Question

Nochance.com has not reported a profit in five years. This year the company would like to narrow its loss to ($10,000). Assuming the selling price of its single product is $36.50 per unit and its variable costs per unit are $24, how many units must be sold to achieve its target given that total fixed costs are $60,000? B. 5,600 4.800 4,000 3,200 A company reported the following cost relationships: Sales price per unit................ Variable cost per unit...... Total fixed costs....... $ 50 S 38 $65,000 Answer the following independent questions: a. The break-even-point in units units b. The number of units that must be sold to achieve a profit of $30,000 units The profit (loss) when sales are 8,100 units d. The sales in dollars when the desired margin of safety is 25 % $

Answer 1

1. Option (A) is correct

First we will calculate contribution margin per unit as per below:

Contribution margin per unit = Selling price per unit - Variable cost per unit

Contribution margin per unit = $36.5 - $24 = $12.5

Now, we will calculate the required number of units to achieve the target of limiting loss to $10000 as per below:

Required number of units = Fixed cost + $10000 / Contribution margin per unit

Putting the values in the above formula, we get,

Required number of units = ($60000 + $10000) / $12.5

Required number of units = $70000 / $12.5 = 5600

2 First we will calculate contribution margin per unit as per below:

Contribution margin per unit = Selling price per unit - Variable cost per unit

Contribution margin per unit = $50 - $38 = $12

(a) Break even point in units = Fixed cost / Contribution margin per unit

Putting the values in the above formula, we get,

Break even point in units = $65000 / $12 = 5417

(b) Required number of units to achieve the desired profit of $30000 is:

Required number of units = Fixed cost + $30000 / Contribution per unit

Putting the values in the above formula, we get,

Required number of units = ($65000 + $30000) / $12

Required number of units = $95000 / $12 = 7917

(c) When sales are 8100 units:

Total sales = 8100 * $50 = $405000

Variable cost = 8100 - $38 = $307800

Fixed cost = $65000

Profit = Total sales - Variable cost - Fixed cost

Profit = $405000 - $307800 - $65000 = $32200

(d) Margin of safety = Sales - Sales at break even level / Sales

where, Sales at break even level = Break even units * selling price per unit

Sales at break even level = 7917 * $50 = $395850

Margin of safety (given) = 25%

Putting the values in the above margin of safety formula, we get,

25% = (Sales - $395850) / Sales

0.25 * Sales = Sales - $395850

Sales - 0.25 * Sales = $395850

0.75 * Sales = $395850

Sales = $395850 / 0.75

Sales = $527800