Question

Question: Use the following information to complete Short Exercises S20-10 through S20-15.

Funday Park competes with Cool World by providing a variety of rides. Funday Park sells tickets at \(70 per person as a one-day entrance fee. Variable costs are \)42 per person, and fixed costs are $170,800 per month.

S20-10 Computing contribution margin per unit, breakeven point in sales units

Compute the contribution margin per unit and the number of tickets Funday Park must sell to break even. Perform a numerical proof to show that your answer is correct.

Short answer

Answer

The number of break-even sales are 6,100.

Step-by-step solution

Calculation of Contribution margin

$$\begin{gathered} \mathbf{Contributionmargin}\mathbf{=}\mathbf{Salesprice}\mathbf{-}\mathbf{-}\mathbf{Variablecost} \\ \mathbf{=}\mathbf{\$}\mathbf{70}\mathbf{-}\mathbf{\$}\mathbf{42} \\ \mathbf{=}\mathbf{\$}\mathbf{28} \end{gathered}$$

 Step 2: Calculation of number of tickets funday park must sell to break even

$$\begin{gathered} \mathbf{Netsalesrevenue}\mathbf{-}\mathbf{Variablecosts}\mathbf{-}\mathbf{Fixedcosts}\mathbf{=}\mathbf{Targetprofit} \\ \left(\mathbf{Numberofunitssold}\mathbf{\times }\mathbf{\$}\mathbf{28}\right)\mathbf{-}\mathbf{\$}\mathbf{170}\mathbf{,}\mathbf{800}\mathbf{=}\mathbf{\$}\mathbf{0} \\ \mathbf{Numberofunitssold}\mathbf{=}\mathbf{6}\mathbf{,}\mathbf{100}\mathbf{Units} \end{gathered}$$

Substituting the number of units into operating income equation

$$\begin{gathered} \mathbf{Totalcontributionmargin}\mathbf{-}\mathbf{Fixedcosts}\mathbf{=}\mathbf{Operatingincome} \\ \left(\mathbf{6}\mathbf{,}\mathbf{100}\mathbf{Units}\mathbf{\times }\mathbf{\$}\mathbf{28}\right)\mathbf{-}\mathbf{\$}\mathbf{170}\mathbf{,}\mathbf{800}\mathbf{=}\mathbf{Operatingincome} \\ \mathbf{\$}\mathbf{170}\mathbf{,}\mathbf{800}\mathbf{-}\mathbf{\$}\mathbf{170}\mathbf{,}\mathbf{800}\mathbf{=}\mathbf{Operatingincome} \\ \mathbf{\$}\mathbf{0}\mathbf{=}\mathbf{Operatingincome} \end{gathered}$$