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 addresses 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) analysis, 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 its product mix in the short run. Understanding a company's sales mix is helpful for budgeting, for managing a company's inventory levels, and for determining breakeven and target profit levels.

Sales mix can be stated two different ways--in terms of units and in terms of sales dollars. To illustrate, suppose Jama Giants produces two products: cakes and pies. 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. The company 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 cakes to 6,000 pies. However, sales mix is always stated in lowest terms, a concept you learned in middle school math classes. 'Lowest terms' is always expressed in whole numbers. Fractions and decimals are unacceptable because partial units cannot be sold. Reducing to lowest terms, the sales mix in units is:

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:

\$24,000 : \$36,000 ==> 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 breakeven point in units for multiple products, you must determine a weighted average contribution margin amount, which considers the differing selling prices, variable costs per unit, and number of units for each products.

When calculating the breakeven point or target profit in units, use the weighted average contribution margin (WACM) per unit. When calculating the breakeven point in sales dollars, use the weighted average contribution margin ratio (WACMR). The table below summarizes which contribution margin amount to use when calculating the breakeven point or target profit for single and multiple products.

 Which Contribution Amount to Use to Calculate the Breakeven Point or Target Profit Number of Products When Calculating the Breakeven Point or Target Profit in Units When Calculating the Breakeven Point or Target Profit in Sales Dollars For a single product Contribution margin per unit Contribution margin ratio For multiple products Weighted average contribution margin per unit Weighted average contribution margin ratio Unit sales mix Revenue sales mix

Breakeven 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 to calculate the breakeven point in units 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. The WACM per unit is calculated as follows:

[\$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 sales mix of the two products. Because selling price per unit minus the variable cost per unit results in the contribution margin per unit, we substitute contribution margin (CM) for (SP - VC) to arrive at the contribution approach form of the profit equation:

SPx - VCx - TFC = Profit

CMx - TFC = Profit

The weighted average contribution margin per unit and total fixed costs are substituted to determine the breakeven point in units for the entire company:

5.5875x - 11,400 = 0

x = 2,040.2684 = 2,041 units

This calculation generates the total number of units of both products that must be sold to breakeven, i.e., Jama Giants must sell a total of 2,041 cakes and pies to breakeven. As with breakeven analysis for a single product, you must always round breakeven points in units up to avoid a loss.

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 2,040.268 = 510.07 = 511 cakes

Pies: 3/4 x 2,040.268 = 1,530.20 = 1,531 pies

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

Breakeven Point in Sales Revenue

To determine sales dollars at breakeven, use the contribution margin ratio instead of contribution margin per unit in the profit equation:

SPx - VCx - TFC = Profit

CMRx - TFC = 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. The weighted average contribution margin ratio is:

[\$60,000 - \$15,300] / \$60,000 = 74.50%

The breakeven point in sales dollars is:

WACMR x - FC = 0

0.7450 x - 11,400 = 0

x = \$15,302.01

This calculation generates the expected sales dollars of both products together. To determine the breakdown of sales dollars for each 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. For every \$5 of sales, \$2 will be generated from selling cakes and \$3 will be from pies.

Cakes: 2/5 x \$15,302.01 = \$6,120.80

Pies: 3/5 x \$15,302.01 = \$9,181.21

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

Profitability Measures

Companies prefer to sell products that produce the highest contribution to 'profit'. However, there are a number of different ratio measures of profit. Among these, two measures are easily determinable from the variable costing income statement---the profit margin ratio and the contribution margin ratio.

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 portion of each sales dollar that contributes to the bottom line profit (operating 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.

Because the contribution margin ratio does not fluctuate when sales levels change, it 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 prefer to sell the products with the higher profitability. Some companies do this by placing products with higher margins in obvious locations in stores, such as near the cash register or on the end cap of an aisle. Other companies 'push' a particular product by instructing the sales personnel to emphasize that product. The answer to this question, "Which product should a company 'push' to its customers?" depends on the customer's 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.

Assume that Barney and Andy stop at Moe's Donut Shop after an exhausting day of writing speeding tickets. They each have \$2 to spend. Barney wants to buy as much food as possible for his \$2, so he selects two of the \$1 chocolate donuts. Andy is certain he wants only one snack, but debates whether he wants 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 unit of product, as is 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 Barney 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 1 pound bags. Information on sales for July follow:

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

Solution

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 determine how many of the 9,000 units (bags) will be sold for each 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 'bundle' of bags sold consists of 5 bags, with 3 of these being chocolate and 2 being 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 to be sold are expected to be caramel:

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

Caramel popcorn = 9,000 x 2/5 = 3,600 bags

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 = 68.18182%

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:

0.6818182x - 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 determine the portion of the \$79,200 of sales revenue that will be generated by each 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 'bundle' 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

This page was last edited on Monday January 19, 2015 12:41 PM
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