3.1 Introduction to Break-Even and Cost-Volume-Profit (CVP) Analysis. Terms Used in Break-Even Analysis

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1 Chapter 3 Break-Even and Cost-Volume-Profit Analysis Introduction to Break-Even and Cost-Volume-Profit (CVP) Analysis Break-even point is the point at which the total revenue equals the total costs. In any business, the goal is to make a profit. To achieve this goal, the total revenue from the business should exceed the total costs associated with it. Revenue is earned from the sales of the product manufactured or produced, but there are numerous costs incurred in manufacturing or producing a product before selling it. Therefore, it is important to determine the number of units of the product that need to be manufactured and sold in order to cover all of the costs related to manufacturing it. The point at which the total sales or total revenue equals the total costs is known as the breakeven point. At the break-even point, the profit (net income) or loss is zero; i.e., there is no profit made or loss incurred. The break-even point is generally expressed in terms of volume (or quantity produced and sold). It may also be expressed in terms of total revenue. Any quantity that is produced and sold over this break-even point will result in a profit, while any quantity that is produced and sold below this break-even point will result in a loss. Businesses analyze the break-even point and their profit or loss in relation to the costs incurred, volume of sales, and selling price using (i) cost-volume-profit analysis (CVP), (ii) the contribution margin (CM) approach, or (iii) break-even charts (graphical analysis). Terms Used in Break-Even Analysis To understand break-even analysis, it is necessary to define the following terms and understand how they relate to each other. Total Costs (TC) There are several types of costs to consider in a business and these are classified into the two most relevant categories: fixed costs (FC) or total variable costs (TVC). The sum of the fixed costs and total variable costs is the total cost of the business and is expressed by the following formula: Formula 3.1(a) are always for a period of time. Total Costs These are costs that remain the same regardless of how many items are produced to sell. Fixed costs are calculated for a specific period (per annum,, etc.) to produce a predetermined quantity of products, known as the maximum Quantity (Q) quantity or capacity of the facility for that period. Examples of fixed costs are administrative salaries, rent or lease of the facility, utility costs, insurance costs, property taxes, equipment rental or depreciation, and marketing and advertising costs. Amount ($) Y Total Costs (TC) Total Variable Costs (TVC) Exhibit 3.1(a): Graph of Total Costs vs. Quantity Maximum Quantity X Total Variable Costs (TVC) These are costs that vary directly with the number of units of items produced. Examples of total variable costs are generally cost of all materials, cost of labour, and revenue-related costs, such as commission, etc., that are necessary to produce the number of items for the specific period. If no quantity is produced, then the total variable costs are zero.

2 86 Chapter 3 Break-Even and Cost-Volume-Profit Analysis Variable Costs per Unit (VC) These are costs from producing one unit of the item. This is the ratio of the total variable costs to the total number of units produced: Variable Costs (VC) VC = TVC and Selling price (P) Q are always. where, Q is the number of units produced and sold. Rearranging results in the following formula for TVC: Formula 3.1(b) Total Variable Costs TVC = VC # Q Selling Price per Unit (P) This is the amount a business charges its customers to buy a single unit of item produced. This is critical in calculating the revenue for the business. Total Revenue (TR) This is the amount of money received or brought into the business from the sales of the items produced and is expressed by the following formula: Formula 3.1(c) Total Revenue TR = P # Q where 'Q' is the number of units produced and sold. Y Formula 3.1(d) Net Profit (PFT) This defines the success of the business by determining the difference between the total revenue (TR) collected and the total costs (TC) incurred in the business. Net Income PFT = TR - TC If the total revenue exceeds the total costs, then there is a net profit. If the total revenue is less than the total costs, then there is a net loss. If the total revenue is equal to the total costs, then the business breaks even. Amount ($) Break-Even Point Loss Profit Quantity (Q) TR = P Q Total Revenue (TR) Total Costs (TC) Exhibit 3.1(b): Graph of Total Costs vs. Quantity and Total Revenue vs. Quantity Maximum Quantity X Formula 3.1(e) At the Break-Even Point At the break-even point, TR = TC If TR > TC, then PFT > 0 (Profit) If TR = TC, then PFT = 0 (Break-Even) If TR < TC, then PFT < 0 (Loss) Contribution Margin per Unit (CM) Contribution margin is the amount remaining from the sales after deducting the variable costs. It is shown in the following formula:

3 Chapter 3 Break-Even and Cost-Volume-Profit Analysis 87 Formula 3.1(f) Contribution Margin CM = P - VC The contribution amount from the sale of all units during a period is first used to cover the fixed costs (FC); the amount that remains is the net profit (PFT). If the contribution amount from the sale of all units exceeds the fixed costs for a period, then there is a profit; similarly, if the contribution amount from the sale of all units is less than the fixed costs, then there is a loss. Assumptions and Limitations There are a number of assumptions made and limitations present in break-even analysis and costvolume-profit analysis in this chapter. These assumptions are made to focus on the main concepts in this topic and to simplify theoretical calculations. However, in practical situations, variations to these assumptions must be taken into account before making business decisions, and this is accomplished using more advanced mathematical models. The following outlines are the assumptions and limitations in this chapter: (i) Selling price (P) is constant and is not affected by a change in the number of units sold. i.e. Total Revenue (TR = P Q) is a linear function. (ii) Quantity of items (Q) produced is equal to the quantity of items sold. (iii) remain the same over the specified period. (iv) Variable Costs (VC) is constant and is not affected by a change in the number of units sold. i.e. Total Cost (TC = FV + VC Q) is a linear function where VC Q = TVC (v) When multiple products are produced in a company, the ratio of various products produced remains constant. Break-even point: The point at which the total revenue (TR) equals the total costs (TC). Break-Even Point As explained earlier, the break-even point in a business is when the total revenue from sales is equal to the total costs. The break-even point may be expressed in terms of the number of units produced or in terms of the total revenue. Note: The break-even point can be lowered by any or all of the following measures: Reducing the variable costs (VC) by using more cost-effective scheduling or technology. Reducing the fixed costs (FC) by using cost-control measures in marketing, rentals, etc. Increasing the selling price (P). However, businesses may be reluctant to increase the price of the product due to a competitor's selling price of similar items. Rounding up to the next unit when calculating the number of units (Q) to have a little more profit than loss.

4 88 Chapter 3 Break-Even and Cost-Volume-Profit Analysis Break-Even Analysis Using a Financial Calculator If you are routinely solving break-even problems, a preprogrammed calculator, like the Texas Instruments BA II Plus calculator, will help you solve them quickly, without the need for you to remember any formulas. The exhibit below shows the methods to access your worksheet and the five break-even variables (fixed costs, variable costs, selling price, profit, and quantity) as seen in your calculator. It also refers to the corresponding algebraic variables. You will get a better idea on how to use your calculator by working through Examples 3.1(a) and 3.1(b). Press the 2ND key then the BRKEVN key (secondary function of the number 6 key) to open the break-even worksheet. Press the 2ND key then the CLR WORK key (secondary function to the CE C key) to clear all values from memory. Press the up and down arrow keys to access the different break-even variables. Fixed Costs Variable Costs Selling Price Profit Quantity Note: At the break-even point, PFT = 0 Example 3.1(a) Solution Calculating the Break- Even Point in Terms of the Number of Units Produced A company manufactures calculators and sells them at $50 each. The fixed costs are $4000 and the variable costs is $32. Calculate the number of units needed to be manufactured and sold to break even. P = $50.00, FC = $ , VC = $32.00 Let Q be the number of units needed to break even. Using Formula 3.1(c), TR = P # Q = # Q Total Cost at the break-even point TC = FC + VC # Q = # Q At the break-even point, TR = TC Therefore, # Q = # Q The number of units Solving for Q, # Q = Q = = 223 units produced must be rounded up to the next whole number. Therefore, 223 units need to be manufactured and sold to break even.

5 Chapter 3 Break-Even and Cost-Volume-Profit Analysis 89 Example 3.1(b) Solution Calculating the Break- Even Point in Terms of the Total Revenue Rubber King must produce 3200 tires to break even. The fixed costs are $12,850 for administrative salaries, $18,600 for rent and utilities, $2400 for insurance costs, and $4550 for equipment rental. The variable costs are $10 per tire for material and $30 per tire for labour. (i) What is the total revenue required to break even? (ii) What is the selling price per tire? Fixed Costs = Administrative Salaries + Rent and Utilities + Insurance Costs + Equipment Rental = 12, , = 38, Variable Costs = Material + Labour = = $40.00 per tire Q = 3200 units (i) Calculating the total revenue required to break even Using Formula 3.1(a), Substituting TVC with Formula 3.1(b), = FC + (VC # Q) = 38, (40.00 # ) Total Cost at the break-even point = $166, At the break-even point, TR = TC Therefore, the total revenue required to break even is $166, (ii) Calculating the selling price per tire Let 'P' be the selling price. Using Formula 3.1(c), TR = P # Q Substituting values, 166, = P (3200) P = $52.00 Therefore, the selling price per tire is $ Exercises Answers to odd-numbered problems are available online For the following problems, express the answers rounded to two decimal places, wherever applicable. Calculate the missing values: 1. Fixed Costs (FC) Variable Costs (VC) Selling Price (P) Break-Even Volume (Q) Total Variable Cost (TVC) Total Revenue (TR) a. $1000 $3 $13??? b. $8000 $70? 200?? c. $5890? $156 62?? d.? $45 $91 50?? 2. Fixed Costs (FC) Variable Costs (VC) Selling Price (P) Break-Even Volume (Q) Total Variable Cost (TVC) Total Revenue (TR) a. $8400 $25 $36??? b. $125,000 $450? 1000?? c. $720? $74 20?? d.? $30 $50 400?? 3. A company sells an item for $75 each. The variable costs are $58 per item and the fixed costs are $4250. How many items does the company have to sell to break even?

6 90 Chapter 3 Break-Even and Cost-Volume-Profit Analysis 4. ClockWork and sells clocks for $150. The fixed costs are $7800 and variable costs are $111 per clock. How many clocks does it have to sell to break even? 5. The selling price of a product is $30, the fixed costs are $12,560, and the total variable costs are $11,440 at the break-even point. Calculate the number of units required to break even. 6. Harris owns a DVD manufacturing factory that produces DVDs and sells them for $0.30 each. The fixed costs are $8640 and the total variable costs at the break-even point are $1800. Calculate the number of DVDs he needs to produce and sell to break even. 7. A small manufacturing company that produces and sells snow boots has variable costs of $65 per pair of boots. The fixed costs are $2100 and it has to sell 84 pairs of boots to break even. b. What is the selling price per pair of boots? 8. A manufacturing company has to produce and sell 225 items every month to break even. The company's fixed costs are $ and variable costs are $10 per item. b. What is the selling price per item? 9. A manufacturing company pays $16,780 for rent and utilities, $41,850 for administrative salaries, $4850 for insurance costs, and $62,789 for equipment rental. The variable costs are $35 for material and $65.50 for labour. It needs to manufacture and sell 3550 units to break even. a. What is the selling price? b. What is the total revenue to break even? 10. A factory that manufactures and sells computer hard-drives pays $20,000 for rent and utilities, $120,850 for management salaries, and $37,500 for equipment rental and lease. The variable costs are $55 for material and $120 for labour. The factory needs to sell 2445 units to break even. a. What is the selling price per hard-drive? b. What is the total revenue to break even? 11. Digital Displays Inc. makes computer monitors and sells them for $317 each. To break even, it needs to sell 500 monitors. If the fixed costs are $8500, calculate the variable costs per monitor. 12. A company that manufactures electronic items, sells them for $155 each. It needs to sell 700 items to break even. If the fixed costs are $24,500, what are the variable costs per item? 13. In order to break even, a manufacturer is required to sell 292 chairs every week. The total revenue per week at the break-even point is $27,000 and the fixed costs are $10,220 per week. Calculate the variable costs per chair. 14. Alora and Jacey run a company that manufactures and sells injection moulding machines. It needs to sell 520 machines to break even and the total revenue at the break-even point is $45,000. Calculate the variable costs per machine if the fixed costs are $26, A company manufactures skis and sells them for $400 per pair. The variable costs to manufacture each pair are $290 and the break-even volume is 740 units. b. What are the fixed costs? 16. Chu-Hua Inc. manufactures automobile components and sells them for $15.40 each. The variable costs to manufacture each component are $12 and the company needs to sell 625 components to break even. b. What are the fixed costs?