How Can a Company With Multiple Products Compute Its Breakevenã¢â‚¬â€¹ Point?

7.5 Multi-product Breakeven Analysis

Up to this point in our CVP assay, we have assumed that a company merely sells one product, but we know that, realistically, this is not the case. Almost companies operate in amulti-product environment, in which they sell different products, industry dissimilar products, or offer unlike types of services. Companies toll each one of their products or services differently, and the costs associated with each of those products or services vary also. In addition, companies have limited resources, such as time and labor, and must determine which products to sell or produce and in what quantities, or which services to offer in guild to be the near assisting. These profitability considerations are often what contributes substance to a sales mix decision

In order to perform a break-even analysis for a company that sells multiple products or provides multiple services, it is of import to sympathise the concept of a sales mix. Asales mix represents the relative proportions of the products that a company sells—in other words, the percentage of the company's total acquirement that comes from product A, product B, product C, so along. Sales mix is important to business owners and managers because they seek to take a mix that maximizes profit, since not all products have the same profit margin. Companies can maximize their profits if they are able to attain a sales mix that is heavy with high-margin products, goods, or services. If a company focuses on a sales mix heavy with low-margin items, overall company profitability will often suffer.

Performing a break-even analysis for these multi-product businesses is more than complex because each production has a different selling price, a different variable toll, and, ultimately, a unlike contribution margin. Nosotros must besides proceed under the supposition that the sales mix remains constant; if information technology does change, the CVP analysis must be revised to reflect the change in sales mix. For the sake of clarity, we will also assume that all costs are companywide costs, and each product contributes toward roofing these companywide costs.

Calculating Suspension-Even Analysis in a Multi-Product Surround

When a company sells more than one product or provides more than ane service, break-even analysis is more than complex because not all of the products sell for the aforementioned price or have the same costs associated with them: Each product has its own margin. Consequently, the pause-even point in a multi-product environment depends on the mix of products sold. Farther, when the mix of products changes, so does the interruption-even point. If demand shifts and customers purchase more depression-margin products, then the break-fifty-fifty indicate rises. Conversely, if customers buy more than high-margin products, the intermission-fifty-fifty point falls. In fact, even if total sales dollars remain unchanged, the break-fifty-fifty point can change based on the sales mix. Let's expect at an case of how break-fifty-fifty analysis works in a multi-product environment.

In multi-product CVP analysis, the visitor'due south sales mix is viewed as ablended unit of measurement, a option of discrete products associated together in proportion to the sales mix. The composite unit is not sold to customers but is a concept used to calculate a combined contribution margin, which is then used to gauge the interruption-fifty-fifty signal. Think of a blended unit every bit a virtual basket of fruit that contains the proportion of individual fruits equal to the company's sales mix. If nosotros purchased these items individually to brand the fruit handbasket, each one would have a separate price and a different contribution margin. This is how a blended unit works in CVP analysis. We calculate the contribution margins of all of the component parts of the composite unit and then use the total to calculate the break-even point. It is of import to notation that fixed costs are allocated among the various components (products) that brand upwardly this blended unit. Should a production be eliminated from the composite unit or sales mix, the fixed costs must exist re-allocated among the remaining products.

If we use the fruit basket as an case, we can look at the private fruits that make up the handbasket: apples, oranges, bananas, and pears. Nosotros see that each individual fruit has a selling price and a cost. Each fruit has its own contribution margin. But how would we determine the contribution margin for a composite of fruit, or in other words, for our basket of fruit?

For our particular baskets, nosotros will use 5 apples, iii oranges, two bananas, and i pear. This means that our product mix is five:three:2:ane, every bit shown in Figure 7.49.

Notice that the composite contribution margin is based on the number of units of each particular that is included in the composite detail. If we change the composition of the basket, then the composite contribution margin would modify even though contribution margin of the individual items would non alter. For example, if we merely include 4 apples, the contribution margin of a unmarried apple tree is still $0.35, but the contribution margin of the apples in the basket is $ane.40, not $ane.75 every bit it is when 5 apples are included in the basket. Permit'south look at an boosted case and meet how we observe the break-fifty-fifty bespeak for a composite good.

We volition consider West Brothers for an example of a multi-production break-even assay. West Brothers manufactures and sells 3 types of house siding: restoration vinyl, architectural vinyl, and builder course vinyl, each with its own sales price, variable cost, and contribution margin, as shown:

Figure vii.50 Past: Rice University Source: Openstax CC BY-NC-SA four.0

The sales mix for West Brothers is v ft² of architect grade to iii ft² of architectural grade to 2 ft^two of restoration grade vinyl (a ratio of 5:3:two). This sales mix represents one blended unit of measurement, and the selling price of one composite unit is:

Figure 7.51 By: Rice Academy Source: Openstax CC BY-NC-SA four.0

West Brothers' fixed costs are $145,000 per year, and the variable costs for 1 composite unit are:

Figure 7.52 By: Rice University Source: Openstax CC BY-NC-SA iv.0

Nosotros volition calculate the contribution margin of a composite unit of measurement for West Brothers using the aforementioned formula as before:

Figure vii.53 By: Rice University Source: Openstax CC BY-NC-SA 4.0

Applying the formula, we decide that $73 – $42.25 = 30.75. We so utilize the contribution margin per blended unit to decide West Brothers' pause-fifty-fifty point:

$$\text{Suspension-Even Bespeak per Composite Unit}=\frac{\text{Total fixed costs}}{\text{Contribution margin per blended unit}}=\frac{\mathrm{\$145,000}}{\mathrm{\$30.75}}=\mathrm{4,715.45}\text{blended units}$$

West Brothers will intermission even when it sells four,715.45 (or 4,716 since it can't sell a partial unit) composite units. To determine how many of each product West Brothers needs to sell, we apply their sales mix ratio (5:3:2) to the break-even quantity equally follows:

Effigy seven.54 By: Rice Academy Source: Openstax CC BY-NC-SA four.0

Using a forecasted or estimated contribution margin income argument, nosotros can verify that the quantities listed will place West Brothers at suspension-even.

Figure seven.55 Past: Rice University Source: Openstax CC By-NC-SA four.0 Long Description

West Brothers can use this CVP analysis for a wide range of business organization decisions and for planning purposes. Recollect, however, that if the sales mix changes from its current ratio, so the suspension-even point will change. For planning purposes, W Brothers can modify the sales mix, sales price, or variable toll of 1 or more than of the products in the composite unit and perform a "what-if" analysis.

YOUR TURN

Margins in the Sales Mix

The sales mix of a company selling ii products, A and B, is 3:i. The per-unit variable costs is $4 for Product A and $5 for Product B. Product A sells for $x and product B sells for $9. Fixed costs for the visitor are $220,000.

1. What is the contribution margin per composite unit?
2. What is the intermission-even point in blended units?
3. How many units of product A and product B will the company sell at the break-even point?

Solution

A.

Figure vii.56 By: Rice University Source: Openstax CC BY-NC-SA 4.0

B.

Effigy 7.57 By: Rice Academy Source: Openstax CC Past-NC-SA 4.0 Long Description

Interruption-fifty-fifty per composite unit of measurement = xv,385.

C.

Effigy 7.58 By: Rice University Source: Openstax CC BY-NC-SA 4.0 Long Description

Long Description

Fruit, Number of Units, Selling Price per Unit, Full Selling Cost, Cost per Unit, Total Toll, Contribution Margin (respectively): Apple 5, $0.60, 3.00, 0.25, ane.25, 1.75; Orange 3, $one.00, 3.00, 0.75, 2.25, 0.75; Banana 2, $0.80, ane.60, 0.l, i.00, 0.60; Pear 1, $i.90, ane.90, ane.50, ane.50, 0.40; Total –, –, $9.50, –, $6.00, $3.fifty. Return

West Brothers Forecasted Contribution Margin Income Statement at Suspension-Even Sales: Builder form (23,577 at $6.25) $147,358, Architectural (14,146 at seven.75) 109,634, Restoration (9,431 at $9.25) 87,236; Total Sales 344,228; Variable Costs: Architect course (23,577 at $3.25) 76,626, Architectural (fourteen,146 at 4.fifty) 63,659, Restoration (9,431 at $6.25) 58,943; Total Variable Costs 199,228, Contribution Margin 145,000 less Fixed Costs 145,000 equals Net Income of 0. Return

Product: A, B; Composite per unit sales (SP times mix): $10 times 3 equals $30, 49 times 1 equals $ix. Total equals $39. Composite per unit variable cost (VC times mix): $4 times 3 equals $12, $5 times ane equals $5. Total equals $17. Composite per unit contribution margin: $18, $iv. Full equals $22. Suspension-even point per blended unit equals FC divided by composite CM x,000 units minus $220,000 divided by $22. Return

Number of units per product (mix times units in one composite unit): A, 3 times 10,000, 30,000; B, 1 times 10,000, ten,000. Composite sales (unit SP times production composite units): Production A $10 times 30,000 units, $xxx,000; Product B $9 times x,000 units, $90,000; Full sales $390,000. Composite variable costs (unit VC times product composite units): Product A $four times 30,000 units, $120,000; Production B $5 times 10,000 units, $50,000; Total variable price $170,000. Contribution Margin (sales minus VC) $220,000. Fixed costs $220,000. Net Income $0. Return

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Source: https://psu.pb.unizin.org/acctg211/chapter/multi-product-breakeven-analysis/

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