Hayden Company currently sells widgets for $160 per unit. The variable cost is $60 per unit and total fixed costs equal $240,000 per year. Sales are currently 40,000 units annually, and the income tax rate is 40 percent. Required: a. Calculate the contribution margin per unit. b. Calculate break-even in units. c. Calculate break-even in sales dollars d. Calculate the current after-tax net income. e. The company is considering a 10% drop in the selling price that it believes will raise units sold by 15%. Assuming all costs stay the same, what is the impact on income if this change is made? f. How many units need to be sold to earn a pre-tax operating income of $100,000?

a. $100

b. 2,400 units

c. $380,952

d. $2,256,000

e. 15.90 %

f. 3,400 units

Explanation:

Contribution margin per unit

Contribution margin per unit = Sales per unit  less Variable Cost per unit

Therefore,

Contribution margin per unit = $160 - $60

                                                = $100

Break-even in units

The Breakeven units is the level of activity where a firm makes neither a profit nor a loss.

Break-even in units = Fixed Cost ÷ Contribution margin per unit

Therefore,

Break-even in units = $240,000 ÷ $100

                                 = 2,400 units

Break-even in sales dollars

Break-even in sales dollars = Fixed Cost ÷ Contribution margin ratio

Where,

Contribution margin ratio = Contribution margin ÷ Sales

                                           = $100 ÷ $160

                                           = 0.63

Therefore,

Break-even in sales dollars = $240,000 ÷ 0.63

                                              = $380,952

After-tax net income

Contribution ( $100 × 40,000 )    $4,000,000

Less Fixed Cost                             ($240,000)

Next Income Before Tax              $3,760,000

Less Income tax at 40 %             ($1,504,000)

Net Income After Tax                   $2,256,000

Effect of the Change on Income

First, calculate the Degree of Operating Leverage (DOL).

The DOL shows the times Net Income Before Interest and Tax will change as a result of a change in sales contribution.

Degree of Operating Leverage (DOL) = Contribution ÷ Net Income

Therefore,

Degree of Operating Leverage (DOL) = $4,000,000 ÷ $3,760,000

                                                               = 1.06

Effect on Income using the DOL = 1.06 × 15% = 15.90 %

Therefore Net Income would also increase by 15.90 %.

Units to be sold to earn an income of $100,000

Units to Earn a Target Profit = (Fixed Costs + Target Profit) ÷ Contribution margin per unit

Therefore,

Units to be sold to earn an income of $100,000 = ($100,000 + $240,000) ÷ $100

                                                                                = 3,400 units

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