Fairfield Company management has budgeted the following amounts for its next fiscal year:
$$\begin{array} { | l | r | }
\hline \text { Total fixed expenses } & \$ 832,500 \
\hline \text { Sale price per unit } & \$ 40 \
\hline \text { Variable expenses per unit } & \$ 25 \
\hline
\end{array}$$ If Fairfield Company can reduce fixed expenses by $41,625, by how much can variable expenses per unit increase and still allow the company to maintain the original breakeven point in units?

Question

Fairfield Company management has budgeted the following amounts for its next fiscal year:
$$\begin{array} { | l | r | } 
\hline \text { Total fixed expenses } & \$ 832,500 \
\hline \text { Sale price per unit } & \$ 40 \
\hline \text { Variable expenses per unit } & \$ 25 \
\hline
\end{array}$$ If Fairfield Company can reduce fixed expenses by $41,625, by how much can variable expenses per unit increase and still allow the company to maintain the original breakeven point in units?

Quizplus · Accepted Answer

The original breakeven point in units is calculated using the formula: $$Breakeven \, Units = \frac{Total \, Fixed \, Expenses}{Sale \, Price \, per \, Unit - Variable \, Expenses \, per \, Unit}$$Substituting the given values: $$Breakeven \, Units = \frac{832,500}{40 - 25} = \frac{832,500}{15} = 55,500 \, units$$If fixed expenses are reduced by $41,625, the new fixed expenses are $832,500 - $41,625 = $790,875.To maintain the original breakeven point with the reduced fixed expenses, we solve for the new variable expenses per unit (V) using the same breakeven formula: $$55,500 = \frac{790,875}{40 - V}$$Solving for V gives: $$40 - V = \frac{790,875}{55,500} \approx 14.25$$$$V = 40 - 14.25 = 25.75$$The increase in variable expenses per unit to maintain the original breakeven point is $25.75 - $25 = $0.75.

Fairfield Company Management Has Budgeted the Following Amounts for Its