The correct answer is given.
This question is asking for the sales volume in dollars given an after-tax net income of $22,500. To solve it, we need to use the version of the breakeven formula for determining the sales volume required to result in a specific dollar amount of profit. Target Sales in $ = (FC + Target Pretax Income) / Contribution Margin Ratio In order to use this formula, we need to calculate three things: (1) the amount of fixed cost in the coming year, (2) the amount of desired net income before tax for the coming year, and (3) the contribution margin ratio for the coming year. (1) We are told that fixed cost for the coming year will be 10% higher than the previous year's fixed cost. So we need to find what the fixed cost was for last year. We know the break-even point in units for last year (20,000) and we know the unit contribution margin for last year ($7.50 ? $2.25 = $5.25). So we can find the fixed cost for last year by using the Break-Even Point in Units formula and solving for FC: FC / Unit Contribution Margin = BEP in Units. FC / 5.25 = 20,000 Solving for FC, we get FC = $105,000 Since fixed cost for the coming year will be 10% higher than last year, fixed cost for the coming year will be $105,000 × 1.10, which is $115,500. (2) The formula to find before-tax net income when we know the after-tax net income is After-Tax NI / (1 - tax rate). Therefore, the desired before tax net income is $22,500 / (1 ? .40), which is $37,500. (3) We are told that variable cost to manufacture will increase by one-third. Variable cost last year was $2.25 per unit. Therefore, variable cost in the coming year will increase by 1/3 of $2.25, which is $.75, so variable cost will be $3 per unit. We are told that the sales price will be $9. Therefore, the Contribution Margin Ratio will be $6 / $9, which is 2/3 or .666667. Now, we can calculate the Target Sales in $, because we have the fixed cost, the target pretax income, and the contribution margin ratio for the coming year. Target Sales in $ = ($115,500 + $37,500) / .666667 = $229,500.
This answer results from using fixed costs of $105,000 to calculate the target sales in dollars. Fixed costs are expected to increase by 10% in the coming year.
This answer results from calculating the desired before-tax net income by dividing the after-tax net income by the tax rate. To calculate the desired before-tax net income, the after-tax net income should be divided by (1 ? the tax rate).
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