Cost-Volume-Profit Relationships Chapter 03 Chapter 5: Cost-volume-profit relationships Cost-volume-profit (CVP) analysis helps managers understand the interrelationships among cost, volume, and profit by focusing their attention on the interactions among the prices of products, volume of activity, per unit variable costs, total fixed costs, and mix of products sold. It is a vital tool used in many business decisions such as deciding what products to manufacture or sell, what pricing policy to follow, what marketing strategy to employ, and what type of productive facilities to acquire.

Racing Bicycle Company Quick Check  Racing Bicycle Company Selling price per unit: $500 Variable costs per unit: $300 Fixed costs per month: $80,000 What is the company’s net operating income if the production and selling is 500 units in January 2014?

Contribution Margin Approach The contribution margin ratio is calculated by dividing the total contribution margin by total sales. In the case of Racing Bicycle, the ratio is 40%. Thus, each $1.00 increase in sales results in a total contribution margin increase of 40¢. What is the implication of Contribution margin per unit?

CVP Graph

CVP Graph $ Sales Total costs Fixed costs units

Contribution Margin Ratio (CM Ratio) The contribution margin ratio is calculated by dividing the total contribution margin by total sales. In the case of Racing Bicycle, the ratio is 40%. Thus, each $1.00 increase in sales results in a total contribution margin increase of 40¢. What is the implication of Contribution margin ratio?

Contribution Margin Ratio (CM Ratio) The contribution margin ratio at Racing Bicycle is: CM per unit SP per unit CM Ratio = = 40% $200 $500 = The CM ratio can also be calculated by dividing the contribution margin per unit by the selling price per unit. Racing Bicycle has a CM ratio of 40%. This means that for each dollar increase in sales the company will produce 40¢ in contribution margin.

Quick Check  Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. 2,100 cups are sold each month on average. What is the CM Ratio for Coffee Klatch? a. 1.319 b. 0.758 c. 0.242 d. 4.139

Changes in Fixed Costs and Sales Volume Wind is currently selling 500 bikes per month. The company’s sales manager believes that an increase of $10,000 in the monthly advertising budget would increase bike sales to 540 units. Should we authorize the requested increase in the advertising budget?

Changes in Fixed Costs and Sales Volume $80,000 + $10,000 advertising = $90,000 Sales increased by $20,000, but net operating income decreased by $2,000.

Changes in Fixed Costs and Sales Volume The Shortcut Solution

Break-Even Analysis Graphical analysis. Equation method. Break-even analysis can be approached in three ways: Graphical analysis. Equation method. Contribution margin method.

At the break-even point Equation Method Profits = Sales – (Variable expenses + Fixed expenses) OR Sales = Variable expenses + Fixed expenses + Profits At the break-even point profits equal zero.

Here is the information from Racing Bicycle Co.: Break-Even Analysis Here is the information from Racing Bicycle Co.:

We calculate the break-even point as follows: Equation Method We calculate the break-even point as follows: Sales = Variable expenses + Fixed expenses + Profits $500Q = $300Q + $80,000 + $0 Where: Q = Number of bikes sold $500 = Unit selling price $300 = Unit variable expense $80,000 = Total fixed expense

We calculate the break-even point as follows: Equation Method We calculate the break-even point as follows: Sales = Variable expenses + Fixed expenses + Profits $500Q = $300Q + $80,000 + $0 $200Q = $80,000 Q = $80,000 ÷ $200 per bike Q = 400 bikes

Equation Method X = 0.60X + $80,000 + $0 We can also use the following equation to compute the break-even point in sales dollars. Sales = Variable expenses + Fixed expenses + Profits X = 0.60X + $80,000 + $0 Where: X = Total sales dollars 0.60 = Variable expenses as a % of sales $80,000 = Total fixed expenses

Equation Method X = 0.60X + $80,000 + $0 0.40X = $80,000 We can also use the following equation to compute the break-even point in sales dollars. Sales = Variable expenses + Fixed expenses + Profits X = 0.60X + $80,000 + $0 0.40X = $80,000 X = $80,000 ÷ 0.40 X = $200,000

Contribution Margin Method The contribution margin method is a variation of the equation method. Fixed expenses Unit contribution margin = Break-even point in units sold Break-even point in total sales dollars Fixed expenses CM ratio =

Quick Check  Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. 2,100 cups are sold each month on average. What is the break-even sales in units? a. 872 cups b. 3,611 cups c. 1,200 cups d. 1,150 cups

Quick Check  Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. 2,100 cups are sold each month on average. What is the break-even sales in dollars? a. $1,300 b. $1,715 c. $1,788 d. $3,129

Target Profit Analysis Suppose Racing Bicycle wants to know how many bikes must be sold to earn a profit of $100,000. We can use our CVP formula to determine the sales volume needed to achieve a target net profit figure.

The CVP Equation Sales = Variable expenses + Fixed expenses + Profits $500Q = $300Q + $80,000 + $100,000 $200Q = $180,000 Q = 900 bikes

The Contribution Margin Approach We can determine the number of bikes that must be sold to earn a profit of $100,000 using the contribution margin approach. Fixed expenses + Target profit Unit contribution margin = Unit sales to attain the target profit $80,000 + $100,000 $200 per bike = 900 bikes

Quick Check  Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. How many cups of coffee would have to be sold to attain target profits of $2,500 per month? a. 3,363 cups b. 2,212 cups c. 1,150 cups d. 4,200 cups

The Margin of Safety Excess of budgeted (or actual) sales over the break-even volume of sales. The amount by which sales can drop before losses begin to be incurred. Margin of safety = Total sales - Break-even sales

The Margin of Safety Racing Bicycle has a break-even point of $200,000. If actual sales are $250,000, the margin of safety is $50,000 or 100 bikes.

The Margin of Safety The margin of safety can be expressed as 20% of sales. ($50,000 ÷ $250,000)

Quick Check  Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. 2,100 cups are sold each month on average. What is the margin of safety? a. 3,250 cups b. 950 cups c. 1,150 cups d. 2,100 cups

Example – SAA School of Accounting & Auditing launches monthly tax accounting courses (10 sessions, 2 hours each). There are three alternatives for tuition fees: tuition fee No. of learners VND 600,000 25 500,000 32 400,000 42 Each course incurs: Instructor expense: VND500,000/session; Classroom rent expense: VND100,000/session; Advertising & administrative expense: VND3,000,000đ/course Learning materials & certification preparation: VND100,000/learner How many leaners should each course have to breakeven? What alternative the School should choose?

Example - SAA

Which cost structure is better? More fixed or more variable? Cost structure refers to the types and relative proportions of variable and fixed costs that a business incurs. Which cost structure is better? More fixed or more variable?

Cost structure Ford Vinaxuki Sales 1.000 Variable costs 500 600 Contribution margin 400 Fixed costs 300 200 Net operating margin

Cost structure What is an increase in net operating income if each company’s sales increase by 20%?

Cost structure Ford Increase in Operating income: Vinaxuki

Cost structure What is an increase in net operating income if each company’s sales decrease by 20%?

Cost structure Vinaxuki Decrease in Operating income: Ford Generally, companies with a high fixed cost structure will show higher net income in good years than companies with lower fixed cost structures. Just the opposite is true in bad years. Companies with low fixed cost structures enjoy greater stability in income across good and bad years. Ford Decrease in Operating income:

Operating Leverage A measure of how sensitive net operating income is to percentage changes in sales. With high leverage, a small percentage increase in sales can produce a much larger percentage increase in net operating income. ∆% Sales Degree of operating leverage (DOL) = ∆%Net operating income Contribution margin Net operating income Degree of operating leverage =

Operating leverage Ford: DOL = 500/200 = 2,5 Vinaxuki: DOL = 400/200 =2,0

∆%Net operating income = DOL x ∆% Sales Operating levegare ∆%Net operating income = DOL x ∆% Sales Ford Increase in Net operating income (%) = 2,5 x 20% = 50% Increase in Net operating income ($) = 50% x 200 = 100 Vinaxuki Increase in Net operating income (%)= 2,0 x 20% = 40% Increase in Net operating income ($) = 40% x 200 = 80

Quick Check  Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. 2,100 cups are sold each month on average. What is the operating leverage? a. 2.21 b. 0.45 c. 0.34 d. 2.92

Quick Check  At Coffee Klatch the average selling price of a cup of coffee is $1.49, the average variable expense per cup is $0.36, and the average fixed expense per month is $1,300. 2,100 cups are sold each month on average. If sales increase by 20%, by how much should net operating income increase? a. 30.0% b. 20.0% c. 22.1% d. 44.2%

The Concept of Sales Mix Sales mix is the relative proportions in which a company’s products are sold. In units In dollars Average contribution margin per unit = ∑ UCMi X unit sales mixi Average contribution margin rate = ∑ CM ratei X $ sales mixi Different products have different selling prices, cost structures, and contribution margins.

Average contribution margin per unit Breakeven analysis with sales mix 70% Pepsi UCM: VND500 per litre 30% 7up UCM: VND600 per litre Average contribution margin per unit 500 x 70% + 600 x 30% = 530 Fixed costs VND318,000,000 6000 x 70% = 4200 litres 6000x 30% = 1800 litres Breakeven point 3.180.000/530 = 6000 litres

Breakeven analysis with sales mix 30% Internet services CM rate 40% 70% Telephone services CM rate 30% Tỷ lệ lợi nhuận góp bình quân 30% x 70% + 40% x 30% = 33% Fixed costs VND3,300 mil. 10,000 x 70% = VND 7,000mil. 10,000x 30% = VND 3,000 mil. Breakeven point 3.300/33% = VND 10,000 mil.

Example 2 Nhu Ngoc is a Mooncake producer. The information for the performance in Jan. and Feb. 2014 as below. Calculate net operating income for each month and explain for the difference. In VND 000’ Sticky rice Mooncake Baked Mooncake Total Unit selling price 20 25 Unit variable costs 8 12,5 Total fixed costs 60,000 Sales for Jan. 2014 40% 60% 300,000 Sales for Feb. 2014

Key Assumptions of CVP Analysis Selling price is constant. Costs are linear and can be accurately divided into variable (constant per unit) and fixed (constant in total) elements. In multiproduct companies, the sales mix is constant. In manufacturing companies, inventories do not change (units produced = units sold). Here are the four key assumptions of cost-volume-profit analysis. You are probably familiar with the first three by now. The forth assumption tells us that there can be no change in inventory levels. That is, all units produced are sold in the current period.

End of Chapter 03 End of Chapter 5.