Evaluate Andre's Hair Styling: Contribution Margin, Break-Ev

Evaluate Andre's Hair Styling: Contribution Margin, Break-Even Point, and Profit Analysis

Consider the following scenario: Andre has asked you to evaluate his business, Andre’s Hair Styling. The business has five barbers, each earning $9.90 per hour, working 40 hours per week for 50 weeks annually. Rent and fixed expenses are $1,750 per month. The only service offered is haircuts, which include shampooing, with a unit price of $12 per haircut. The shampoo cost per client is $0.40. Andre wants to determine the contribution margin per haircut, the annual break-even point in haircuts, and the operating income at 20,000 haircuts. Additionally, he proposes a new compensation structure for the barbers: $4 per hour plus $6 per haircut. He requests the contribution margin and break-even point under this new scheme as well.

Understanding the Financial Components

Analyzing Andre’s Hair Styling requires understanding fixed and variable costs, as well as how these influence contribution margin and break-even points. Fixed costs include rent and salaries, which remain unchanged regardless of sales volume, while variable costs like shampoo depend on the number of haircuts performed. The contribution margin per haircut is a critical metric, reflecting how much revenue from each haircut contributes to covering fixed costs and generating profit.

Contribution Margin per Haircut Calculation

Under the current compensation scheme, each barber is paid a fixed weekly salary, which can be considered a fixed cost because it does not vary with the number of haircuts. The total weekly salary expense per barber is calculated as:

Weekly salary per barber = $9.90/hour × 40 hours = $396
Total weekly salary for five barbers = 5 × $396 = $1,980
Annual salary expense = $1,980 × 50 weeks = $99,000

Since salaries are fixed costs, they are not directly included in the contribution margin calculation per haircut; instead, we focus on variable costs which are shampoo costs. The variable cost per haircut is $0.40.

Each haircut is priced at $12, and with a shampoo cost of $0.40, the contribution margin per haircut is calculated as:

Contribution margin per haircut = Selling price - Variable costs
= $12 - $0.40 = $11.60

Annual Break-Even Point Calculation

The break-even point in units (haircuts) is achieved when total contribution margins equal total fixed costs. Fixed costs include rent plus salary expenses. The monthly rent of $1,750 amounts to:

Annual fixed costs = (Rent per month × 12 months) + total salaries
= ($1,750 × 12) + $99,000
= $21,000 + $99,000 = $120,000

Therefore, the break-even number of haircuts is:

Break-even haircuts = Total fixed costs / Contribution margin per haircut
= $120,000 / $11.60 ≈ 10,345.95

Rounding up, approximately 10,346 haircuts must be performed annually to break even.

Operating Income at 20,000 Haircuts

To calculate the operating income at 20,000 haircuts, the total contribution margin is:

Total contribution = Number of haircuts × Contribution margin per haircut
= 20,000 × $11.60 = $232,000

The total fixed costs remain at $120,000. Thus, operating income is:

Operating income = Total contribution - Fixed costs
= $232,000 - $120,000 = $112,000

Therefore, performing 20,000 haircuts would generate an operating income of $112,000 under the current compensation scheme.

Revised Compensation Structure Analysis

If Andre revises the compensation scheme such that barbers receive $4 per hour plus $6 per haircut, the calculation of contribution margin per haircut changes. The variable cost component now includes the barber's compensation per haircut, which must be determined.

The hourly wage under the new scheme is $4, and with a 40-hour workweek, each barber earns:

Weekly wage per barber = $4 × 40 = $160
Total weekly wage for five barbers = 5 × $160 = $800
Annual wage expense = $800 × 50 = $40,000

However, since the barber is paid $6 per haircut, this becomes a variable cost per haircut, amounting to:

Variable labor cost per haircut = $6

Additionally, the shampoo cost remains at $0.40 per haircut. Therefore, the total variable cost per haircut is:

Variable costs per haircut = $6 (barber's per haircut pay) + $0.40 (shampoo) = $6.40

The contribution margin per haircut under new scheme is:

Contribution margin = Price - Variable costs
= $12 - $6.40 = $5.60

Break-Even Point under New Compensation Scheme

The fixed costs now include rent plus the total fixed portion of salaries. The fixed salary component is now only the portion not dependent on number of haircuts. Since the barber’s payment includes a $4/hour fixed component for 40 hours weekly:

Weekly fixed salary per barber = $4 × 40 = $160
Total weekly fixed salary for 5 barbers = 5 × $160 = $800
Annual fixed salary expense = $800 × 50 = $40,000

Adding rent, total fixed costs are:

Total fixed costs = Rent ($21,000 annually) + Fixed salary ($40,000) = $61,000

The break-even volume is:

Break-even haircuts = Total fixed costs / Contribution margin per haircut
= $61,000 / $5.60 ≈ 10,893 haircuts

Thus, under the new compensation scheme, approximately 10,893 haircuts are needed annually to break even.

Conclusion

In summary, the current fixed salary scheme yields a contribution margin of $11.60 per haircut, with a break-even of roughly 10,346 haircuts annually. Performing 20,000 haircuts would result in an operating income of $112,000. Under the revised scheme, because barbers receive $6 per haircut plus a fixed hourly component, the contribution margin drops to $5.60, and the break-even point increases to approximately 10,893 haircuts. These analyses highlight how compensation structures significantly impact profitability and operational thresholds, emphasizing the importance of carefully selecting payment models aligned with business volume and financial goals.

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