Break-Even Analysis A security software company invests ...

Break-Even Analysis A security software company invests $\$ 76,500$ to produce software packages that will sell for $\$ 49.95$ each. Each software package can be produced for $\$ 11.70 .$ How many software packages must the company sell to break even?

Key Concepts

Contribution Margin

The contribution margin is the amount remaining from sales revenue after variable expenses have been deducted. It is calculated by subtracting the variable cost per unit from the selling price per unit and is used to cover fixed costs and then contribute to profit.

Investment Analysis

Investment analysis involves evaluating the initial costs incurred for a project or production process. This assessment helps in understanding the time and sales volume required to recoup the amount invested, which is critical in break-even analysis.

Break-even Analysis

Break-even analysis is a financial method used to determine the point at which total revenues equal total expenses, indicating that a business is not making a profit or a loss. It is essential for understanding how many units need to be sold to cover all costs.

Fixed and Variable Costs

Fixed costs are expenses that remain constant regardless of the level of production, such as initial investments or rent, while variable costs change with the quantity produced, such as production costs per unit. Distinguishing between these is important for analyzing profitability.

Transcript

00:01 Now over here in this question it has been stated that there is a company and that company has invested $16 ,000.

00:11 So $16 ,000 is the investment over here.

00:17 Apart from that, each unit that it is producing takes around 9 .45 of the cost.

00:27 So that means the total cost over here that is c will be.

00:31 The investment plus the cost of production per unit.

00:37 So that means let x be the, you can say the number of units over here.

00:43 So the total cost will be 9 .45x plus 16 ,000 right.

00:51 Now coming on to the revenue part over here, it is being said that each package will sell for 55 .95 dollars.

00:59 So that means the total revenue will be 55 .95x.

01:08 Right.

01:09 Now coming on to the question, it is asking you, the first part is asking you that how many units the company should sell in order to break even.

01:19 So for the condition, to reach the break even point is what? r should be equal to c.

01:26 The total revenue should be equal to the total cost.

01:30 So now if i use the substitution method over here, that means c will be equal to 5 .55 .95x.

01:39 Just substitute that over here.

01:41 So that will give you 55 .95x equal to 9 .45x plus 16 ,000.

01:50 Now just subtract 9 .45x from both the sides of the equation.

01:55 So that will give you 46 .5x equal to 16 ,000.

02:03 So x will be what? x will be simply 16 ,000 divided by 46 .5.

02:09 And that is approximately equal to 344.

02:13 So that means 344 units should be said to break even...