Question
Birch Company normally produces and sells 30,000 units of RG-6 each month. The selling price is $22 per unit, variable costs are $14 per unit, fixed manufacturing overhead costs total $150,000 per month, and fixed selling costs total $30,000 per month.
Employment-contract strikes in the companies that purchase the bulk of the RG-6 units have caused Birch Company’s sales to temporarily drop to only 8,000 units per month. Birch Company estimates the strikes will last for two months, after which time sales of RG-6 should return to normal. Due to the current low level of sales, Birch Company is thinking about closing its own plant during the strike, which would reduce fixed manufacturing overhead costs by $45,000 per month and fixed selling costs by 10%. Start-up costs at the end of the shutdown would total $8,000. Because Birch Company uses Lean Production methods, no inventories are on hand.
At what level of unit sales for the two month period would Birch Company be indifferent between closing the plant or keeping it open?
Employment-contract strikes in the companies that purchase the bulk of the RG-6 units have caused Birch Company’s sales to temporarily drop to only 8,000 units per month. Birch Company estimates the strikes will last for two months, after which time sales of RG-6 should return to normal. Due to the current low level of sales, Birch Company is thinking about closing its own plant during the strike, which would reduce fixed manufacturing overhead costs by $45,000 per month and fixed selling costs by 10%. Start-up costs at the end of the shutdown would total $8,000. Because Birch Company uses Lean Production methods, no inventories are on hand.
At what level of unit sales for the two month period would Birch Company be indifferent between closing the plant or keeping it open?
Answers
GPT-4o mini
To determine at what level of unit sales Birch Company would be indifferent between closing the plant or keeping it open during the strike, we need to assess the costs involved in both scenarios.
### Current Situation (Keeping the Plant Open)
1. **Sales Revenue**:
- Selling Price: $22 per unit
- Units Sold per Month: 8,000 units
- Monthly Revenue = 8,000 units * $22/unit = $176,000
2. **Variable Costs**:
- Variable Cost: $14 per unit
- Monthly Variable Costs = 8,000 units * $14/unit = $112,000
3. **Fixed Manufacturing Overhead**:
- Monthly Fixed Manufacturing Overhead = $150,000
4. **Fixed Selling Costs**:
- Monthly Fixed Selling Costs = $30,000
5. **Total Costs**:
- Total Costs (Fixed + Variable) = Fixed Manufacturing + Fixed Selling + Variable Costs
- Monthly Total Costs when open = $150,000 + $30,000 + $112,000 = $292,000
6. **Monthly Profit when keeping the plant open**:
- Monthly Profit = Revenue - Total Costs
- Monthly Profit = $176,000 - $292,000 = -$116,000
### Scenario of Closing the Plant
1. **Costs when Closing the Plant**:
- Reduced Fixed Manufacturing Overhead = $150,000 - $45,000 = $105,000
- Reduced Fixed Selling Costs = $30,000 - (10% of $30,000) = $30,000 - $3,000 = $27,000
2. **Total Costs after Closing**:
- Total Costs when closed = Reduced Fixed Manufacturing + Reduced Fixed Selling + Start-up Costs
- For two months: (Fixed Manufacturing + Fixed Selling) * 2 + Start-up Cost = ($105,000 + $27,000) * 2 + $8,000
- Total Costs for two months = $132,000 * 2 + $8,000 = $264,000 + $8,000 = $272,000
### Indifference Point
To find the indifference point, we need to equate the profits from both scenarios.
Let \( x \) be the number of units sold per month that would make the profits from keeping the plant open equal to the losses from closing it.
Keeping the plant open for 2 months:
- Revenue = \( 2 \times (x \times 22) = 44x \)
- Variable Costs = \( 2 \times (x \times 14) = 28x \)
- Total Fixed Costs = $150,000 * 2 + $30,000 * 2 = $360,000
- Profit/Loss when keeping open = Revenue - Total Costs
Profit/Loss = \( 44x - (28x + 360,000) \)
Now, calculate the profit/loss equation:
\( 44x - 28x - 360,000 = 16x - 360,000 \)
Loss when closing for two months:
- $272,000 during shutdown.
Equating both:
\( 16x - 360,000 = -272,000 \)
Now, solving for \( x \):
\[
16x = 360,000 - 272,000
\]
\[
16x = 88,000
\]
\[
x = \frac{88,000}{16} = 5,500 \text{ units}
\]
### Conclusion
Birch Company will be indifferent between closing the plant or keeping it open at a sales level of **5,500 units per month** during the two-month period.
### Current Situation (Keeping the Plant Open)
1. **Sales Revenue**:
- Selling Price: $22 per unit
- Units Sold per Month: 8,000 units
- Monthly Revenue = 8,000 units * $22/unit = $176,000
2. **Variable Costs**:
- Variable Cost: $14 per unit
- Monthly Variable Costs = 8,000 units * $14/unit = $112,000
3. **Fixed Manufacturing Overhead**:
- Monthly Fixed Manufacturing Overhead = $150,000
4. **Fixed Selling Costs**:
- Monthly Fixed Selling Costs = $30,000
5. **Total Costs**:
- Total Costs (Fixed + Variable) = Fixed Manufacturing + Fixed Selling + Variable Costs
- Monthly Total Costs when open = $150,000 + $30,000 + $112,000 = $292,000
6. **Monthly Profit when keeping the plant open**:
- Monthly Profit = Revenue - Total Costs
- Monthly Profit = $176,000 - $292,000 = -$116,000
### Scenario of Closing the Plant
1. **Costs when Closing the Plant**:
- Reduced Fixed Manufacturing Overhead = $150,000 - $45,000 = $105,000
- Reduced Fixed Selling Costs = $30,000 - (10% of $30,000) = $30,000 - $3,000 = $27,000
2. **Total Costs after Closing**:
- Total Costs when closed = Reduced Fixed Manufacturing + Reduced Fixed Selling + Start-up Costs
- For two months: (Fixed Manufacturing + Fixed Selling) * 2 + Start-up Cost = ($105,000 + $27,000) * 2 + $8,000
- Total Costs for two months = $132,000 * 2 + $8,000 = $264,000 + $8,000 = $272,000
### Indifference Point
To find the indifference point, we need to equate the profits from both scenarios.
Let \( x \) be the number of units sold per month that would make the profits from keeping the plant open equal to the losses from closing it.
Keeping the plant open for 2 months:
- Revenue = \( 2 \times (x \times 22) = 44x \)
- Variable Costs = \( 2 \times (x \times 14) = 28x \)
- Total Fixed Costs = $150,000 * 2 + $30,000 * 2 = $360,000
- Profit/Loss when keeping open = Revenue - Total Costs
Profit/Loss = \( 44x - (28x + 360,000) \)
Now, calculate the profit/loss equation:
\( 44x - 28x - 360,000 = 16x - 360,000 \)
Loss when closing for two months:
- $272,000 during shutdown.
Equating both:
\( 16x - 360,000 = -272,000 \)
Now, solving for \( x \):
\[
16x = 360,000 - 272,000
\]
\[
16x = 88,000
\]
\[
x = \frac{88,000}{16} = 5,500 \text{ units}
\]
### Conclusion
Birch Company will be indifferent between closing the plant or keeping it open at a sales level of **5,500 units per month** during the two-month period.