Cost-volume-profit (CVP) analysis is a helpful tool regardless of the number of products a company sells. CVP analysis is more complex with multiple products. Two complications are encountered when multiple products are sold by companies. First, companies rarely sell exactly the same number of units of each product. Second, most products differ in their selling price and variable cost per unit. As a consequence, in order to determine sales levels at breakeven or target profit levels, these two issues must be addressed.

 

This chapter covers CVP analysis with multiple products, and address the choice of which profit measure is used to maximize profit when choosing between multiple products to sell.

 


Sales Mix


In addition to the assumptions introduced in chapter 7 for basic cost-volume-profit (CVP), one additional assumption must be specified: The sales mix is expected to remain steady. Sales mix refers to the relative proportions in which a company’s products are sold. For example, suppose a deli sells 2 sandwiches for every bag of chips sold for every 3 soft drinks sold. The sales mix in units for the deli is 2 to 1 to 3. The sales mix is expressed in standard form as 2 : 1 : 3. In other words, out of every 6 items sold, the company typically sells 2 sandwiches, 1 bag of chips, and 3 soft drinks. This group of 6 items is often known as a bundle. It is important to note that it may take multiple customers to sell all items in the bundle, however, on average, a company can rely on such a product mix. Understanding a company's sales mix is helpful for budgeting, for managing a company's inventory levels, and for determining break even and target profit levels. 

Sales mix can be stated two different ways--in terms of units and in terms of sales dollars. Sales mix in units differs from sales mix in revenue dollars because both the selling price of cakes and pies and the number of pies and cakes sold differ. To illustrate, suppose Jama Giants produces two products: cakes and pies--and has provided the following expected sales information for its products for the month of May:

 

Cakes

Pies

Total

Budgeted units to be sold

2,000

6,000

8,000

Sales revenue

$24,000

$36,000

$60,000

Sales Mix in Units

The unit sales mix is 2,000 to 6,000 units. However, sales mix is stated in lowest terms, a concept you learned in middle school math classes. Recall that 'lowest terms' is always expressed in whole numbers. Fractions and decimals are unacceptable as partial units cannot be sold. Reducing it to lowest terms, the sales mix in units is 1 to 3:

 

2000 : 6000  ==> 2 : 6 ==> 1 : 3

The unit sales mix tells us that Jama Giants sells one cake for every three pies sold. 

Sales Mix in Sales Dollars (Revenue)

The company's sales mix based on sales dollars is determined in much the same manner by comparing revenues of each product and then reducing to lowest terms.

$24000 : $36000 ==> 2 : 3

The revenue sales mix tells us that Jama Giants sells $2 of cakes for every $3 of pies.

 


Using the Profit Equation with Multiple Products


In order to consider the sales mix when calculating the break even point in units for multiple products, you must determine a weighted average contribution margin amounts. A weighted average considers the differing selling prices, variable costs per unit, and number of units for all products.  When calculating the break even point or target profit in units, you must use the weighted average contribution margin (WACM) per unit. When calculating the break even point in sales dollars, you must use the weighted average contribution margin ratio (WACMR).

 


Break Even Point in Units


The weighted average contribution margin (WACM) per unit calculation considers the unit sales mix of all of a company's products. Consider the budgeted income statement for Jama Giants for its two products for the month of May:

 

Cakes

Pies

Total

Budgeted Units to be Sold

2,000

6,000

8,000

Sales revenue

$24,000

$36,000

$60,000

Variable costs

4,500

10,800

15,300

Fixed costs

 6,000

 5,400

11,400

Net operating income

$13,500

$19,800

$33,300

The weighted average contribution margin per unit is used because it indicates the amount from each unit sold that is available to cover fixed costs and contribute to profit. Note the emphasis on sales in units. Because the breakeven calculation desired is to determine unit sales, the contribution margin component of the profit equation must use the contribution margin per unit. The WACM per unit is calculated as follows:

 WACM per unit =  Total contribution margin of all products

                           Total units for all products

[$60,000 - $15,300] / 8,000 units = $5.5875 = $5.59 per unit

 

Simply adding unit contribution margins of both products together is not sufficient because it does not consider the different sales mixes. The contribution margin form of the profit equation is used when considering multiple products. Because selling price per unit minus variable cost per unit gives you the contribution margin per unit, we substitute contribution margin (CM) for (SP - VC) to arrive at the condensed form of the profit equation:

 

SPx - VCx - FC = Profit

CMx - FC = Profit

 

Using the contribution approach, the breakeven point in units is:  

                                            

CM x - FC = 0    

5.5875x - 13,400 = 0

x = 2,398.21 = 2,399 units

 

As you learned for break even analysis with only one product, we must always round break even points in units up to avoid a loss. This calculation generates the total number of units of both products that must be sold to break even, i.e., Jama Giants must sell a total of 2,399 cakes and pies to break even.

 

To determine the breakdown of units by product, use the unit sales mix, 1 : 3.  The company expects to sell one cake for every 3 pies. Cake sales will be 1 of every 4 items sold (1/4), and pie sales will be 3 of every 4 items sold (3/4). 

Cakes: 1/4 x 2,398.21 = 599.55 = 600 cakes

Pies: 3/4 x 2,398.21 = 1798.66 = 1,799 pies

Because a partial unit cannot be produced and sold, break even points must always be rounded up.

 


Break Even Point in Sales Revenue


To calculate the breakeven point in sales dollars, you must a weighted average contribution margin amount in the profit equation due to differing selling prices per unit and sales mix. To determine sales dollars at breakeven, use the contribution margin ratio instead of contribution margin per unit in the profit equation:

 

SP x - VC x - FC = Profit

CMR x - FC = Profit

The CMR is used because it indicates the portion of each sales dollar available to cover fixed costs and contribute to profit. Note the emphasis on sales dollars. Because the breakeven calculation desired is to determine sales revenue, the contribution margin component of the profit equation must use the contribution margin amount based on revenue.

The weighted average contribution margin ratio is:

   $44,700 / $60,000 = 74.50%

WACM =  Total contribution margin of all products

            Total units of all products

[$60,000 - $15,300] / 8,000 units = $5.5875 = $5.59 per unit

The breakeven point in sales dollars is:     

                                         

                                                    WACMR x - FC = 0    

                                                    0.745 x - 13,400 = 0

                                                    x = $17,986.58 = $17,987

       

This calculation of BEP generates the sales dollars of all products together. To determine the breakdown of sales dollars by product, use the sales mix in sales dollars.

 

Sales mix in sales revenue dollars is 2 to 3, based on the original sales amounts of $24,000 and $36,000. The company plans to sell $2 of cakes for every $3 of pies. So for every $5 of sales, $2 will be for cakes and $3 will be pies.

 

Cakes: 2/5 x $17,987 = $7,194.80 = $7,195

Pies: 3/5 x $17,987 = $10,792,22 = $10,792

 

When the products sold are substantially different, CVP analysis must always be performed using the weighted average contribution margin amounts.

 


Profitability Measures


Companies prefer to sell products that produce the highest contribution to profit. However, there are a number of terms that describe profit.

 

Profit margin ratio: A company's profit margin ratio is calculated by comparing the amount of profit to sales revenue. The profit margin ratio indicates the amount of each sales dollar that contributes to the profit (net income) of a company. It represents the profit left after both fixed and variable costs have been deducted. This ratio changes when volume changes because the fixed cost per unit differs when activity changes.

 

Contribution margin ratio: The contribution margin ratio indicates the portion of each sales dollar available to cover fixed costs and contribute to profit. This percentage remains the same regardless of the fixed costs incurred by a company. As such, the CMR is more reliable in comparing profitability of multiple products. 

 


Which Product Should We Sell?--The Impact of Customer Spending Attitudes


Because managers want to maximize profit, they always want to sell the products with the higher profitability. The question, "Which product should a company 'push' to its customers?" depends on the customers spending attitude. Some customers prefer to buy one particular item and are not concerned about the total price, such as choosing between the $4 cheeseburger, or the $5 bacon burger. Other customers plan to spend a fixed sum of money, perhaps buying one burger with a price of $4.00, or two smaller burgers with a price of $2.00 each. As such, two different answers exist to the question of which product to push:

1.    A customer plans to buy one item: Push the product with the higher contribution margin per unit.

2.   A customer plans to spend a set amount of money: Push the product with the higher contribution margin ratio.

For example, assume that Barney and Andy stopped at Moe's Donut Shop after an exhausting day of writing speeding tickets. They each had $2 to spend. Barney wanted to buy as much food as possible for his $2, so he selected two of the $1 chocolate donuts. Andy was certain he wanted only one snack, but debated whether he wanted a donut for $1 or a muffin for $2. Selling prices, variable costs, and contribution margins appear below for the two products at Moe's Donut Shop:

 

 

Donuts

Muffins

Unit sales price

$1.00

$2.00

Variable cost per unit

0.45

1.40

Contribution margin per unit $0.55 $0.60

 

The respective contribution margin ratios are:

Donuts: $0.55 / $1.00 = 55%

Muffins: $0.60 / $2.00 = 30%

 

If Moe's sells only one item, as the case with Andy, Moe's should 'push' the product with the highest contribution margin per unit to generate the highest profit. Moe's will generate $0.60 on one muffin compared to $0.55 on one donut, so the muffin should be 'pushed' to Andy. 

 

Because Andy is willing to spend a fixed amount of money, the company should push the product that generates the largest contribution from each sales dollar, i.e., use the contribution margin ratio. Of the $2 that Barney plans to spend, Moe's should push donuts because out of each $2 of revenue, the sale will generate $1.10 of profit (55% times $2). The sale of $2 of muffins will generate only $0.60 of profit (30% times $2).

 


Walk Through Problem


PopARoo sells two flavors of popcorn – chocolate and caramel, both sold in 12 ounce bags. Information on sales for July:

 

 

Chocolate

Caramel

Totals

Number of bags

9,000

6,000

15,000

Sales

$72,000

$60,000

$132,000

Variable costs

27,000

15,000

42,000

Fixed costs

24,000

30,000

54,000

Operating Income

$21,000

$15,000

$ 36,000

Selling price per unit

$8.00

$10.00

 

Contribution margin per unit

$5.00

$7.50

 

 

 

 

Determine the (A) number of units and (B) sales revenue for each product at the breakeven point for PopARoo. The sales mix is expected to remain steady.

 

Solution

Part A - Breakeven point in units

Step 1: Calculate the weighted average contribution margin per unit which will be used in the profit equation.

WACM/unit = ($132,000 - $42,000) / 15,000 = $6.00 per bag

 

Step 2: Determine the breakeven point in units for the entire company. Because you are calculating the breakeven point in units, you will use the WACM per unit in the profit equation.  

 

 6.00x - 54,000 = 0

    x = 9,000 total bags

The 9,000 units represents the total chocolate and caramel popcorn bags that the company will sell at breakeven.

Step 3: Determine the sales mix to be used to allocate the 9,000 units (bags) by product. Because you are determining number of units (bags of popcorn), you will calculate the unit sales mix. PopARoo sells 9,000 bags of chocolate popcorn for every 6,000 bags of caramel popcorn. Reducing this to lowest terms, the company sells 3 bags of chocolate to every 2 bags of caramel popcorn.

Unit sales mix: 9,000 : 6,000 ==> 3 : 2

 

Step 4: Determine the number of bags of each popcorn flavor that PopARoo will sell at breakeven. Each 'set' of bags sold consists of 5 bags, with 3 of these being chocolate and 2 begin caramel. As such, 3 of 5 bags, or 3/5 of the total bags sold are chocolate, and 2 of 5 bags, or 2/5 of total bags sold are caramel.

 

Chocolate popcorn = 9,000 x 3/5 = 5,400 bags

Caramel popcorn = 9,000 x 3/5 = 5,400 bags

Part B - Breakeven point in sales revenue

Step 1: Calculate the weighted average contribution margin ratio which will be used in the profit equation.

WACMR = ($132,000 - $42,000) / $132,000 = 68.18181%

 

Step 2: Determine the breakeven point in sales revenue for the entire company. Because you are calculating the breakeven point in revenue dollars, you will use the WACMR in the profit equation.  

 

0.68181x - 54,000 = 0

        $x = $79,200

The $79,200 represents the total revenue the company will report for both chocolate and caramel popcorn bags at breakeven.

Step 3: Determine the sales mix to be used to allocate the $79,200 of sales revenue by product. Because you are determining revenue, you will calculate the revenue sales mix. PopARoo generates $72,000 of revenue for chocolate popcorn for every $60,000 of caramel popcorn. Reducing this to lowest terms, the company generates revenue of $6 for chocolate to every $5 of revenue for caramel popcorn.

Revenue sales mix: $72,000 : $60,000 ==> $6 : $5  

 

Step 4: Determine the sales revenue of each popcorn flavor that PopARoo will generate at breakeven. Each 'set' of sales consists of $11 of revenue, with $6 of this for chocolate and $5 for caramel. As such, $6 of $11 of revenue, or 6/11 of the total revenue is for chocolate, and $5 of $11 of revenue, or 5/11 of total revenue is for caramel.

 Chocolate popcorn = $79,200 x 6/11 = $43,200

Caramel popcorn = $79,200 x 5/11 = $36,000


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