Question

CVP analysis—what-if questions; sales mix issue Miller Metal Co. makes a single product that sells for $32 per unit. Variable costs are $20.80 per unit, and fixed costs total $47,600 per month.

Required:
Calculate the number of units that must be sold each month for the firm to break even. Assume current sales are $418,000.
Calculate the margin of safety and the margin of safety ratio.
Calculate operating income if 7,000 units are sold in a month.
Calculate operating income if the selling price is raised to $47 per unit, advertising expenditures are increased by $8,000 per month, and monthly unit sales volume becomes 7,600 units.
Assume that the firm adds another product to its product line and that the new product sells for $22 per unit, has variable costs of $14 per unit, and causes fixed expenses in total to increase to $83,000 per month. Calculate the firm's operating income if 7,000 units of the original product and 4,300 units of the new product are sold each month. For the original product, use the selling price and variable cost data given in the problem statement.
Calculate the firm's operating income if 3,500 units of the original product and 7,800 units of the new product are sold each month. Why operating income is different in parts e and f, even though sales totaled 11,300 units in each case.

Answer 1

Answer: See explanation

Step-by-step explanation:

a. Calculate the number of units that must be sold each month for the firm to break even.

Breakeven units = Fixed cost / Contribution margin per unit

= $47600 / ($32 - $20.80)

= $47600 / $11.20

= 4250 units

b. Calculate the margin of safety and the margin of safety ratio.

Margin of safety = $418000 - ($32 × 4250)

= $418000 - $136000

= $282000

Margin of safety ratio = $282000/$418000 = 0.68

c. Calculate operating income if 7,000 units are sold in a month.

= [($32 - $20.80) × 7000] - $47600

= $78400 - $47600

= $30800

d. Calculate operating income if the selling price is raised to $47 per unit, advertising expenditures are increased by $8,000 per month, and monthly unit sales volume becomes 7,600 units.

Sales = 7600 × $47 = $357200

Less: Variable cost at $20.8 = $158080

Contribution = $199120

Less: Fixed cost = $47600

Less: Advertising expense = $8000

Operating income = $143520