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Sagot :
Sure! Let's go through the solution step-by-step to determine the financial advantage or disadvantage of discontinuing the Beta product line, assuming Cane normally produces and sells 91,000 Betas per year.
### Step 1: Calculate Revenue from Beta
First, we need to calculate the revenue generated by selling 91,000 units of Beta. The selling price of Beta is [tex]\( \$85 \)[/tex] per unit.
[tex]\[ \text{Revenue from Beta} = \text{Selling Price} \times \text{Units Sold} \][/tex]
[tex]\[ \text{Revenue from Beta} = 85 \times 91,000 \][/tex]
[tex]\[ \text{Revenue from Beta} = \$7,735,000 \][/tex]
### Step 2: Calculate Total Cost per Unit for Beta
Next, we need to find the total cost per unit for Beta by summing up the different cost components given in the table, excluding the common fixed expenses since they are unavoidable.
- Direct materials: [tex]\( \$12 \)[/tex]
- Direct labor: [tex]\( \$20 \)[/tex]
- Variable manufacturing overhead: [tex]\( \$6 \)[/tex]
- Traceable fixed manufacturing overhead: [tex]\( \$19 \)[/tex]
- Variable selling expenses: [tex]\( \$9 \)[/tex]
[tex]\[ \text{Total Cost per Unit for Beta} = 12 + 20 + 6 + 19 + 9 \][/tex]
[tex]\[ \text{Total Cost per Unit for Beta} = \$66 \][/tex]
### Step 3: Calculate Total Cost for Producing and Selling Beta
Now, we calculate the total cost of producing and selling 91,000 units of Beta. This is done by multiplying the total cost per unit by the number of units sold.
[tex]\[ \text{Total Cost for Beta} = \text{Total Cost per Unit for Beta} \times \text{Units Sold} \][/tex]
[tex]\[ \text{Total Cost for Beta} = 66 \times 91,000 \][/tex]
[tex]\[ \text{Total Cost for Beta} = \$6,006,000 \][/tex]
### Step 4: Determine Financial Advantage/Disadvantage
The financial advantage or disadvantage of discontinuing the Beta product line is determined by subtracting the total cost from the revenue. This tells us how much profit the Beta product line is generating.
[tex]\[ \text{Financial Advantage/Disadvantage} = \text{Revenue from Beta} - \text{Total Cost for Beta} \][/tex]
[tex]\[ \text{Financial Advantage/Disadvantage} = 7,735,000 - 6,006,000 \][/tex]
[tex]\[ \text{Financial Advantage/Disadvantage} = \$1,729,000 \][/tex]
### Conclusion
The financial impact of discontinuing the Beta product line would be a loss of [tex]\(\$1,729,000\)[/tex]. Therefore, the financial disadvantage of discontinuing the Beta product line is [tex]\(\$1,729,000\)[/tex].
[tex]\[ \boxed{\text{Financial disadvantage} = \$1,729,000} \][/tex]
### Step 1: Calculate Revenue from Beta
First, we need to calculate the revenue generated by selling 91,000 units of Beta. The selling price of Beta is [tex]\( \$85 \)[/tex] per unit.
[tex]\[ \text{Revenue from Beta} = \text{Selling Price} \times \text{Units Sold} \][/tex]
[tex]\[ \text{Revenue from Beta} = 85 \times 91,000 \][/tex]
[tex]\[ \text{Revenue from Beta} = \$7,735,000 \][/tex]
### Step 2: Calculate Total Cost per Unit for Beta
Next, we need to find the total cost per unit for Beta by summing up the different cost components given in the table, excluding the common fixed expenses since they are unavoidable.
- Direct materials: [tex]\( \$12 \)[/tex]
- Direct labor: [tex]\( \$20 \)[/tex]
- Variable manufacturing overhead: [tex]\( \$6 \)[/tex]
- Traceable fixed manufacturing overhead: [tex]\( \$19 \)[/tex]
- Variable selling expenses: [tex]\( \$9 \)[/tex]
[tex]\[ \text{Total Cost per Unit for Beta} = 12 + 20 + 6 + 19 + 9 \][/tex]
[tex]\[ \text{Total Cost per Unit for Beta} = \$66 \][/tex]
### Step 3: Calculate Total Cost for Producing and Selling Beta
Now, we calculate the total cost of producing and selling 91,000 units of Beta. This is done by multiplying the total cost per unit by the number of units sold.
[tex]\[ \text{Total Cost for Beta} = \text{Total Cost per Unit for Beta} \times \text{Units Sold} \][/tex]
[tex]\[ \text{Total Cost for Beta} = 66 \times 91,000 \][/tex]
[tex]\[ \text{Total Cost for Beta} = \$6,006,000 \][/tex]
### Step 4: Determine Financial Advantage/Disadvantage
The financial advantage or disadvantage of discontinuing the Beta product line is determined by subtracting the total cost from the revenue. This tells us how much profit the Beta product line is generating.
[tex]\[ \text{Financial Advantage/Disadvantage} = \text{Revenue from Beta} - \text{Total Cost for Beta} \][/tex]
[tex]\[ \text{Financial Advantage/Disadvantage} = 7,735,000 - 6,006,000 \][/tex]
[tex]\[ \text{Financial Advantage/Disadvantage} = \$1,729,000 \][/tex]
### Conclusion
The financial impact of discontinuing the Beta product line would be a loss of [tex]\(\$1,729,000\)[/tex]. Therefore, the financial disadvantage of discontinuing the Beta product line is [tex]\(\$1,729,000\)[/tex].
[tex]\[ \boxed{\text{Financial disadvantage} = \$1,729,000} \][/tex]
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