Question

Vaughn Company reports the following operating results for the month of April.

VAUGHN COMPANY CVP Income Statement For the Month Ended April 30, 2020
		Total		Per Unit
Sales (8,000 units)		$400,000		$50
Variable costs		200,000		25.00
Contribution margin		200,000		$25.00
Fixed expenses		195,075
Net income		$4,925

Management is considering the following course of action to increase net income: Reduce the selling price by 5%, with no changes to unit variable costs or fixed costs. Management is confident that this change will increase unit sales by 20%.

Using the contribution margin technique, compute the break-even point in units and dollars and margin of safety in dollars: (Round intermediate calculations to 4 decimal places e.g. 0.2522 and final answer to 0 decimal places, e.g. 2,510.)

(a) Assuming no changes to selling price or costs.

1)Break-even point: Units

2)Break-even point: $

3)Margin of safety: $

(b1) Assuming changes to sales price and volume as described above.

1)Break-even point: Units

2)Break-even point: $

3)Margin of safety: $

Answer 1

Answer:

(a) Assuming no changes to selling price or costs.

1)Break-even point:	7,803	Units
2)Break-even point:	$ 390,150
3)Margin of safety:	$ 9,850

(b1) Assuming changes to sales price and volume as described above.

1)Break-even point:	8,670	Units
2)Break-even point:	$ 411,811
3)Margin of safety:	$ 44,189

Calculation:

(a) Assuming no changes to sales price or costs:

1. Break-even point in units:

Here, first we need to calculate the Break-even point in units. It is calculated by dividing the fixed cost with the contribution margin per unit. Both the fixed cost and the contribution margin per unit is given in the question. So,

Break-even point in units = Fixed Costs / Selling price - Variable cost = $195,075 ÷ $25 = 7,803 units

2. Break-even point in sales dollars:

Now, we need to calculate the Break-even point in sales dollars. It is calculated by dividing the fixed cost with the Contribution margin percentage. The fixed cost is given in the question. Now, we need to calculate the Contribution margin percentage.

Contribution margin percentage = Contribution margin per unit / Sales per unit = 25 / 50 = 50%

So,

Break-even point in sales dollars = Fixed Costs / Contribution margin percentage = $195,075 ÷.50 = 390,150

3. Margin of safety in dollars

Now, we need to calculate the Margin of safety in dollars. It is calculated by deducting the Break-even point in sales from total sales.

Margin of safety in dollars = Sales - Break-even point in sales = $400,000 - $390,150 = 9,850

(b1) Assuming changes to sales price and volume as described above.

1. Break-even point in units :

Here, first we need to calculate the Break-even point in units. It is calculated by dividing the fixed cost with the contribution margin per unit. Both the fixed cost and the contribution margin per unit is given in the question. But, the sales price is reduced by 5%, hence the contribution margin per unit will change.

So, we need to first calculate the new contribution margin per unit. Hence we are calculaing new sales price with effect of reduced 5%.

New sales price =50 - (50 x 5%) = 47.5

So, new contribution margin = New sales price - variable cost = 47.5 - 25 = 22.5

Break-even point in units = Fixed Costs / Selling price - Variable cost = $195,075 ÷ $22.5 = 8,670 units

2. Break-even point in sales dollars:

Now, we need to calculate the Break-even point in sales dollars. It is calculated by dividing the fixed cost with the Contribution margin percentage. The fixed cost is given in the question. Now, we need to calculate the new Contribution margin percentage. New contribution margin and new sales per unit is already calculated.

New Contribution margin percentage = new Contribution margin per unit / New Sales per unit = 22.5 / 47.5 = 47.37%

So,

Break-even point in sales dollars = Fixed Costs / New Contribution margin percentage = $195,075 ÷.4737 = 411,811

3.Margin of safety in dollars:

Now, we need to calculate the Margin of safety in dollars. It is calculated by deducting the Break-even point in sales from total sales. The unit sales will increase by 20%.

So, new sales unit will be = 8,000 +(8,000 x 20%) = 9,600 units

The new sales price per unit = 47.5

So total sales = 9,600 x 47.5 = 456,000

Margin of safety in dollars = Sales - Break-even point in sales = $456,000 - $411,811 = 44,189