7-35 Algoritmic P and Solutio- ABC
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Dec 6, 2023
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Problem 7-35 Basic CVP Computations (LO 7-1, 7-2, 7-4)
CollegePak Company produced and sold 60,000 backpacks during the year just ended at an average price of $20 per unit. Variable
manufacturing costs were $8 per unit, and variable marketing costs were $4 per unit sold. Fixed costs amounted to $180,000 for
manufacturing and $72,000 for marketing. There was no year-end work-in-process inventory. (Ignore income taxes.)
Required:
1.
Compute CollegePak’s break-even point in sales dollars for the year.
2.
Compute the number of sales units required to earn a net income of $580,000 during the year.
3.
CollegePak's variable manufacturing costs are expected to increase by 10 percent in the coming year. Compute the firm’s break-
even point in sales dollars for the coming year.
4.
If CollegePak’s variable manufacturing costs do increase by 10 percent, compute the selling price that would yield the same
contribution-margin ratio in the coming year.
Explanation:
1.
Break-even point in sales dollars, using the contribution-margin ratio:
Break-even
point
=
Fixed expenses
Contribution-margin ratio
=
$180,000 + $72,000
=
$252,000
$20.00 – $8.00 – $4
0.4
$20.00
=
$630,000
2.
Target net income, using contribution-margin approach:
Sales units
required to earn
income of $180,000
=
Fixed expenses + Target net income
Unit contribution margin
=
$252,000 + $180,000
=
$432,000
$20.00 – $8.00 – $4
$8
=
54,000 units
3.
New unit variable manufacturing
cost
=
$8.00 × 110%
= $8.80
Break-even point in sales dollars:
Break-even point
=
$252,000
=
$252,000
$20.00 – $8.80 – $4
0.36
$20.00
=
$700,000
4.
Let
P
denote the selling price that will yield the same contribution-margin ratio:
$20.00 – $8.00 – $4
=
P
– $8.80 – $4
$20.00
P
0.4 =
P
– $4.8
P
0.4
P
=
P
– $4.8
$4.8 =
12P
P
= $2.5/0.12
P
=
$20.83 (rounded)
Check: New contribution-margin ratio is:
$20.83 − $8.80 − $4
=
0.39 (rounded)
$20.83
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