Question

CVP and Sensitivity Analysis (Single Product). Victoria, Inc., has annual fixed costs totaling $240,000 and variable costs of $6 per unit. Each unit of product is sold for $30. Victoria expects to sell 12,000 units this year (this is the base case).

Required:

1. Find the break-even point in units.

2. How many units must be sold to earn an annual profit of $100,000? (Round to the nearest unit.)

3. Find the break-even point in sales dollars.

4. What amount of sales dollars is required to earn an annual profit of $140,000?

5. Find the margin of safety in units and in sales dollars.

6. Prepare a contribution margin income statement for the base case.

7. What will the operating profit (loss) be if the sales price decreases 30 percent? (Assume total sales remains at 12,000 units.)

8. Go back to the base case. What will the operating profit (loss) be if the variable cost per unit increases 10 percent? (Assume total sales remains at 12,000 units, and round to the nearest cent where appropriate.)

Answer 1

Answer a.

Breakeven Point in units = (Fixed Costs + Target Profit) / (Selling Price per unit - Variable Cost per unit)
Breakeven Point in units = ($240,000 + $0) / ($30 - $6)
Breakeven Point in units = $240,000 / $24
Breakeven Point in units = 10,000

Answer b.

Target Profit in units = (Fixed Costs + Target Profit) / (Selling Price per unit - Variable Cost per unit)
Target Profit in units = ($240,000 + $100,000) / ($30 - $6)
Target Profit in units = $340,000 / $24
Target Profit in units = 14,167

Answer c.

Breakeven Point in sales dollars = (Fixed Costs + Target Profit) / Contribution Margin Ratio
Breakeven Point in sales dollars = (Fixed Costs + Target Profit) / [(Selling Price per unit - Variable Cost per unit) / Selling Price per unit]
Breakeven Point in sales dollars = ($240,000 + $0) / [($30 - $6) / $30]
Breakeven Point in sales dollars = $240,000 / 0.80
Breakeven Point in sales dollars = $300,000

Answer d.

Target Profit in sales dollars = (Fixed Costs + Target Profit) / Contribution Margin Ratio
Target Profit in sales dollars = (Fixed Costs + Target Profit) / [(Selling Price per unit - Variable Cost per unit) / Selling Price per unit]
Target Profit in sales dollars = ($240,000 + $140,000) / [($30 - $6) / $30]
Target Profit in sales dollars = $380,000 / 0.80
Target Profit in sales dollars = $475,000