We are starting a business and want to decide how much leverage to assume. In one scenario, we can invest $60,000 in the business and have variable cost of $.80 per unit. In the second scenario, we can invest $12,000; however, variable cost will now be $1.60 per unit, reflecting the higher labor contribution required to compensate for our minimal investment. In either case, revenue per unit will be $2.00.

a) What is the break-even point in volume for each scenario?
b) If our expected volume will be 40,000 units, which scenario would you choose, and why?
c) At 40,000 units and your preferred scenario, what is the profit or loss of the company?

a) To calculate the break-even point in volume for each scenario, we need to find the point where the total revenue equals the total cost.

In the first scenario, the total cost is the sum of the fixed investment ($60,000) and the variable cost per unit ($0.80).

Break-even point = Total cost / Revenue per unit
Break-even point = ($60,000 + (Variable cost per unit * x)) / $2.00

In the second scenario, the total cost is the sum of the fixed investment ($12,000) and the variable cost per unit ($1.60).

Break-even point = Total cost / Revenue per unit
Break-even point = ($12,000 + (Variable cost per unit * x)) / $2.00

To solve for x (the break-even point in volume) in both scenarios, we need to set the total cost equal to the total revenue and solve for x.

b) To compare the two scenarios and choose the more favorable one, we need to determine which scenario yields higher profitability at the expected volume of 40,000 units.

For the first scenario:
Total cost = $60,000 + (Variable cost per unit * 40,000)
Total revenue = $2.00 * 40,000

For the second scenario:
Total cost = $12,000 + (Variable cost per unit * 40,000)
Total revenue = $2.00 * 40,000

Calculate the profit for each scenario by subtracting the total cost from the total revenue.

c) At the preferred scenario determined in part b), the profit or loss of the company can be calculated by subtracting the total cost from the total revenue at the expected volume of 40,000 units.