2. How do you calculate the sales required to break even or achieve a target operating income in a multiproduct setting?
3. What assumption is required in multiproduct CVP analysis but is not necessary in single-product CVP analysis?
G U I D E D U N I T P R E P A R A T I O N
same baseball jerseys as Universal, but it also sells athletic shoes. Unit data for the jerseys and shoes are as follows:
Note that Landon prices its jerseys the same as Universal (to be competitive) and offers employees the same 6% commission on sales. The athletic shoes that Landon sells are priced higher than the jerseys, and they cost the company more to sell.
Last year, Landon sold 40,000 jerseys and 10,000 pairs of shoes, so the sales mix is four jerseys for every pair of shoes sold. Exhibit 3-5 shows Landon’s in- come statement by product type and in total. Note that no fi xed expenses are assigned to either jerseys or shoes. As long as the company keeps selling jerseys and shoes, the fi xed expenses will not change, so they are deducted in total rather than allocated to the individual product lines.
Jerseys Shoes
Sales price $20.00 $45.00
Cost of goods sold 14.80 36.00
Sales commission 1.20 2.70
Total variable expenses 16.00 38.70
Contribution margin $ 4.00 $ 6.30
Jerseys Shoes Total Company Total Per Unit Percentage Total Per Unit Percentage Total Percentage
Sales $800,000 $20.00 100.00% $450,000 $45.00 100.00% $1,250,000 100.00%
Cost of goods sold 592,000 14.80 74.00% 360,000 36.00 80.00% 952,000 76.16%
Sales commission 48,000 1.20 6.00% 27,000 2.70 6.00% 75,000 6.00%
Variable expenses 640,000 16.00 80.00% 387,000 38.70 86.00% 1,027,000 82.16%
Contribution margin $160,000 $ 4.00 20.00% $ 63,000 $ 6.30 14.00% 223,000 17.84%
Selling and marketing 125,000
Administrative expenses 53,400
Fixed expenses 178,400
Operating income $ 44,600
LANDON SPORTS Income Statement
for the 52 Weeks Ended February 1, 2014
EXHIBIT 3-5 Landon Sports’ income statement.
1Salesjerseys–Variable expensesjerseys2+1Salesshoes–Variable expensesshoes2–FC=OI or
Contribution marginjerseys+Contribution marginshoes–FC=OI
The profi t formula for a company with multiple products (in this case, jerseys and shoes) and a specifi ed sales mix is:
This equation can be expanded to accommodate as many products as the com- pany sells.
Unit 3.3 Multiproduct CVP Analysis 99 Landon Sports breaks even when:
As Warner’s sales mix moves toward digital recordings, the amount of sales revenue
required to break even will decrease.
REALITY CHECK —What’s in the mix?
The preceding equation has two unknowns and an infi nite number of solutions.
However, when we require that the sales mix is held constant, then we know the number of jerseys sold is four times the number of pairs of shoes sold. If we let x equal the number of pairs of shoes sold, we have the following equation and solution:
1$4.003 4x2 + 1$6.303 x2 –$178,400= $0
$16x+ $6.30x= $178,400 x= 8,000 pairs of shoes
4x =32,000 jerseys
Breakeven in sales dollars is $1,000,000: $640,000 for jerseys ($20 3 32,000) and $360,000 ($45 3 8,000) for shoes.
1$4.003# of jerseys sold2+1$6.303# of pairs of shoes sold2–$178,400=$0
Tim Robberts/The Image Bank/Getty Images
Warner Music Group is a leading player in the music industry. According to its 2011 annual report, the company has established itself “as a leader in the music industry‘s transition to the digital era.” Sales of digital music at Warner exploded between 2006 and 2011—up 427% during the period. And in 2011, digital revenue provided almost 29% of the com- pany’s total revenues, up from 4.5% in 2005.
Because digital fi les do not require a case or printed materials, digital recordings cost less than CDs to manufacture. Moreover, there are no inventory storage costs for digital re- cordings, and distribution costs are much lower (there is no shipping cost for a downloaded digital fi le). Warner reports that two-thirds of online sales come from older releases, whose marketing costs are lower than those for new releases.
All these savings mean that the contribution margin ratio for digital recordings is much higher than that for CDs. While the sales price of a digital download is less than that of a CD, more of each sales dollar is available to cover fi xed costs and provide a profi t. As Warner’s sales mix moves more toward digital recordings, the amount of sales revenue required to break even will decrease. That’s how Warner was able to achieve higher income on lower sales revenue. Clearly, sales mix is an important consideration in decision making.
Sources: Rob Curran, “Warner Music’s Earnings Surge 92% on Digital Sales, Lower Costs,” The Wall Street Journal, February 15, 2006; “Warner Music Group Corp. Reports Fiscal First Quarter Results for the Period Ended December 31, 2005,” Warner Music Group news release, February 14, 2006, http://investors.wmg.com/phoenix.
zhtml?c5182480&p5irol-news (accessed February 22, 2006); Warner Music Group 2008 Annual Report; Warner Music Group 2007 Annual Report; Warner Music Group 2011 Annual Report.
The formula is easily adapted to target income problems. Suppose the CFO at Landon Sports wanted to know how many jerseys and pairs of shoes needed to be sold to earn $66,900 in operating income:
1$4.003 4x2 + 1$6.303 x2 –$178,400= $66,900
$16x + $6.30x=$245,300 x= 11,000 pairs of shoes
4x= 44,000 jerseys
original formula with 1.5x in the new formula:
are 1.5 times the number of shoe sales a30,000
20,000b, we will replace 4x from the Let’s see what the breakeven point is with this new sales mix. Since sales of jerseys
Do not split fi xed expenses between the multiple prod- ucts and try to come up with individual product break- even points or target income points. This will result in units sold that do not adhere to the sales mix ratio.
WATCH OUT!
Jerseys Shoes Total Company Total Per Unit Percentage Total Per Unit Percentage Total Percentage Sales $600,000 $20.00 100.00% $900,000 $45.00 100.00% $1,500,000 100.00%
Cost of goods sold 444,000 14.80 74.00% 720,000 36.00 80.00% 1,164,000 77.60%
Sales commission 36,000 1.20 6.00% 54,000 2.70 6.00% 90,000 6.00%
Variable expenses 480,000 16.00 80.00% 774,000 38.70 86.00% 1,254,000 83.60%
Contribution margin $120,000 $ 4.00 20.00% $126,000 $ 6.30 14.00% 246,000 16.40%
Selling and marketing 125,000
Administrative expenses 53,400
Fixed expenses 178,400
Operating income $ 67,600
LANDON SPORTS Revised Income Statement
for the 52 Weeks Ended February 1, 2014
EXHIBIT 3-6 Landon Sports’ revised income statement.
1$4.003 1.5x2+ 1$6.303x2 –$178,400= $0
$6x+ $6.30x= $178,400 x 5 14,504.065 pairs of shoes
1.5x=21,756.0975 jerseys
Since Landon Sports cannot sell part of a shoe or part of a jersey, the breakeven points must be rounded up to the next whole unit—14,505 pairs of shoes and 21,757 jer- seys. Breakeven in sales dollars is $1,087,865: $435,140 for jerseys ($20 3 21,757) and $652,725 ($45 3 14,505) for shoes. More sales dollars are needed to break even and achieve other income targets relative to the original sales mix because, although the shoes have a higher contribution margin per unit than the jerseys ($6.30 If the sales mix changes, so do the breakeven point and the other targets.
Exhibit 3-6 shows what Landon’s income statement would look like if Landon Sports still sold a total of 50,000 units, but the sales mix changed to 30,000 jerseys and 20,000 pairs of shoes (instead of 40,000 jerseys and 10,000 pairs of shoes). The company would make more money, even though it sold the same number of units as in the previous scenario because more of those units sold were shoes, which generate a higher contribution margin per unit.
Unit 3.3 Review 101 compared to $4.00), the contribution margin ratio for shoes is lower than the contri-
bution margin ratio for jerseys. That means that with this mix, less of each sales dol- lar is available after covering variable expenses to cover fi xed expenses and profi t.
U N I T 3 . 3 R E V I E W
KEY TERMS
Sales mix p. 97
1. LO 5 If a company sells more than one product, it cannot use CVP analysis to examine the effect of changes in costs on operating income. True or False?
2. LO 5 Which of the following is not a limiting assump- tion of multiproduct CVP analysis?
a. Fixed cost per unit remains constant within the relevant range.
b. All variable cost relationships are linear with respect to activity.
c. All costs can be easily separated into variable and fi xed categories.
d. The sales mix can be determined and remains constant over time.
3. LO 5 Blalock Training sells three online training courses in database programming skills. For every 12 people who take the introductory course, 5 take the intermediate course and 3 take the advanced course. Blalock’s CFO has calculated a breakeven point of 10,000 courses. How many of those 10,000 courses will be introductory?
tribution margin of $12. Montelone sells fi ve standard packages for every one deluxe package. If fi xed expenses total $74,000, how many standard and deluxe packages must be sold to break even?
a. 14,800 standard; 6,167 deluxe b. 4,353 standard; 4,353 deluxe c. 9,280 standard; 2,300 deluxe d. 10,000 standard; 2,000 deluxe
5. LO 5 Assume a company sells 10,000 units—5,000 of product A and 5,000 of product B. Product A has a con- tribution margin of $6.00 per unit, while Product B has a contribution margin of $4.00 per unit. If the sales mix changes to 5,500 units of Product A and 4,500 units of product B, which of the following is true?
a. The company will make more money because more of the product with the higher contribution margin per unit is being sold.
b. It will take fewer total units to break even now that more of the product with the higher contribu- tion margin per unit is being sold.
c. The breakeven point depends on the current sales volume as it effects the sales mix.
d. All of the above are true.
PRACTICE QUESTIONS
Limitations of Multiproduct CVP Analysis
In Unit 3.2, you learned about the assumptions of CVP analysis, and all those assumptions apply in a multiproduct environment. However, there is another assumption that we make in a multiproduct environment: The sales mix can be determined and will remain constant.
Consider Landon’s original sales mix of 40,000 jerseys and 10,000 shoes. In an effort to stimulate jersey sales, Landon has increased the sales commission paid on each jersey to 12.3%. The company believes that this move will generate additional sales of 10,000 jerseys, with no effect on shoe sales. How will this move alter Landon’s sales mix? How will it affect the breakeven point? Do you think this change is a good move?