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For a table manufacturing company, selling price for a table is $159.00 per Unit, Variable cost is $24.00 per Unit, rent is $4,603.00 per month and insurance is $276.00 per month. Company wants to expand its business and improve the table quality, it wants to increase the selling price for a table to $324.00 per Unit, Variable cost to $41.00 per Unit, bigger area will have rent $5,137.00 per month and insurance is $429.00 per month At what point will the company be indifferent between the current mode of operation and the new option?

1 answer

To determine the point at which the company will be indifferent between the current mode of operation and the new option, we need to calculate the break-even point for both options in terms of units sold.

Current Operation

  1. Selling Price per Unit (SP): $159.00
  2. Variable Cost per Unit (VC): $24.00
  3. Fixed Costs (FC):
    • Rent: $4,603.00
    • Insurance: $276.00
    • Total Fixed Costs: \( 4,603 + 276 = 4,879 \)

Contribution Margin (CM): \[ \text{CM} = \text{SP} - \text{VC} = 159 - 24 = 135 \]

Break-even Point in Units (BEP): \[ \text{BEP} = \frac{\text{FC}}{\text{CM}} = \frac{4,879}{135} \approx 36.2 \text{ units} \]

New Operation

  1. Selling Price per Unit (SP): $324.00
  2. Variable Cost per Unit (VC): $41.00
  3. Fixed Costs (FC):
    • Rent: $5,137.00
    • Insurance: $429.00
    • Total Fixed Costs: \( 5,137 + 429 = 5,566 \)

Contribution Margin (CM): \[ \text{CM} = \text{SP} - \text{VC} = 324 - 41 = 283 \]

Break-even Point in Units (BEP): \[ \text{BEP} = \frac{\text{FC}}{\text{CM}} = \frac{5,566}{283} \approx 19.7 \text{ units} \]

Indifferent Between Current and New Option

We need to find the level of sales where the total profit from both options is equal. Let \(x\) be the number of units sold.

Profit for Current Operation: \[ \text{Profit} = (\text{Selling Price} - \text{Variable Cost}) \cdot x - \text{Fixed Costs} = (135 \cdot x) - 4,879 \]

Profit for New Operation: \[ \text{Profit} = (324 - 41) \cdot x - 5,566 = 283 \cdot x - 5,566 \]

Setting Them Equal

Set the profits equal to find \(x\): \[ 135x - 4,879 = 283x - 5,566 \] Rearranging the equation: \[ 4,879 - 5,566 = 283x - 135x \] \[ -687 = 148x \] \[ x = \frac{-687}{148} \approx -4.64 \]

Since we cannot sell a negative quantity, we need to determine a more straightforward approach for comparison under feasible conditions (e.g., what break-even sales would mean in profit terms). The company will likely need to evaluate projected sales based on expected market demand versus current offerings.

Under the current model, if they achieve breakeven, they will start earning profits from the new model sooner at a lesser quantity of units sold than the current operation.

Conclusion

The company will need to sell at least around 37 units in the current model to break even compared to only around 20 units in the new model. The lower threshold in units with the new operation indicates that the new model is aligned with potential profitability expansion, despite greater fixed and variable costs.

For strict indifference, analyze sales projections accounting for market responses to the price increase.