Multiproduct Break$-$Even Analysis for a Clothing Store

Analyze a clothing store that sells two main types of clothing:

Jackets and T$-$shirts. We'll calculate the break$-$even point for each product and the overall store, considering the sales mix and contribution margin.

Assumptions

The store sells jackets for $$100$ each and T$-$shirts for $$20$ each.

The variable cost per jacket is $$60$ and the variable cost per T$-$shirt is $$8.$

Fixed costs for the store total $$5,000$ per month.

$1.$ Contribution Margin per Unit

The contribution margin per unit shows the profit available after variable costs are deducted from the selling price.

Jackets: Contribution Margin $=$ Selling Price $-$ Variable Cost

Contribution Margin $($ Jackets$)=$$$100-$$$60=$$$40$

T$-$shirts: Contribution Margin $($T$-$shirts$)=$ $$20-$$$8=20$

$2.$ Sales Mix

The sales mix represents the proportion of total sales contributed by each product.

Let's assume.

Jackets: $30\%$ of total sales

T$-$shirts: $70\%$ of total sales

$3.$ Weighted Average Contribution Margin Ratio

This ratio shows the average contribution margin per dollar of sales, considering the sales mix.

Weighted Average Contribution Margin Ratio $=($Sales Mix for Jackets $*$ Contribution Margin per Jacket$)+($Sales Mix for T$-$shirts Contribution Margin per T$-$shirt$)$

Weighted Average Contribution Margin Ratio $=(0\mathrm{.}3*$ $$40)+(0\mathrm{.}7*$$$12)$

Weighted Average Contribution Margin Ratio $=$ $$12+$ $$8\mathrm{.}40=$ $$20\mathrm{.}40$

Break$-$Even Point Calculations

a$)$ Break$-$Even Point per Unit

The break$-$even point per unit tells us how many units of each product need to be sold to cover the variable costs associated with that product.

Break$-$Even Point $($Units$)$ per Product $=$ Fixed Costs $/$ Contribution Margin per Unit

Break$-$Even Point $($Units$)$ for Jackets $=$ $$500/$$$40=12\mathrm{.}5$

Break$-$Even Point $($Units$)$ for T$-$shirts $=$ $$5000/$$$12=416\mathrm{.}67$

T$-$shirts $($rounded to $417$ due to whole units being sold$)$

b$)$ Break$-$Even Point $($Sales$)$

The break$-$even point $($sales$)$ is the total sales amount at which the store covers all its costs $($fixed and variable$)$ and makes no profit or loss.

Break$-$Even Point $($Sales$)=$ Fixed Costs $/$ Weighted Average Contribution Margin Ratio

Break$-$Even Point $($Sales$)=$ $$5,000/$ $$20\mathrm{.}40$

Break$-$Even Point $($Sales$)=$ $$245\mathrm{.}09($rounded to $$245$ due to representing total sales$)$

Interpretation

The store needs to sell at least $125$ jackets or $417$ t$-$shirts individually to recover their variable costs for each product.

To cover all costs $($fixed and variable$)$ and break even, the store needs to generate a total of $$245$ in sales. This can be achieved through any combination of jackets and T$-$shirts that reaches that total sales amount.

Benefits of Multiproduct Break$-$Even Analysis

Helps identify which product contributes more to covering fixed costs.

Provides insights into how changes in sales mix can affect the overall break$-$even point. Allows for setting sales targets for each product to achieve the overall break$-$even goal.

SO ANSWER THESE QUESTIONS

$1.$ Sales Mix Impact: How might changes in the sales mix, such as an increase in the proportion of jacket sales compared to T$-$shirts, affect the overall break$-$even point and profitability of the store? How can the store strategically adjust its sales mix to optimize profitability?

$2.$ Contribution Margin Variations: What factors could cause fluctuations in contribution margins for jackets and T$-$shirts over time? How should the store monitor and manage these factors to ensure consistent profitability?

$3.$ Fixed Costs Allocation: The fixed costs are assumed to be shared equally between jackets and T$-$shirts. Do you think this assumption accurately reflects the cost structure of the store? How might allocating fixed costs based on the relative contribution of each product impact the break$-$even analysis?

$4.$ Scenario Analysis: Can you provide a scenario where the store aims to achieve a target profit rather than just breaking even? How would you adjust the break$-$even analysis to determine the sales volume needed to attain the desired profit level?

THANK YOU PLS ANSWERS THE $4$ QUESTION DO NOT COPY PASTE FROM GOOGLE