Question

Day Company produces and sells three products: Alpha, Beta, and Gamma. Their respective selling prices are $1, $2, and $3. Variable costs per unit are $0.50, $1.50, and $2.00. Total fixed costs amount to $60,000. For every unit of Alpha sold, three units of Beta and four units of Gamma are sold.

1. What is the contribution margin per unit for each product?
2. Determine the operating income, assuming that sales in units for the three products were 20,000, 40,000, and 50,000.
3. Compute the breakeven point in units and dollars.
4. Compute the number of units required to earn a before tax profit of $100,000.
5. Compute the number of units required to earn an after-tax profit of $120,000 assuming a 25% tax rate.

Answer 1

(a) What is the contribution margin per unit for each product?

Contribution Margin = SP – VC

Alpha = $1 - $0.5 = $0.5

Beta = $2 - $1.5 = $0.5

Gamma = $3 - $2 = $1

(b) Determine the operating income, assuming that sales in units for the three products were 20,000, 40,000, and 50,000.

Operating Income = (Alpha Units sold * Contribution margin) + (Beta Units sold * Contribution margin) + (Gamma Units sold * Contribution margin) – Fixed cost

         = (20000 * $0.5) + (40000 * $0.5) + (50000 * $1) - $60000 = $20000

(c) compute the breakeven point in units and dollars

Fixed cost/Combined contribution

Combined contribution = (Alpha contribution * 1 unit) + (Beta contribution * 3 unit) + (Gamma contribution * 4 unit)

= ($0.5 * 1) + ($0.5 * 3) + ($1 * 4) = $6

$60000/$6 = 10000 units

Alpha = 10000 units

In dollars = 10000 * $1 = $10000

Beta = 10000 * 3 = 30000 units

In dollars = 30000 * $2 = $60000

Gamma = 10000 * 4 = 40000 units

In dollars = 40000 * $3 = $120000

(d) compute the number of units required to earn a before tax profit of $100,000

(Profit + Fixed cost)/Combined contribution

($100000 + $60000)/$6 = 26667 units

Alpha = 26667 units

Beta = 26667 * 3 = 80000 units

Gama = 26667 * 4 = 106667 units

(e) Compute the number of units required to earn an after-tax profit of $120,000 assuming a 25% tax rate.

After Tax Profit = $120000

Before Tax = $120000/75% = $160000

($160000 + $60000)/$6 = 36667 units

Alpha = 36667 units

Beta = 36667 * 3 = 110000 units

Gamma = 36667 * 4 = 146667 units