How much sales are required to earn a target net income of $80,000 if total fixed costs are $100,000, the contribution margin ratio is 40% and the tax rate is 25%?

Question

Quizplus · Accepted Answer

First, we need to calculate the contribution margin (CM) per unit:

CM ratio = Contribution Margin / Sales
40% = (Sales - Variable Costs) / Sales
0.4 = (Sales - Variable Costs) / Sales
0.4 * Sales = Sales - Variable Costs
0.6 * Sales = Variable Costs

Next, we can use the contribution margin ratio to calculate the contribution margin per unit:

CM per unit = Sales price per unit * CM ratio
CM per unit = SP - VC
0.4 * SP = SP - 0.6 * SP
0.4 * SP = 0.4 * SP
SP = $1

Now, we can use the contribution margin per unit to calculate the break-even point:

Break-even point (units) = Fixed Costs / CM per unit
Break-even point (units) = 100,000 / 0.4
Break-even point (units) = 250,000

To calculate the sales needed for a target net income of $80,000:

Sales needed = (Fixed Costs + Target Net Income) / CM ratio
Sales needed = (100,000 + 80,000) / 0.4
Sales needed = 450,000

However, this is the amount of sales before taxes. To account for taxes, we need to divide the amount by (1 - tax rate):

Sales needed (after taxes) = Sales needed / (1 - tax rate)
Sales needed (after taxes) = 450,000 / (1 - 0.25)
Sales needed (after taxes) = 600,000

Therefore, the answer is C) $516,667.

How Much Sales Are Required to Earn a Target Net