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Break-Even Analysis

Break-even occurs when total income equals total expenses.

$$Total\ Revenue=Total\ Cost$$

Problem: CE Board Nov. 2015

A new computer desk requires $6,000 equipment cost and $200 construction cost per desk. Revenue is $450 per desk. Find the break-even quantity.

$$200x+6000=450x$$
$$x=24$$

Final answer: 24 desks.

Problem: CE Board Nov. 2018

Revenue from selling computer boards is $R=60x$ and cost is $C=50x+5000$. Find the break-even number of boards and production cost at break-even.

$$60x=50x+5000 \Rightarrow x=500$$
$$C=50(500)+5000=30,000$$

Final answer: 500 boards and $30,000 cost.

Problem: CE Board Nov. 2021

An electric pump costs P3,200, maintenance is P50/year, efficiency is 0.85, life 14 years, used 400 hr/year, electricity costs P0.04/kWh, and horsepower is 200 hp. Find monthly cost.

$$Annual\ cost=\frac{400(0.04)(200)(0.746)}{0.85}+50=2,858.47$$
$$Monthly\ cost=\frac{2,858.47}{12}=238.20$$

Final answer: P238.20 per month.

Problem: Break-Even Quantity

Fixed cost is P180,000, selling price is P95 per unit, and variable cost is P55 per unit. Find break-even quantity.

$$Q=\frac{F}{p-v}=\frac{180000}{95-55}=4500$$

Answer: Break-even quantity is 4,500 units.

Problem: Profit at a Given Output

Using fixed cost P180,000, price P95, and variable cost P55, find profit at 6,000 units.

$$Profit=(95-55)(6000)-180000=60000$$

Answer: Profit is P60,000.

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Exam Generator Problems

Additional board-style practice items for this topic.

Question Bank: q237

MSTE - Engineering Economy / Breakeven / Engr. Janclyde Espinosa (Clidez)

CE Board November 2015
The planning department of Abstract Office Supplies has been asked to determine whether the company should introduce a new computer desk each year. The department estimates that 6000 dollars of new manufacturing equipment will need to be purchased and the cost of constructing each desk will be 200 dollars. The department also estimates that the revenue from each desk will be 450 dollars. Find the company’s break- even point for this desk.

Answer:

  1. 24
  2. 22
  3. 20
  4. 26
Break-even occurs when revenue equals cost:
$450x=6000+200x$
$250x=6000$
$\boxed{x=24}$

Question Bank: q239

MSTE - Engineering Economy / Breakeven / Engr. Janclyde Espinosa (Clidez)

CE Board November 2018
The revenue R from selling x number of computer boards is given as R = 60x and the cost C of producing them is given by C = 50x + 5000. Find how many boards must be sold to break-even and how much money is needed to produce the breakeven number of boards.

Answer:

  1. 500, 30000
  2. 600, 36000
  3. 700, 42000
  4. 800, 48000
Set revenue equal to cost:
$60x=50x+5000$
$10x=5000$, so $x=500$ boards.
Production cost at break-even:
$C=50(500)+5000=30000$
$\boxed{500, 30000}$

Question Bank: t1092

MSTE - Engineering Economy / Engineering Economy / Gemini mapped Chapter 7 to 10

The cost of producing a certain commodity consist of P125.00 per unit for labor and material cost and P320.00 per unit for other variable cost. The unit can be sold at P1,200.00. If the production capacity per month is 5200 units, what maximum fixed amount can the company spend each month to break even?

  1. P3,850,000
  2. P4,126,000
  3. P2,520,000
  4. P3,926,000
Contribution margin per unit $= 1{,}200 - (125 + 320) = 755$.
At break-even, total contribution covers the fixed cost:
$$FC_{max} = 755 \times 5{,}200$$
$$\boxed{FC_{max} = \text{P}3{,}926{,}000}$$

Question Bank: t1093

MSTE - Engineering Economy / Engineering Economy / Gemini mapped Chapter 7 to 10

A telephone company have a production capacity of 500,000 units per month. At its present capacity of 350,000 units per month, the company have a total monthly income of P350,000,000. The company has a fixed cost of P100,000,000 per month and a variable cost of P200 per unit.

What is the present profit or loss in millions of pesos?

  1. 200
  2. 210
  3. 180
  4. 190

What is the break-even quantity?

  1. 135,000
  2. 125,000
  3. 155,000
  4. 165,000

If the production is increased to 80% of its capacity, what is the profit or loss in millions of pesos?

  1. 220
  2. 250
  3. 200
  4. 190

Part 1.

Unit price $= 350{,}000{,}000 / 350{,}000 = \text{P}1{,}000$. Profit = income − fixed − variable:
$$\text{Profit} = 350\text{M} - 100\text{M} - 200(350{,}000)$$
$$= 350 - 100 - 70 = \boxed{\text{P}180\text{M (profit)}}$$

Part 2.

Contribution margin per unit $= 1{,}000 - 200 = 800$. Break-even quantity = fixed cost / contribution:
$$Q_{BE} = \frac{100{,}000{,}000}{800} = \boxed{125{,}000 \text{ units}}$$

Part 3.

80% of capacity $= 0.80(500{,}000) = 400{,}000$ units.
$$\text{Profit} = 1{,}000(400{,}000) - 100\text{M} - 200(400{,}000)$$
$$= 400 - 100 - 80 = \boxed{\text{P}220\text{M (profit)}}$$

Question Bank: t1096

MSTE - Engineering Economy / Engineering Economy / Gemini mapped Chapter 7 to 10

The cost of producing a commodity consist of P102.00 per unit for labor and material cost and P54.00 per unit for other variable cost. The fixed cost per month amounts to P850,000. The commodity is sold at P740.00 each.

What is the break-even quantity per month?

  1. 1465
  2. 1645
  3. 1546
  4. 1456

How many units must be produced each month in order that the net profit equals the cost?

  1. 3874
  2. 3972
  3. 3547
  4. 2912

What is the net profit if for a production of 4000 units per month, in pesos?

  1. 1,486,000
  2. 1,563,000
  3. 1,254,000
  4. 1,632,000

Part 1.

Contribution margin per unit $= 740 - (102 + 54) = 584$. Break-even quantity:
$$Q_{BE} = \frac{850{,}000}{584} = \boxed{1456 \text{ units}}$$

Part 2.

Net profit equals total cost when revenue is twice the total cost. With profit $= 584Q - 850{,}000$ and cost $= 850{,}000 + 156Q$:
$$584Q - 850{,}000 = 850{,}000 + 156Q$$
$$428Q = 1{,}700{,}000 \;\Rightarrow\; \boxed{Q \approx 3972 \text{ units}}$$

Part 3.

Net profit $= $ contribution × units − fixed cost:
$$\text{Profit} = 584(4{,}000) - 850{,}000 = 2{,}336{,}000 - 850{,}000$$
$$\boxed{\text{Profit} = \text{P}1{,}486{,}000}$$

Question Bank: t1100

MSTE - Engineering Economy / Engineering Economy / Gemini mapped Chapter 7 to 10

DITG company invested P1.73M in a fish pond. The useful life of the pond is expected to be six years. If the pond pays a profit of P67.00 per kilogram of fish sold, how many kilograms of fish per year will DITG sell in order to break even? Assume the company's Minimum Attractive Rate of Return (MARR) is 15%:

  1. 5475
  2. -4571
  3. 6214
  4. 6823

Solution pending in psadquestions/t1100.json.