Wren Co. manufactures and sells two products with selling prices and variable costs as follows:
Selling price
A $18.00
B $22.00
Variable costs
A 12.00
B 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. 10,500
b. 5,486
c. 6,000
d. 9,600
Answer: a
I don't understand why Product A = 4 x Product B? It says selling 4 units of A for every unit of B.
Shouldn't be: Product B=4x Product A?
Can someone please explain this? Thank you!
IChoice “a” is correct. Wren will have sold a total of 10,500 units to achieve a $28,800 operating profit assuming the fact pattern described above. The question requires the candidate to recall the basic contribution margin formula and apply some algebra.
The fact pattern describes that the operating income is $28,800 and the fixed costs are $38,400. The contribution margin is; therefore, the total of the two $67,200.
The basic formula to compute units sold is:
CM per unit x Units = $67,200
The fact pattern indicates that Wren has two products with unique selling and cost patterns.
First, compute the contribution margin:
Product A: 18-12=6
Product B: 22-14=8
Second, quantify the selling pattern and the relationship between the products. Wren sells 4 units of Product A for every unit of Product B, so expressing Product A in terms of Product B:
Product A = 4 x Product B
Third, determine the number of units of Product B that were sold:
$6 contribution margin x (4B) + $8 contribution margin x B = $67,200
24B + 8B = 67,200
32B = 67,200
B = 2,100
Fourth, determine the number of Product A and the total number of products sold:
A = 4 x B (4 x 2,100) or 8,400
Total units = 2,100 + 8,400 or 10,500
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BEC - May 28 2014
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