Break-Even Analysis using Algebraic Method

Introduction

From the previous section, we already know that:
NI = TR − TC

If TR = TC, NI = 0 Break Even
If TR > TC, NI > 0 Profit
If TR < TC, NI < 0 Loss

The business will start making a profit when the total revenue gets bigger than the total costs.
Most businesses need to know the point at which they will begin making profit.
This point begins after they break even and is known as the break-even point.

The Algebraic Method

In the algebraic method, we make the total revenue and the total cost equations equal and solve the resulting equation.
The solution gives us the break-even point in units.
The following steps are used to find the break-even point algebraically:

Step 1: Find the Total Revenue (TR) equation
Step 2: Find the Total Cost (TC) equation
Step 3: Write the equation TR = TC and solve it to find the break-even point in units
Step 4: Substitute the break-even point in units into the TR equation to find the break-even point in dollars.

Example:

Zoho Enterprises makes genuine leather jackets. The variable costs to make each jacket are $90.
Fixed costs for the period are $6000. The selling price is $150 per jacket.
The factory's production capacity for the period is 100 jackets.

Question: Using the algebraic method, find the break-even point in units and in dollars.
Solution:
Step 1: Find the TR equation
TR = SP × Q = 150Q;

Step 2: Find the TC equation.
TC = TVC + FC; TVC = VC × Q = 90Q;
FC = 6000; TC = 90Q + 6000

Step 3: Write the equation TR = TC and solve it to find the break-even point in units.
At the break-even point TR = TC which means that 150Q = 90Q + 6500;
Now, we need to solve this equation for the break-even point in units, (Q).
150x − 90x = 6000 ⇒ 60x = 6000 ⇒ Q = 6000 ÷ 60 ⇒ Q = 100

The break-even point in units is 100. Zoho Enterprises have to make 100 jackets to break-even. Once they make more than 100 jackets, they will enter the profit zone.
But if they make less than 100 jackets, they incur a loss.

Step 4: Substitute the break-even point in units into the TR equation to find the break-even point in dollars.
TR = 150Q ⇒ TR = 150 × 100 ⇒ TR = $15000
The break-even point in dollars is $15000.

Extra Exercise

Please access the following link to do a similar exercise about algebraic break-even analysis:
algebraic break-even exercise