Question

Computing margin of safety

Robbie’s Repair Shop has a monthly target profit of \(31,000. Variable costs are 20%of sales, and monthly fixed costs are \)19,000.

Requirements

1. Compute the monthly margin of safety in dollars if the shop achieves its income goal.

2. Express Robbie’s margin of safety as a percentage of target sales.

3. Why would Robbie’s management want to know the shop’s margin of safety?

Short answer

1. If the shop achieves its income goal the margin of safety is $38,750.
2. The margin of safety as a percentage of target sales is 62%.
3. Margin of safety is a principle of investing that protects business against loss. Thus to maintain risk and investment managegment wants to know the margin of safety.

Step-by-step solution

Computation of Sales-

$\begin{array}{rcl}\mathbf{Sales}& \mathbf{=}& \left(\frac{\mathrm{Fixed}\mathrm{cost}+\mathrm{Target}\mathrm{profit}}{\mathrm{Contribution}\mathrm{margin}\mathrm{ratio}}\right)\\ & \mathbf{=}& \frac{\mathbf{\$}\mathbf{19}\mathbf{,}\mathbf{000}\mathbf{+}\mathbf{\$}\mathbf{31}\mathbf{,}\mathbf{000}}{\mathbf{1}\mathbf{-}\mathbf{0}\mathbf{.}\mathbf{20}}\\ & \mathbf{=}& \frac{\mathbf{\$}\mathbf{50}\mathbf{,}\mathbf{000}}{\mathbf{0}\mathbf{.}\mathbf{80}}\\ & \mathbf{=}& \mathbf{\$}\mathbf{62}\mathbf{,}\mathbf{500}\end{array}$

Computation of Break even sales-

$\begin{array}{rcl}\mathbf{Break}\mathbf{}\mathbf{even}\mathbf{}\mathbf{sales}& \mathbf{=}& \frac{\mathbf{Fixed}\mathbf{}\mathbf{expense}}{\mathbf{Contribution}\mathbf{}\mathbf{margin}\mathbf{}\mathbf{ratio}}\\ & \mathbf{=}& \frac{\mathbf{\$}\mathbf{19}\mathbf{,}\mathbf{000}}{\mathbf{1}\mathbf{-}\mathbf{0}\mathbf{.}\mathbf{2}}\\ & \mathbf{=}& \frac{\mathbf{\$}\mathbf{19}\mathbf{,}\mathbf{000}}{\mathbf{0}\mathbf{.}\mathbf{8}}\\ & \mathbf{=}& \mathbf{\$}\mathbf{23}\mathbf{,}\mathbf{750}\end{array}$

1. Computation of Margin of safety-

$\begin{array}{rcl}\mathbf{Margin}\mathbf{}\mathbf{of}\mathbf{}\mathbf{safety}& \mathbf{=}& \mathbf{Sales}\mathbf{-}\mathbf{Break}\mathbf{}\mathbf{even}\mathbf{}\mathbf{sales}\\ & \mathbf{=}& \mathbf{\$}\mathbf{62}\mathbf{,}\mathbf{500}\mathbf{-}\mathbf{\$}\mathbf{23}\mathbf{,}\mathbf{750}\\ & \mathbf{=}& \mathbf{\$}\mathbf{38}\mathbf{,}\mathbf{750}\end{array}$

2. Computation of Margin of safetyas a percentage of target sales-

$\begin{array}{rcl}\mathbf{Margin}\mathbf{}\mathbf{of}\mathbf{}\mathbf{safety}\mathbf{}\mathbf{percentage}& \mathbf{=}& \frac{\mathbf{Margin}\mathbf{}\mathbf{of}\mathbf{}\mathbf{safety}}{\mathbf{Sales}}\mathbf{\times }\mathbf{100}\\ & \mathbf{=}& \frac{\mathbf{\$}\mathbf{38}\mathbf{,}\mathbf{750}}{\mathbf{\$}\mathbf{62}\mathbf{,}\mathbf{500}}\mathbf{\times }\mathbf{100}\\ & \mathbf{=}& \mathbf{62}\mathbf{\%}\\ & & \end{array}$

Reason to know the shop’s margin of safety-

Margin of Safety is the quantity or the percentage of sales over the break-even sales. It is like a safety cover that protects a business against a loss. Higher the Margin of Safety, lower the risk of incurring loss on the other hand lower the Margin of Safety, higher the risk of carrying business.