The Can-Do Co. is analyzing a proposed project. The company expects to sell 12,000 units, give or take 4%. The expected variable cost per unit is $7 and the expected fixed cost is $36,000. The fixed and variable cost estimates are considered accurate within a plus or minus 6% range. The depreciation expense is $30,000. The tax rate is 34%. The sale price is estimated at $14 a unit, give or take 5%. The company bases its sensitivity analysis on the expected case scenario.
-What is the contribution margin for a sensitivity analysis using a variable cost per unit of $8?

Question

Quizplus · Accepted Answer

To calculate the contribution margin, we need to subtract the variable cost per unit from the sale price per unit.

Contribution Margin = Sale Price per Unit - Variable Cost per Unit

Using the expected sale price of $14 and the expected variable cost per unit of $7:

Contribution Margin = $14 - $7 = $7

Now, let's calculate the contribution margin for a sensitivity analysis using a variable cost per unit of $8:

Contribution Margin = $14 - $8 = $6

Therefore, the contribution margin for the sensitivity analysis using a variable cost per unit of $8 is $6.

To determine the best choice(s), we need to calculate the following:

1. Breakeven point in units 
2. Breakeven point in dollars 
3. Profit at expected sales volume

1. Breakeven point in units:

Breakeven Point = Fixed Costs / Contribution Margin per Unit

Breakeven Point = $36,000 / $7 = 5,143 units

2. Breakeven point in dollars:

Breakeven Point = Fixed Costs / Contribution Margin Ratio

Contribution Margin Ratio = Contribution Margin per Unit / Sale Price per Unit

Contribution Margin Ratio = $7 / $14 = 0.5

Breakeven Point = $36,000 / 0.5 = $72,000

3. Profit at expected sales volume:

Expected Sales Revenue = Expected Sales Volume x Sale Price per Unit

Expected Sales Revenue = 12,000 x $14 = $168,000

Expected Variable Costs = Expected Sales Volume x Variable Cost per Unit

Expected Variable Costs = 12,000 x $7 = $84,000

Expected Contribution Margin = Expected Sales Revenue - Expected Variable Costs

Expected Contribution Margin = $168,000 - $84,000 = $84,000

Expected Profit = Expected Contribution Margin - Depreciation Expense

Expected Profit = $84,000 - $30,000 = $54,000

Based on the calculations, the project is expected to generate a profit of $54,000 at the expected sales volume of 12,000 units.

However, we also need to consider the sensitivity analysis using a variable cost per unit of $8.

Expected Sales Revenue = Expected Sales Volume x Sale Price per Unit

Expected Sales Revenue = 12,000 x $14 = $168,000

Expected Variable Costs = Expected Sales Volume x Variable Cost per Unit

Expected Variable Costs = 12,000 x $8 = $96,000

Expected Contribution Margin = Expected Sales Revenue - Expected Variable Costs

Expected Contribution Margin = $168,000 - $96,000 = $72,000

Expected Profit = Expected Contribution Margin - Depreciation Expense

Expected Profit = $72,000 - $30,000 = $42,000

Therefore, if the variable cost per unit increases to $8, the expected profit will decrease to $42,000.

The best choice(s) depend on the company's goals and risk tolerance. If the company is risk-averse and wants to ensure a higher probability of profitability, they may choose not to pursue the project. If the company is more risk-tolerant and believes they can still generate a profit with a variable cost per unit of $8, they may choose to move forward with the project.