Stan's Cans, Inc. expects to earn $150,000 next year after taxes on sales of $2,200,000. Stan's manufactures only one size of garbage can and is located in the small, but beautiful, town of Mount Dora, Florida. Stan sells his cans for $8 a piece and they have a variable cost of $2.40 a piece. Stan's tax rate is currently 34%.
a. What are the firm's expected fixed costs for next year?
b. What is the break-even point in units?
after-tax revenue = 66% of 2,200,000 = 1452000
revenue from n cans = 8n
cost for n cans is f + 2.4n
where f is the fixed cost.
after-tax income = 8n*.66 = 5.28n
earnings = income less expenses
2200000/8 = 275000 cans
150000 = 1452000 - f - 2.4(275000)
150000 = 792000 - f
f = 642000
So, earnings = 5.28n - f - 2.4n
= 2.88n - 642000
at breakeven, earnings = 0, so
0 = 2.88n - 642000
n = 222916.6, or 222917
To find the fixed costs, we can start by calculating the firm's expected profit. The formula for profit is:
Profit = Sales - Variable Costs - Fixed Costs - Taxes
We are given that the expected profit after taxes is $150,000, the sales are $2,200,000, and the variable costs per unit are $2.40. We also know the tax rate is 34%.
a. To calculate the fixed costs, we rearrange the formula:
Fixed Costs = Sales - Variable Costs - Profit before Taxes - Taxes
The profit before taxes can be calculated by dividing the expected profit after taxes by (1 - tax rate). Substituting the given values into the formula, we get:
Profit before Taxes = $150,000 / (1 - 0.34) = $150,000 / 0.66 ≈ $227,273.
Fixed Costs = $2,200,000 - ($2.40 per unit * Number of units) - $227,273 - (0.34 * $227,273).
Since we don't have the number of units, we cannot calculate the exact fixed costs.
b. To find the breakeven point in units, we need to determine the quantity of units sold where the firm's total revenue equals its total costs (fixed costs plus variable costs).
Total Revenue = Total Costs
Total Revenue = Price per unit * X (number of units)
Total Costs = Fixed Costs + (Variable Cost per unit * X)
where X is the number of units sold at the breakeven point.
Since we don't have the fixed costs, we can't calculate the breakeven point either.