Barrey, Inc. is subject to a 40% income tax rate. The following data pertain to the period just ended when the company produced and sold 45,000 units: $$\begin{array} { l r }
\text { Sales revenue } & \$ 1,350,000 \
\text { Variable costs } & 810,000 \
\text { Fixed costs } & 432,000
\end{array}$$ How many units must Barrey sell to earn an after-tax profit of $225,000?

Question

Barrey, Inc. is subject to a 40% income tax rate. The following data pertain to the period just ended when the company produced and sold 45,000 units: $$\begin{array} { l r } 
\text { Sales revenue } & \$ 1,350,000 \
\text { Variable costs } & 810,000 \
\text { Fixed costs } & 432,000
\end{array}$$ How many units must Barrey sell to earn an after-tax profit of $225,000?

Quizplus · Accepted Answer

To earn an after-tax profit of $225,000, Barrey must first calculate its taxable income. Taxable income is calculated by subtracting variable costs and fixed costs from sales revenue. In this case, taxable income is $1,350,000 - $810,000 - $432,000 = $108,000.Next, Barrey must calculate its income tax liability. Income tax liability is calculated by multiplying taxable income by the income tax rate. In this case, income tax liability is $108,000 x 40% = $43,200.Finally, Barrey must calculate the number of units it must sell to earn an after-tax profit of $225,000. After-tax profit is calculated by subtracting income tax liability from taxable income. In this case, after-tax profit is $108,000 - $43,200 = $64,800.To calculate the number of units Barrey must sell, we divide after-tax profit by the contribution margin per unit. Contribution margin per unit is calculated by subtracting variable cost per unit from sales price per unit. In this case, contribution margin per unit is ($1,350,000 / 45,000) - ($810,000 / 45,000) = $12.Therefore, the number of units Barrey must sell to earn an after-tax profit of $225,000 is $64,800 / $12 = 5,400 units.

Barrey, Inc Sales revenue $1,350,000 Variable costs 810,000 Fixed costs 432,000\begin{array} { l r } \text { Sales revenue } & \$ 1,350,000 \\\text { Variable costs } & 810,000 \\\text { Fixed costs } & 432,000\end{array} Sales revenue Variable costs Fixed costs ​$1,350,000810,000432,000​

Barrey, Inc $\begin{array} { l r } \text { Sales revenue } & \$ 1,350,000 \\\text { Variable costs } & 810,000 \\\text { Fixed costs } & 432,000\end{array}$