Question

Q5. For United Africa Company the following projected reports the following operating results for the month of June 30, 2023 availed for analysis. Round all percentage answers to one decimal place.

United Africa Company
CVP projected income statement
For the Month Ended June 30, 2023
Total Per unit
Sales (5000 units ) $600,000 $120
Variable cost 360,000 72
Contribution margin 240,000 48
Total Fixed cost 200,000
Net income 40,000

Instructions:
To increase net income, project management team is considering reducing the selling price by 10%, with no changes to unit variable costs or fixed costs. Project Management team is confident that this change will increase unit sales by 25%. Using the contribution margin technique, compute the break-even point in units and dollars and margin of safety in dollars.
A. Assuming no changes to sales price or costs,
B. Assuming changes to sales price and volume as described above.
C. Assuming change (B) approved, Calculate the number of units that the company must sell to earn operating income of $80,000.
D. Comment on your findings.

Answer 1

A. Assuming no changes to sales price or costs:

Break-even point (in units) = Total Fixed Cost / Contribution Margin per unit

Break-even point (in units) = $200,000 / $48 = 4,167 units

Break-even point (in dollars) = Break-even point (in units) x Sales price per unit

Break-even point (in dollars) = 4,167 x $120 = $500,040

Margin of safety (in dollars) = Total Sales - Break-even point (in dollars)

Margin of safety (in dollars) = $600,000 - $500,040 = $99,960

B. Assuming changes to sales price and volume as described above:

New selling price per unit = $120 - (10% of $120) = $108

New sales volume = 5000 x 1.25 = 6250 units

New total sales = New sales volume x New selling price per unit = 6250 x $108 = $675,000

New contribution margin = New total sales - Variable costs = $675,000 - ($72 x 6250) = $270,000

New net income = New contribution margin - Total Fixed costs = $270,000 - $200,000 = $70,000

Break-even point (in units) = Total Fixed Cost / Contribution Margin per unit

Break-even point (in units) = $200,000 / $48 = 4,167 units

Margin of safety (in dollars) = Total Sales - Break-even point (in dollars)

Margin of safety (in dollars) = $675,000 - ($200,000 / 0.6) - $500,040 = $174,960

C. Assuming change (B) approved, Calculate the number of units that the company must sell to earn operating income of $80,000:

Required contribution margin = Total Fixed costs + Operating income

Required contribution margin = $200,000 + $80,000 = $280,000

Required sales revenue = Required contribution margin / Contribution margin ratio

Contribution margin ratio = Contribution margin per unit / Sales price per unit = $48 / $108 = 0.4444

Required sales revenue = $280,000 / 0.4444 = $630,063

Required sales volume = Required sales revenue / Selling price per unit = $630,063 / $108 = 5,834 units

D. Based on the analysis, reducing the selling price by 10% and increasing unit sales by 25% results in an increase in net income from $40,000 to $70,000. The break-even point in units remains the same at 4,167 units, but the break-even point in dollars increases from $500,040 to $525,042. The margin of safety increases from $99,960 to $174,960. To earn operating income of $80,000, the company needs to sell 5,834 units, which is less than the new projected sales volume of 6,250 units. Overall, the proposed changes seem to be beneficial for the company.