Question

Mi Tierra Driving School charges \(680 per student to prepare and administer written and driving tests. Variable costs of \)408 per student include trainers’ wages, study materials, and gasoline. Annual fixed costs of \(63,920 include the training facility and fleet of cars.

Requirements

1. For each of the following independent situations, calculate the contribution margin per unit and the breakeven point in units by first referring to the original data provided:

a. Breakeven point with no change in information.

b. Decrease sales price to \)544 per student.

c. Decrease variable costs to \(340 per student.

d. Decrease fixed costs to \)53,040.

2. Compare the impact of changes in the sales price, variable costs, and fixed costs on the contribution margin per unit and the breakeven point in units.

Short answer

(1)

1. Contribution margin per unit =$272, Breakeven point in units =235
2. Contribution margin per unit =$136, Breakeven point in units =470
3. Contribution margin per unit =$340, Breakeven point in units =188
4. Contribution margin per unit =$272, Breakeven point in units =195

(2) Impact of changes are explained in Step 2

Step-by-step solution

Calculation of breakeven sales in units and contribution margin per unit

a.

$\begin{array}{rcl}\mathbf{Contributionmarginperunit}& \mathbf{=}& \mathbf{Salespriceperunit}\mathbf{-}\mathbf{Variablecostperunit}\\ & \mathbf{=}& \mathbf{\$}\mathbf{680}\mathbf{-}\mathbf{\$}\mathbf{408}\\ & \mathbf{=}& \mathbf{\$}\mathbf{272}\\ \mathbf{Breakevenpointinunits}& \mathbf{=}& \frac{\mathbf{fixedcost}}{\mathbf{Contributionmarginperunit}}\\ & \mathbf{=}& \frac{\mathbf{\$}\mathbf{63}\mathbf{,}\mathbf{920}\mathbf{+}\mathbf{\$}\mathbf{0}}{\mathbf{\$}\mathbf{272}}\\ & \mathbf{=}& \mathbf{235}\\ & & \end{array}$

b.

$\begin{array}{rcl}\mathbf{Contributionmarginperunit}& \mathbf{=}& \mathbf{Salespriceperunit}\mathbf{-}\mathbf{Variablecostperunit}\\ & \mathbf{=}& \mathbf{\$}\mathbf{544}\mathbf{-}\mathbf{\$}\mathbf{408}\\ & \mathbf{=}& \mathbf{\$}\mathbf{136}\\ \mathbf{Breakevenpointinunits}& \mathbf{=}& \frac{\text{F}\mathbf{ixedcost}}{\mathbf{Contributionmarginperunit}}\\ & \mathbf{=}& \frac{\mathbf{\$}\mathbf{63}\mathbf{,}\mathbf{920}\mathbf{+}\mathbf{\$}\mathbf{0}}{\mathbf{\$}\mathbf{136}}\\ & \mathbf{=}& \mathbf{470}\\ & & \end{array}$

$\begin{array}{rcl}\mathbf{Contributionmarginperunit}& \mathbf{=}& \mathbf{Salespriceperunit}\mathbf{-}\mathbf{Variablecostperunit}\\ & \mathbf{=}& \mathbf{\$}\mathbf{544}\mathbf{-}\mathbf{\$}\mathbf{408}\\ & \mathbf{=}& \mathbf{\$}\mathbf{136}\\ \mathbf{Breakevenpointinunits}& \mathbf{=}& \frac{\text{F}\mathbf{ixedcost}}{\mathbf{Contributionmarginperunit}}\\ & \mathbf{=}& \frac{\mathbf{\$}\mathbf{63}\mathbf{,}\mathbf{920}\mathbf{+}\mathbf{\$}\mathbf{0}}{\mathbf{\$}\mathbf{136}}\\ & \mathbf{=}& \mathbf{470}\\ & & \end{array}$

c.

$\begin{array}{rcl}\mathbf{Contributionmarginperunit}& \mathbf{=}& \mathbf{Salespriceperunit}\mathbf{-}\mathbf{Variablecostperunit}\\ & \mathbf{=}& \mathbf{\$}\mathbf{680}\mathbf{-}\mathbf{\$}\mathbf{340}\\ & \mathbf{=}& \mathbf{\$}\mathbf{340}\\ \mathbf{Breakevenpointinunits}& \mathbf{=}& \frac{F\mathbf{ixedcost}}{\mathbf{Contributionmarginperunit}}\\ & \mathbf{=}& \frac{\mathbf{\$}\mathbf{63}\mathbf{,}\mathbf{920}}{\mathbf{\$}\mathbf{340}}\\ & \mathbf{=}& \mathbf{188}\\ & & \end{array}$

d.

$\begin{array}{rcl}\mathbf{Contributionmarginperunit}& \mathbf{=}& \mathbf{Salespriceperunit}\mathbf{-}\mathbf{Variablecostperunit}\\ & \mathbf{=}& \mathbf{\$}\mathbf{680}\mathbf{-}\mathbf{\$}\mathbf{408}\\ & \mathbf{=}& \mathbf{\$}\mathbf{272}\\ \mathbf{Breakevenpointinunits}& \mathbf{=}& \frac{\mathbf{fixedcost}}{\mathbf{Contributionmarginperunit}}\\ & \mathbf{=}& \frac{\mathbf{\$}\mathbf{53}\mathbf{,}\mathbf{040}}{\mathbf{\$}\mathbf{272}}\\ & \mathbf{=}& \mathbf{195}\\ & & \end{array}$

Comparative analysis 

	Contribution margin per unit	Breakeven points in units	Analysis
A	$272	235	This is the breakeven level with original data
B	$136	470	If sales price decreases. then the contribution margin per unit will also decrease and breakeven level will increase
C	$340	188	If variable cost decreases then the contribution margin will increase and breakeven level will decrease.
D	$272	195	If fixed cost decreases, the contribution margin will remain unchanged but the breakeven sales will decrease.