[Mujahid_ Abu Dahda]

I met this question and I am totally confused by the way the answer is worked. The Break even point is derived at by dividing Total Contribution Margin by CM per composite unit. Answer choice D (10,500 units) was chosen as the best answer Why Total contribution margin and not Fixed cost divided by CM per composite unit? I chose B (6,000) because I used the Fixed cost formula.

Here is the question:
Wren Co. manufactures and sells two products with selling prices and variable costs as follows:

A B
SELLING PRICE $18.00 $22.00
VARIABLE COSTS $12.00 $14.00

WREN’S TOTAL ANNUAL FIXED COSTS ARE $38,400. WREN SELLS FOUR UNITS OF A FOR EVERY UNIT OF B. IF OPERATING INCOME LAST YEAR WAS $28,800, WHAT WAS THE NUMBER OF UNITS WREN SOLD?
A. 5,486
B. 6,000
C. 9,600
D. 10,500

ANY HELP WOULD BE APPRECIATED! THANK YOU AND BE SAFE.

[Han]

Using the fixed cost formula gives you the number of composite units that cause CM = FC, which means the operating income will be zero. However, the question said that the operating income last year was $28,800. Therefore, you need the contribution margin not only cover the fixed cost, but also generate additional $28,800 operating income. So the composite contribution margin should equal the sum of fixed cost and operating income. That's why we divide $67,200 by the CM.

[Mujahid_ Abu Dahda]

Thank you @Han! I got it.

[Author]

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