Colin Was A Professional Classical Guitar Player Until His M

Colin Was A Professional Classical Guitar Player Until His Motorcycle

Colin was a professional classical guitar player until his motorcycle accident that left him disabled. After long months of therapy, he hired an experienced luthier (maker of stringed instruments) and started a small shop to make and sell Spanish guitars. The guitars sell for $700 and the fixed monthly operating costs are below. Colin's accountant told him about contribution margin ratios and he understood clearly that for every dollar of sales, $0.75 went to cover his fixed costs, and that anything past that point was pure profit. Colin wishes to earn $5,100 of operating profit each month. Calculate the amount of sales revenue required to achieve the target profit.

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To determine the sales revenue Colin needs to generate in order to achieve his target operating profit, we need to understand the relationship between sales, contribution margin ratio, fixed costs, and profit. The core concept here revolves around the contribution margin ratio, which indicates what percentage of each sales dollar contributes to covering fixed costs and generating profit. Given that the contribution margin ratio is 75% (or 0.75), this implies that for every dollar of sales, $0.75 contributes towards fixed costs and profit after variable costs are deducted.

First, it is important to clarify the structure of the contribution margin ratio. It is derived from the selling price minus variable costs, divided by the selling price. Since the contribution margin ratio is 75%, the variable cost per guitar is 25% of the selling price ($700). This means the variable cost per unit is:

Variable cost per guitar = 0.25 × $700 = $175

With the contribution margin ratio (CMR) of 75%, the contribution margin per guitar is:

Contribution margin per guitar = CMR × selling price = 0.75 × $700 = $525

This is the amount each guitar sale contributes to covering fixed costs and profit after variable costs are paid.

Now, to determine the sales revenue necessary to meet the target profit of $5,100, we use the formula based on contribution margin and fixed costs. The fixed costs are not specified explicitly, but since the contribution margin ratio and profit goal are known, we can apply the formula:

Required sales in dollars = (Fixed costs + Target profit) / Contribution margin ratio

However, without explicit fixed costs provided, the general approach is to find the number of units needed to reach the profit target and then multiply by the selling price:

Number of units needed = (Fixed costs + Target profit) / Contribution margin per unit

Assuming the fixed costs are denoted as F, then using the contribution margin ratio (since fixed costs are a component of the ratio), the calculation simplifies to:

Sales revenue needed = (Fixed costs + Target profit) / Contribution margin ratio

Since the fixed costs are not explicitly given, the problem suggests that the contribution margin ratio is 0.75 and the target profit is $5,100; thus, the sales revenue to cover fixed costs and achieve the profit is calculated by adding fixed costs to profit, dividing by the contribution margin ratio, which effectively gives the total sales revenue required assuming fixed costs are included as part of the contribution margin coverage.

In many cases, fixed costs (F) are the expenses fixed regardless of sales volume. To find the sales revenue that corresponds to target profit, it is often understood that:

Sales revenue = (Fixed costs + target profit) / contribution margin ratio

But since fixed costs are not provided directly, the other interpretation is that the contribution margin ratio helps determine the break-even point and profit target based on sales.

Given the data provided, we can approximate the sales revenue requirement as follows:

Target profit in contribution margin dollars = Contribution margin per guitar × number of units needed

Number of units needed = (Fixed costs + Target profit) / Contribution margin per unit

However, in the problem context, available data implies that fixed costs are absorbed within the contribution margin ratio, and the focus is on sales revenue to meet profit goals; thus, the calculation is simplified to:

Sales revenue = (Fixed costs + Target profit) / contribution margin ratio

Assuming fixed costs are covered by the contribution margin ratio, and the goal is to reach a specific profit, then:

Sales revenue = (Fixed costs + $5,100) / 0.75

Since fixed costs are not specified, the most straightforward approach is to consider the contribution margin ratio and the profit goal directly, concluding that:

Sales revenue = ($5,100) / 0.75 = $6,800

Thus, Colin needs to generate approximately $6,800 in sales revenue per month to achieve his desired operating profit of $5,100, assuming the contribution margin ratio adequately covers fixed costs and desired profit without explicitly knowing fixed costs.

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