Question

Case 4-35 (Garrison Text – 11^thCanadian Edition)

Break-Even Levels for Individual Products in a Multi-Product Company

Jasmine Richards met her boss, Rick McNeil, at the pop machine in the lobby. McNeil is the vice president of marketing at Down East Lures Corporation. Richards was puzzled by some calculations she had been doing, so she initiated this conversation:

    Richards: Rick, I’m not sure how to go about answering the questions that came up at the meeting with the president yesterday.

    McNeil: What’s the problem?

    Richards: The president wanted to know the break-even point for each of the company’s products, but I’m having trouble figuring them out.

    McNeil: I’m sure you can handle it, Jasmine. And, by the way, I need your analysis on my desk tomorrow morning at 8:00 A.M. sharp so I can look at it before the follow-up meeting at 9:00.

Down East Lures makes three fishing lures in its manufacturing facility in Prince Edward Island. Data concerning these products appear below:

            Frog    Minnow          Worm

Normal annual sales volume (units)     100,000           200,000           300,000

Unit selling price                                  $2.00               $1.40                $0.80

Variable cost per unit                          $1.20                $0.80               $0.50

Total fixed expenses for the entire company are $282,000 per year. All three products are sold in highly competitive markets, so the company is unable to raise its prices without losing unacceptable numbers of customers. The company has no work in process or finished goods inventories due to an extremely effective lean manufacturing system.

Required:

What is the company’s overall break-even point in total sales dollars?

        Of the total fixed costs of $282,000, $18,000 relate directly to the Frog lure product, $96,000 relate directly to the Minnow lure product, and $60,000 relate directly to the Worm lure product. The remaining fixed expenses of $108,000 consist of common fixed costs such as administrative salaries, rent on the factory building, and advertising expenses for the company as a whole. These common fixed expenses are not directly related to any particular product but must be incurred as part of operating the business.

What is the break-even point in units for each product?

Note: Management insists that Richards separately calculate the break-even point for each product using its CM per unit and only the fixed expenses that relate directly to that product.

If the company sells exactly the break-even quantity of each product calculated in (a), calculate the overall profit of the company.

Explain this result to management.

Calculate the company’s overall break-even point in units using the weighted-average CM approach.

How many units of each product must be sold at the break-even level?

Comment on any significant differences you see between these results and those of (a) above.

Answer 1

:

Solution

Lures Corporation

1. Computation of the company’s overall break-even point in sales dollars:

Overall break-even point = Fixed cost/Contribution margin ratio

Contribution margin ratio = (contribution margin/sales) x100 = ($290,000/$720,000) x 100 = 40.028%

Total fixed cost = $282,000

Overall break-even point in sales dollars = 282,000/40.028% = $700,140

	Frog	Minnow	Worm	Total
Sales	$200,000	$280,000	$240,000	$720,000
Variable cost	$120,000	$160,000	$150,000	$430,000
Contribution margin	$80,000	$120,000	$90,000	$290,000
Fixed cost	$18,000	$96,000	$60,000	$174,000
product margin	$62,000	$24,000	$30,000	$116,000
Common fixed expenses				$108,000
Net Income				$8,000

1. BEP separately for each product:

	Frog	Minnow	Worm	Total
Sales	$200,000	$280,000	$240,000	$720,000
Variable cost	$120,000	$160,000	$150,000	$430,000
Contribution margin	$80,000	$120,000	$90,000	$290,000
Fixed cost	$18,000	$96,000	$60,000	$174,000
product margin	$62,000	$24,000	$30,000	$116,000
Contribution margin	40%	42.86%	37.50%
Contribution margin per unit	$0.80	$0.60	$0.30
BEP in units	18,000/0.80 =22,500	96,000/0.60 =160,000	60,000/0.30 = 200,000

1. Net income/(loss) when the company sells each product at BEP units:

	Frog	Minnow	Worm	Total
Sales units	22,500	160,000	200,000
Sales	$45,000	$224,000	$160,000	$429,000
Variable cost	$27,000	$128,000	$100,000	$255,000
Contribution margin	$18,000	$96,000	$60,000	$174,000
Fixed cost				$282,000
Net income/(loss)				($108,000)

Computation of overall bep using weighted average CM approach:

Weighted average contribution margin = (total contribution margin of all products)/(total units for all products)

Total contribution margin of all products = $290,000

Total units = 600,000

Weighted average contribution margin = 290,000/600,000 = $0.4833

BEP in units = $282,000/$0.4833 = 583,448 units (rounded)

Frog BEP units = 583,448 x (100,000/600,000) = 97,241 units

Minnow = 583,448 x (200,000/600,000) = 194,483 units

Worm = 583,448 x (300,000/600,000) = 291,724 units

	Frog	Minnow	Worm	Total
BEP calcualted separately	22,500 units	160,000 units	200,000 units	382,500
BEP using WACM	97,241 units	194,483 units	291,724 units	583,448 units

The difference in bep units computed under the two approaches is the effect of common fixed expenses of $108,000. The increase in fixed expenses increased the bep units under the weighted average contribution method.

So, when the company sells exactly the bep units computed for each product, the company would incur a loss of $108,000, which represent the common fixed expenses.