Question

Scotty’s Scooters plans to sell a standard scooter for \(55 and a chrome scooter for \)70. Scotty’s purchases the standard scooter for \(30 and the chrome scooter for \)40. Scotty’s expects to sell one standard scooter for every three chrome scooters. Scotty’s monthly fixed costs are \(23,000.

Requirements

1. How many of each type of scooter must Scotty’s Scooters sell each month to break even?

2. How many of each type of scooter must Scotty’s Scooters sell each month to earn \)25,300?

3. Suppose Scotty’s expectation to sell one standard scooter for every three chrome scooters was incorrect and for every four scooters sold two are standard scooters and two are chrome scooters. Will the breakeven point of total scooters increase or decrease? Why? (Calculation not required.)

Short answer

1. Standard scooter =200 units, Chrome scooters =600 units
2. Standard scooter =420 units, Chrome scooters =1,260 units
3. The breakeven point of total scooters will increase

Step-by-step solution

Calculation of operating leverage 

	Standard Scooter	Chrome Scooter	Total
Sales price per unit	$55	$70
Variable cost per unit	$30	$40
Contribution margin per unit	$25	$30
Sales mix in units	X 1	X 3	4
Contribution margin	$25	$90	$115
Weighted average contribution margin per unit ($115/4)			$28.75

$\begin{array}{rcl}\mathbf{Requiredsalesinunits}& \mathbf{=}& \frac{\mathbf{Fixedcosts}\mathbf{+}\mathbf{Targetprofit}}{\mathbf{Weightedaveragecontributionmarginperunit}}\\ & \mathbf{=}& \frac{\mathbf{\$}\mathbf{23}\mathbf{,}\mathbf{000}\mathbf{+}\mathbf{\$}\mathbf{0}}{\mathbf{\$}\mathbf{28}\mathbf{.}\mathbf{75}}\\ & \mathbf{=}& \mathbf{800}\mathbf{Scooters}\\ \mathbf{Breakevensalesofstandardscooter}& \mathbf{=}& \mathbf{800}\mathbf{\times }\frac{\mathbf{1}}{\mathbf{4}}\\ & \mathbf{=}& \mathbf{200}\mathbf{Scooters}\\ \mathbf{BreakevensalesofChromescooter}& \mathbf{=}& \mathbf{800}\mathbf{\times }\frac{\mathbf{3}}{\mathbf{4}}\\ & \mathbf{=}& \mathbf{600}\mathbf{Scooters}\\ & & \end{array}$

Calculation of each type of scooter Scotty’s scooter must sell to earn $25,300

$\begin{array}{rcl}\mathbf{Requiredsalesinunits}& \mathbf{=}& \frac{\mathbf{Fixedcosts}\mathbf{+}\mathbf{Targetprofit}}{\mathbf{Weightedaveragecontributionmarginperunit}}\\ & \mathbf{=}& \frac{\mathbf{\$}\mathbf{23}\mathbf{,}\mathbf{000}\mathbf{+}\mathbf{\$}\mathbf{25}\mathbf{,}\mathbf{300}}{\mathbf{\$}\mathbf{28}\mathbf{.}\mathbf{75}}\\ & \mathbf{=}& \mathbf{1}\mathbf{,}\mathbf{680}\mathbf{Scooters}\\ & & \end{array}$

$\begin{array}{rcl}\mathbf{Breakevensalesofstandardscooter}& \mathbf{=}& \mathbf{1}\mathbf{,}\mathbf{680}\mathbf{\times }\frac{\mathbf{1}}{\mathbf{4}}\\ & \mathbf{=}& \mathbf{420}\mathbf{Scooters}\\ \mathbf{BreakevensalesofChromescooter}& \mathbf{=}& \mathbf{1}\mathbf{,}\mathbf{680}\mathbf{\times }\frac{\mathbf{3}}{\mathbf{4}}\\ & \mathbf{=}& \mathbf{1}\mathbf{,}\mathbf{260}\mathbf{Scooters}\\ & & \end{array}$

Sensitivity Analysis

If for every four scooters sold two are standard scooters and two are chrome scooters the breakeven point of total scooters will increase because total composite contribution margin will decrease by $5.