This answer results from two mistakes: (1) Using 30% as the amount of variable cost percentage instead of 70%. Since the contribution margin is 30%, the variable cost percentage must be 70% of sales (100% ? 30%), not 30%. (2) Forgetting to convert the 6% desired after-tax profit margin to its equivalent before-tax profit margin. The before-tax profit margin is equal to the after-tax profit margin divided by (1 ? the tax rate).
This answer results from using 30% as the amount of variable cost percentage instead of 70%. Since the contribution margin is 30%, the variable cost percentage must be 70% of sales (100% ? 30%), not 30%.
This answer results from using the desired after-tax net income to calculate the needed revenue. The desired after-tax net income needs to be converted to the desired before-tax net income, since revenue is a before-tax amount. The before-tax profit margin is equal to the after-tax profit margin divided by (1 ? the tax rate).
The company wants to earn a 6% return on sales after taxes. Since the amount of sales is the unknown, we will let X equal the sales revenue. Therefore, the desired after-tax profit is .06X. Target pre-tax net income = Target after-tax income ÷ (1 – tax rate) Target after-tax net income = .06X The tax rate is .40, so 1 – the tax rate = .60 So the formula for the target pre-tax income is: Target pre-tax income = .06X ÷ .60 Target pre-tax income = .10X Now, we can use the profit formula to find X: Sales – Variable Costs – Fixed Costs = Pre-tax Profit Sales = X. Since the contribution margin ratio is .30, variable costs are .70 of sales, or .70X. Fixed costs are given as $240,000. The target pre-tax income, per our calculations above, is .10X. Therefore: X – .70X – 240,000 = .10X Solving for X: .30X – 240,000 = .10X .20X = $240,000 X = $1,200,000 Here is an alternate equation that also results in the correct answer, provided by a student: 240,000 + .10X = .30X Solving for X: 240,000 = .20X 1,200,000 = X
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