Break-Even Analysis

Breakeven analysis is used to determine when your a business will be able to cover all its expenses and start to make a profit. it describes the relationship between costs and revenue. it is also called cost-volume analysis since it is useful to identify the volume of production at which the business break-even.

In Break-Even Analysis a profit occur after the Total revenue (TR) exceed the Total cost (TC). Total cost includes fixed cost (FC) and variable costs (VC).

Break-Even happen when TC = TR

Variable Cost:

variable costs are costs that change proportionally according to the production volume. They are increased when the production volume rise and vise versa. variable cost mostly contribute to the production of a product such as the labor and materials required to produce a product.

Fixed Cost:

Fixed costs are expenses that should be paid by the company regardless of the production volume and business activity. example of fixed cost for a project, rent and utility bills, management, insurance premium and loan payment.

Example x-x: Company manufactures a specific car part, each part costs $50 and sells for $120. if the company has $100,000 of annual overhead cost. how many pieces the company needs to produce to break-even.

let Z = the number of car parts

To break-Even Total cost (TC) should equal the total revenue (TR).

TC = 50 x z + $100,000

TR = 120 x z

50z +$100,000 = 120z

z = 1429 unit

Example x-x: a product sells for $600 per unit, cost $250 per unit and there is production cost overhead of $120,000. what is the volume of production to Break-Even?

let Z = the number of units

To break-Even Total cost (TC) should equal the total revenue (TR).

TC = 250 x z + $120,000

TR = 600 x z

250z + $120,000 = 600z

z = 343 unit

Example x-x: production of product X has fixed cost of $200,000 and variable cost of $10 per unit, whereas the production of product Y has a fixed cost of $60,000 and variable cost of $20 per unit. at what production volume, the total cost of X and Y equal?

Cost of X = Cost of Y

let z = production volume

$200,000 + $10 x z = $60,000 + 20 x z

$(200,000 - 60,000) = (20-10) x z

$140,000 = 10 x z

z = 14000 units

Example : A firm has annual overhead cost of $1.2 millions and variable cost of $200 per unit. To reduce it variable cost to $150, the company decided to spend extra $150,000 as an annual fixed cost. the sale price is $500 per unit and the sale volume assumed to be steady. what is the quantity of production to break even?

let z = Production units to break even

The increase in overhead cost by $150,000 will decrease the variable cost by $50.

1.2 millions + $150,000 = $(500 - 150) x z

z = 3858 units

Example : a project manager trying to decide whether to buy a piece of equipment for $120,000 and $1000 of monthly maintenance, or to lease that equipment for $5000 per month. what is the rewarding usage time of that equipment so the lease cost equal the buying cost?

let z = age in months for the equipment to be used on the project.

Cost of leasing = cost of buying

$5000 x z = $120,000 + $1000 x z

$120,000 = $4000 x z

z = 30 months

Example a company produces hair shampoo sells it for $15 each. The production of 4000 units cost $32000 and there is an annual overhead cost of $150,,000 for each production volume of 4000 unit. How many unit per year the company needs to produce to break even?

let z = no of shampoo units

shampoo unit cost is $32,000 / 4000 = $8

To Break even, Total cost = total revenue

$8z + $150,000 = $15z

z = 21429 unit of shampoo.

Questions and Problems

1. Fixed costs are $35,000 per year, variable costs are $40 per unit, and the selling price is $75 each. Find the Break-even point?

Answer: let z be the break even no of units.

Break-Even happens when TC = TR

Total cost = fixed cost + variable cost

= $40,000 + $40z

Total revenue = selling price x no of units

= $75 x z

Break-Even Point

$35,000 + $40z = $75z

z = $35,000 / $35

= 1000 units.

2. Project manager has to decided whether to hire a web developer for his project for $4000 per month, or contract the web development package to a web development company for $30,000 and $500 as monthly maintenance fee. what decision should he take?

Answer: Use the Break-Even Analysis to calculate the find the point where hiring cost will be equal or greater the contracting cost.

let z = no of months to break-even

$4000 z = $30,000 + $500 z

Z = $30,000 / $3500, or 8.6 months

Breakeven analysis is used to determine when your a business will be able to cover all its expenses and start to make a profit. it describes the relationship between costs and revenue. it is also called cost-volume analysis since it is useful to identify the volume of production at which the business break-even.

In Break-Even Analysis a profit occur after the Total revenue (TR) exceed the Total cost (TC). Total cost includes fixed cost (FC) and variable costs (VC).

Break-Even happen when TC = TR

Variable Cost:

variable costs are costs that change proportionally according to the production volume. They are increased when the production volume rise and vise versa. variable cost mostly contribute to the production of a product such as the labor and materials required to produce a product.

Fixed Cost:

Fixed costs are expenses that should be paid by the company regardless of the production volume and business activity. example of fixed cost for a project, rent and utility bills, management, insurance premium and loan payment.

Example x-x: Company manufactures a specific car part, each part costs $50 and sells for $120. if the company has $100,000 of annual overhead cost. how many pieces the company needs to produce to break-even.

let Z = the number of car parts

To break-Even Total cost (TC) should equal the total revenue (TR).

TC = 50 x z + $100,000

TR = 120 x z

50z +$100,000 = 120z

z = 1429 unit

Example x-x: a product sells for $600 per unit, cost $250 per unit and there is production cost overhead of $120,000. what is the volume of production to Break-Even?

let Z = the number of units

To break-Even Total cost (TC) should equal the total revenue (TR).

TC = 250 x z + $120,000

TR = 600 x z

250z + $120,000 = 600z

z = 343 unit

Example x-x: production of product X has fixed cost of $200,000 and variable cost of $10 per unit, whereas the production of product Y has a fixed cost of $60,000 and variable cost of $20 per unit. at what production volume, the total cost of X and Y equal?

Cost of X = Cost of Y

let z = production volume

$200,000 + $10 x z = $60,000 + 20 x z

$(200,000 - 60,000) = (20-10) x z

$140,000 = 10 x z

z = 14000 units

Example : A firm has annual overhead cost of $1.2 millions and variable cost of $200 per unit. To reduce it variable cost to $150, the company decided to spend extra $150,000 as an annual fixed cost. the sale price is $500 per unit and the sale volume assumed to be steady. what is the quantity of production to break even?

let z = Production units to break even

The increase in overhead cost by $150,000 will decrease the variable cost by $50.

1.2 millions + $150,000 = $(500 - 150) x z

z = 3858 units

Example : a project manager trying to decide whether to buy a piece of equipment for $120,000 and $1000 of monthly maintenance, or to lease that equipment for $5000 per month. what is the rewarding usage time of that equipment so the lease cost equal the buying cost?

let z = age in months for the equipment to be used on the project.

Cost of leasing = cost of buying

$5000 x z = $120,000 + $1000 x z

$120,000 = $4000 x z

z = 30 months

Example a company produces hair shampoo sells it for $15 each. The production of 4000 units cost $32000 and there is an annual overhead cost of $150,,000 for each production volume of 4000 unit. How many unit per year the company needs to produce to break even?

let z = no of shampoo units

shampoo unit cost is $32,000 / 4000 = $8

To Break even, Total cost = total revenue

$8z + $150,000 = $15z

z = 21429 unit of shampoo.

Questions and Problems

1. Fixed costs are $35,000 per year, variable costs are $40 per unit, and the selling price is $75 each. Find the Break-even point?

Answer: let z be the break even no of units.

Break-Even happens when TC = TR

Total cost = fixed cost + variable cost

= $40,000 + $40z

Total revenue = selling price x no of units

= $75 x z

Break-Even Point

$35,000 + $40z = $75z

z = $35,000 / $35

= 1000 units.

2. Project manager has to decided whether to hire a web developer for his project for $4000 per month, or contract the web development package to a web development company for $30,000 and $500 as monthly maintenance fee. what decision should he take?

Answer: Use the Break-Even Analysis to calculate the find the point where hiring cost will be equal or greater the contracting cost.

let z = no of months to break-even

$4000 z = $30,000 + $500 z

Z = $30,000 / $3500, or 8.6 months