Lesson 1, Topic 1
In Progress

Multi-product analysis


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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 companies sell multiple products. First, companies rarely sell the same number of units of each product. Second, most products differ in their selling price and variable cost per unit. Therefore, in order to determine sales levels at breakeven or target profit levels, these two issues must be addressed.

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.

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:


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:
 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 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.
 
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:
WACMR = Total contribution margin of all products
            Total sales revenue of all products
[$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 dollarsfor each product, use the sales mix insales 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 product by instructing the sales personnel to emphasize that product. 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:

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:

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

SELF-CHECK ACTIVITY

  1. Describe the multiple product analysis in CVP analysis?