Units Sold} \][/tex]
[tex]\[ \text{Total Contribution Margin Lost} = 28 \times 91,000 = 2,548,000 \][/tex]
So, the total contribution margin lost is \[tex]$2,548,000. ### Step 3: Calculate Traceable Fixed Manufacturing Overhead Saved The traceable fixed manufacturing overhead is avoidable if the Beta product line is discontinued. Multiply the fixed overhead per unit by the number of units sold. Given: - Traceable Fixed Manufacturing Overhead of Beta: \$[/tex]6
- Units Sold of Beta: 91,000
[tex]\[ \text{Fixed Manufacturing Overhead Saved} = \text{Traceable Fixed Manufacturing Overhead per Unit} \times \text{Units Sold} \][/tex]
[tex]\[ \text{Fixed Manufacturing Overhead Saved} = 6 \times 91,000 = 546,000 \][/tex]
So, the traceable fixed manufacturing overhead saved is \[tex]$546,000. ### Step 4: Determine the Financial Impact Finally, calculate the overall financial impact of discontinuing the Beta product line. Subtract the fixed manufacturing overhead saved from the total contribution margin lost. \[ \text{Financial Impact} = -\text{Total Contribution Margin Lost} + \text{Fixed Manufacturing Overhead Saved} \] \[ \text{Financial Impact} = -2,548,000 + 546,000 = -2,002,000 \] So, the financial impact (disadvantage) of discontinuing the Beta product line is \$[/tex]-2,002,000 or a \[tex]$(2,002,000) disadvantage. Therefore, discontinuing the Beta product line would result in a financial disadvantage of \$[/tex](2,002,000).
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