34E - Horngren'S Financial And Managerial Accounting

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?

Step-by-Step Solution

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 1: Computation of Sales-

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

Step 3: Computation of Break even sales-

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

Step 4: 1. Computation of Margin of safety-

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

Step 5: 2. Computation of Margin of safetyas a percentage of target sales-

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

Step 6: 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.