Question

Comprehensive In Class Problem Cost Profit Relationships

1. A manufacturer predicts fixed costs of $502,000 for next year. Its one product sells for $180 per unit and it incurs variable costs of $126 per unit. Its target (pretax) income is $200,000.
   1. Compute the contribution margin ratio
   2. Compute the dollars sales needed to yield the target income
   3. Compute the unit sales needed to yield the target income

2. The sales mix of a company’s two products, X and Y, is 2:1. Unit variable costs for both products are $2, and unit selling prices are $5 for X and $4 for Y. The company has $640,000 of fixed costs.
   1. What is the contribution margin per composite unit?
   2. What is the break-even point in composite units?
   3. How many units of X and how many units of Y will be sold at the break-even point?

Answer 1

1)

Contribution margin = Selling price - Variable cost

= 180 - 126

= $54

Ratio = 54/180

= 30%

Dollar sales required

= ( Fixed cost + Target income )/Contribution margin ratio

= ( 502,000 + 200,000)/30%

= $2,340,000

Units sales required

= ( Fixed cost + Target income )/ Contribution margin per unit

= ( 502,000 + 200,000)/54

= 13,000 units

2)

Contribution margin

For X

= 5 - 2

= $3

For Y

= 4 - 2

= $2

Sales ratio = 2:1

Contribution margin for composite unit

= 3*2/3 + 2*1/3

= 2 + 0.67

= $2.67

Fixed cost = 640,000

Breakeven = Fixed cost / Contribution margin per unit

= 640,000/2.67

= 239,700

Units to be sold for individual product

For X

= 239,700*2/3

= 159,800 units

For Y

= 239,700*1/3

= 79,900 units.