Lesson II Break-Even Analysis PDF

Preview

Summary

LESSON II: BREAK EVEN ANALYSISLearning Objectives: At the end of this lesson, students are expected to: Identify the mathematical approach and application of break even analysis linear function. Solve problems involving break-even analysis. Prepare and analyze business case related to break even ana...

Description

LESSON II: BREAK EVEN ANALYSIS Learning Objectives: At the end of this lesson, students are expected to: 1. Identify the mathematical approach and application of break even analysis linear function. 2. Solve problems involving break-even analysis. 3. Prepare and analyze business case related to break even analysis.

Introduction For any business to be successful, the management should be able to determine in advance the effects that certain decisions may have on the sales of its products, as well as on the total cost of production. The firm should also be able to estimate its revenue derived from the sales forecast during the year and then build enough safety values to assure itself that thus revenue is large enough to cover the cost of production, cost of transporting the goods and cost of advertising and promotion. In general, the revenue from sales is expressed as linear function of the number of units (q) the firm expects to sell during the year. The total cost of production can be expressed as: Y = mx + b

Where: b = fixed cost m = variable cost When the total sales just equals the total cost, the firm has neither gained profit nor incurs a loss, it has just reached its break-even point. Break Even Point Analysis: Linear Function The break even analysis has three components: The Cost ( C ), Volume ( q ) and Profit ( P ) The Cost refers to the cost incurred by the firm during the production of a particular product. These costs are the fixed cost (FC) and variable cost (VC). Fixed cost are the cost incurred that are independent of the volume (q) of units produced, variable cost are the cost per unit of the product. The total cost is expressed as: TC = VC + FC Variable Expenses - are directly proportional to sales income. Examples: materials and manufacturing labor costs; staff commission based on the sales made during the period. If sales increase = Variable expense should increase vice versa Fixed Expense - remain constant whatever the sales activity may be. These are not directly proportional to units of product sold, except for time factor. Examples: insurance for the year, administrative salaries for the month, rent for the quarter Volume (q) refers to the level of production which can be expressed as quantity of units produced and sold as volume of sales in pesos or as a percentage of total capacity available.

8

Profit (P) is the difference between the total revenue (TR) and total cost (TC). It can be expressed as; P=TR-TC. Break-even Formula: TR (Total Revenue) = TC (Total Costs) Where: TR = SPu selling price per unit x q quantity or volume TC = (VCu variable costs per unit x q) + FC fixed costs P = TR - TC Therefore:

FC Break-even sales in units/volume = SPu  VCu Break-even sales in peso/revenue =

BES u xSPu

Sample Problem: 1. A company sells its product at P12 per unit. The product has a variable cost of P6 per unit and the fixed cost is P42,000. Determined each of the following: a. TR, TC, and Profit Functions. b. Sales volume when profit is P18,000. c. Profit when sales are 12,000 units d. The break even quantity and revenue. e. The amount by which the unit variable cost has to be decreased or increased for the company to break even at 4,000 units, assuming that the selling price and the fixed cost remain constant. f. The new selling price per unit to break even at 600 units, assuming that FC and UVC are constant. g. The number of units to sell to cover the fixed cost. Solution: a. ) TR =12q TC = 6q + 42,000 P = 12q - (6q + 42,000)

b. ) 18,000 = 12q - 6q - 42,000 18,000 + 42,000 = 6q 6q =60,000 q = 10,000 units c. ) P = 12(12,000) - [6(12,000) + 42,00] = 144,000 - (72,000+42,000) = 144,000 -114,000 P = ₱30,000 d. ) TR = TC 12q = 6q + 42,000 12-6q = 42,000 6q = 42,000 q = 7000 units

e.) Let x = new VCu 12(4,000) = 4,000X + 42,000 48,000 - 42,000 = 4,000x 4,000x = 6000 x = ₱ 1.50 f.) let x = new SPu 600x = 6(600) + 42,000 600x = 3600 + 42,000 600x = 45,600 x = ₱ 76 g.) 12q = 42,000 q = 3,500 units should sell to cover the entire fixed costs

9

2. A company which produces novelty items incurs the following monthly costs in producing a particular novelty item. Fixed cost = P10,000; variable cost = P8 per item If the Company produces 400 units and sold them at P23 per unit (assume all the units are sold), how much is the; a. total cost; total revenue ; total profit b. at what volume will it break even c. profit at a volume of 700 units d. suppose the selling price was changed from P23 per unit to P30 per unit, what would be its new break-even volume? its break even revenue? Solution: a. ) TC = 8(400) +10,000 = 3,200 + 10,000 = ₱ 13,200 TR = 23 (400) = ₱ 9,200 P = 9,200 -13,200 = ₱ (-4,000) loss b. ) TR = TC 23q = 8q = 10,000 23q - 8q = 10,000 15q = 10,000 q = 667 units

c.) P = 23(700) - 8(700) +10,000 = 16,100 - (5,600 + 10,000) = 16,100 - 15,600 P = ₱ 500

d.) BESu = FC/SPu - VCu = 10,000 / 30 - 8 = 10,000/22 BESu = 455 units BESp = 455 x ₱ 30 = ₱13,650

3. Hazel Rae Garments produces hand towels at a cost of P15 per unit and sells them at P23 each. The weekly cost of production is P5,000. Determine a. The TR, TC, and Profit Functions: b. The break even quantity and revenue c. If the selling price per hand towel is increased to P35 find the new break-even point (FC and VC remain constant). d. If Hazel Rae is able to reduce the price to P20 per unit of the hand towel, but at the same time an increase of P200 in operational overhead is incurred, as it to her advantage? (Assume VC to be constant). Solution: a. ) TR = 23(q) TC = 15q + 5,000 P = 23q - (5q + 5,000) b. ) BESu = 5,000/23-15 = 5,000/8 BESu = 625 units ₱23 X BESp ₱ 14,375

c.) BESu = 5,000/35-15 = 5,000/20 BESu = 250 units x ₱35 = ₱8,750 d.) at Break-even TR = TC 20q = 15q + 5,200 20q-15q = 5,200 5q = 5,200 q = 1,040 units x ₱20 = ₱20,800 *This will give disadvantage for Hazel Rae in terms of the number of units and peso value require to meet the break-even while getting

1 0

competitive advantage in terms lowering the selling price.

EXERCISES Direction: Solve the following problem. 1. A company produces and sells a particular product. Unit selling price is P80. and unit variable cost is P60. The fixed cost is P120,000. Find the following: a. TR, TC and Profit function. b. Profit when sales is 20,000 units. c. The break-even quantity and revenue. d. The volume of sales to cover the fixed cost. e. The volume of sales if profit is P18,000. f. The amount by which the selling price will have to be decrease or increased to breakeven at 4,000 units. g. The amount by which the fixed cost has to be increased or decreased to allow the company to break even at 1,000 units. Assume UVC and USP are constant. 2. A firm buys merchandise at P20 per unit and sells them at P30 per unit. Fixed cost are at P15,000. Determine the following: a. Sales volume when profit isP16,000. b. Profit when sales volume are 1,000 units. c. The break-even quantity and revenue. d. The new break-even point if the selling price is increased by 10% but the FC and UVC are constant. e. The amount by which the variable cost per unit has to be increased or decreased in order to break even at 1,000 units, assuming FC and USP are constant. f. If UVC and FC are constant, the new unit selling price (USP) to break even at 1,000 units. 3. A small scale industry sells its products at P2.80 per unit. The variable cost is P1.80 per unit. The total fixed cost is P20,000. Determine the following: a. The break even quantity and revenue. b. The profit (or loss) at a sales volume of 15,000 units. c. How can profit be generated if there is a loss in (b)? d. Up to how much should the selling price per unit be increased or decreased to break even at 15,000, assuming that FC and UVC remain constant? e. TC when sales are 10,000 units? 4. DJA Company manufactures and sells a particular product. Unit variable cost is P90 and unit selling price is P120. Fixed cost is P180,000. Determine the following: a. The break even quantity and revenue. b. Profit when sales are 30,000 units c. Volume of sales when profit is P27,000. d. If the unit variable cost is increased by 10%, what is the new break even quantity and revenue? e. What is the volume of sales to cover FC?

1 1

f. If the company would like to break even at 4,000 units, how much should be the increase or decrease of the FC, assuming that USP and UVC are constant. 5. The following data are given on the sole product of Silva Corporation. Unit selling price P 800 Unit variable cost 350 Variable operating expenses per unit 70 Annual sales volume, 620 units The company's annual fixed costs and expenses amount to P190,000. Required: Compute for break even sales in units and in peso value. 6. The ABC company sells product X. Some selected data is given below: Selling price per unit of product X: P16 Variable cost per unit of product X: P12 Total Fixed Cost: P160,000 a. What is the break even sales in units and in peso value? b. How many units of product X would be required to sell to earn an operating income of P20,000? 7. Basic Illustration Corp. Produces and sells a single product. The selling price is P25 and the variable costs is P15 per unit. The corporation’s fixed costs is P100,000 per month. Average monthly sales is 11,000 units. a.The corporations’ break-even point is? b. If fixed costs will increase by P20,000, the break-even point in units will increase (decrease) by? c. If the variable costs per unit will go up by P5, the peso break-even sales will increase (decrease) to? d. If selling price will increase to P30, the break-even point in units will? 8. Genevieve Co. And Odessa Co. sell the same product in a competitive industry. Thus, the selling price of the product for each company is the same. Other data about the two companies are as follows: Genevieve Co. Odessa Co. Fixed Costs P50,000 P70,000 Variable Costs per unit 70 50 Selling price per unit 150 120 Break-even sales in units ??? ??? Break-even sales in peso ??? ???

1 2...