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To determine whether the Boot Department at the Omaha Department Store should be closed, follow these steps:
### Step 1: Calculate Total Fixed Operating Costs
The total fixed operating costs include both fixed and variable costs related to the boot department’s activity:
[tex]\[ \text{Fixed Operating Costs Total} = \text{Sales Revenue} + \text{Variable Costs} + \text{Cost of Goods Sold} + \text{Sales Commissions} \][/tex]
Plug in the given values:
[tex]\[ 363,000 + 290,000 + 32,000 + 93,000 = \$778,000 \][/tex]
### Step 2: Calculate Contribution Margin
The contribution margin represents the amount remaining from sales revenue after deducting all variable costs, cost of goods sold, and sales commissions:
[tex]\[ \text{Contribution Margin} = \text{Sales Revenue} - (\text{Variable Costs} + \text{Cost of Goods Sold} + \text{Sales Commissions}) \][/tex]
Plug in the given values:
[tex]\[ 363,000 - (290,000 + 32,000 + 93,000) = 363,000 - 415,000 = -\$52,000 \][/tex]
### Step 3: Calculate Avoidable and Unavoidable Fixed Operating Costs
Determine the portion of the total fixed operating costs that are avoidable or unavoidable:
[tex]\[ \text{Fixed Operating Costs Avoidable} = 0.8 \times \text{Fixed Operating Costs Total} \][/tex]
[tex]\[ \text{Fixed Operating Costs Unavoidable} = 0.2 \times \text{Fixed Operating Costs Total} \][/tex]
Plug in the total fixed operating costs:
[tex]\[ \text{Fixed Operating Costs Avoidable} = 0.8 \times 778,000 = \$622,400 \][/tex]
[tex]\[ \text{Fixed Operating Costs Unavoidable} = 0.2 \times 778,000 = \$155,600 \][/tex]
### Step 4: Determine Profit/Loss if the Boot Department is Closed
Calculate the financial impact of closing the department considering only unavoidable fixed costs:
[tex]\[ \text{Profit/Loss if Closed} = -\text{Fixed Operating Costs Unavoidable} \][/tex]
[tex]\[ -\$155,600 \][/tex]
### Step 5: Determine Profit/Loss if the Boot Department Continues Operating
Calculate the financial outcome if the department remains open, which involves the contribution margin minus the total fixed operating costs:
[tex]\[ \text{Profit/Loss if Open} = \text{Contribution Margin} - \text{Fixed Operating Costs Total} \][/tex]
[tex]\[ -52,000 - 778,000 = -\$830,000 \][/tex]
### Step 6: Make the Decision
Compare the outcomes of closing and operating the department:
- Profit/Loss if Closed: -\[tex]$155,600 - Profit/Loss if Open: -\$[/tex]830,000
If the department remains open, Omaha would face a loss of \[tex]$830,000, but if the department closes, the loss would reduce to \$[/tex]155,600. Clearly, closing the department results in a smaller loss.
### Conclusion
Omaha would be better off by closing the Boot Department.
Answer: Yes, Omaha would be better off by \$52,000.
### Step 1: Calculate Total Fixed Operating Costs
The total fixed operating costs include both fixed and variable costs related to the boot department’s activity:
[tex]\[ \text{Fixed Operating Costs Total} = \text{Sales Revenue} + \text{Variable Costs} + \text{Cost of Goods Sold} + \text{Sales Commissions} \][/tex]
Plug in the given values:
[tex]\[ 363,000 + 290,000 + 32,000 + 93,000 = \$778,000 \][/tex]
### Step 2: Calculate Contribution Margin
The contribution margin represents the amount remaining from sales revenue after deducting all variable costs, cost of goods sold, and sales commissions:
[tex]\[ \text{Contribution Margin} = \text{Sales Revenue} - (\text{Variable Costs} + \text{Cost of Goods Sold} + \text{Sales Commissions}) \][/tex]
Plug in the given values:
[tex]\[ 363,000 - (290,000 + 32,000 + 93,000) = 363,000 - 415,000 = -\$52,000 \][/tex]
### Step 3: Calculate Avoidable and Unavoidable Fixed Operating Costs
Determine the portion of the total fixed operating costs that are avoidable or unavoidable:
[tex]\[ \text{Fixed Operating Costs Avoidable} = 0.8 \times \text{Fixed Operating Costs Total} \][/tex]
[tex]\[ \text{Fixed Operating Costs Unavoidable} = 0.2 \times \text{Fixed Operating Costs Total} \][/tex]
Plug in the total fixed operating costs:
[tex]\[ \text{Fixed Operating Costs Avoidable} = 0.8 \times 778,000 = \$622,400 \][/tex]
[tex]\[ \text{Fixed Operating Costs Unavoidable} = 0.2 \times 778,000 = \$155,600 \][/tex]
### Step 4: Determine Profit/Loss if the Boot Department is Closed
Calculate the financial impact of closing the department considering only unavoidable fixed costs:
[tex]\[ \text{Profit/Loss if Closed} = -\text{Fixed Operating Costs Unavoidable} \][/tex]
[tex]\[ -\$155,600 \][/tex]
### Step 5: Determine Profit/Loss if the Boot Department Continues Operating
Calculate the financial outcome if the department remains open, which involves the contribution margin minus the total fixed operating costs:
[tex]\[ \text{Profit/Loss if Open} = \text{Contribution Margin} - \text{Fixed Operating Costs Total} \][/tex]
[tex]\[ -52,000 - 778,000 = -\$830,000 \][/tex]
### Step 6: Make the Decision
Compare the outcomes of closing and operating the department:
- Profit/Loss if Closed: -\[tex]$155,600 - Profit/Loss if Open: -\$[/tex]830,000
If the department remains open, Omaha would face a loss of \[tex]$830,000, but if the department closes, the loss would reduce to \$[/tex]155,600. Clearly, closing the department results in a smaller loss.
### Conclusion
Omaha would be better off by closing the Boot Department.
Answer: Yes, Omaha would be better off by \$52,000.
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