Chapter 7: Cost-Volume-Profit (Part 3 of 3)

Sections 1 and 2Feb 8, 2013

Professor: Khim KellyOffice: HH386B

Office Hours: Mon/Wed 11:30am – 12:30pm and AppointmentEmail: kokelly@uwaterloo.ca

TA: Kun HuoEmail: khuo@uwaterloo.ca

Ch. 7 Assignment due Feb 11(Mon), 11.59pm

Kun will be teaching Ch. 7 expect mass confusion

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8 Feb 2013 Overview

• Last lecture …– More break-even analysis – Margin of Safety analysis– Target operating profit analysis

• Today’s lecture …– Cost Structure Choice and Leverage– Indifference analysis– Multi-product Settings

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Cost structure choice

• Company can choose a particular cost structure (i.e., relative proportion of fixed and variable costs)

• Which cost structure is better (more fixed costs or more variable costs)?

– Depends on many factors• Concept of leverage plays a key role in the

analysis

“Give me a place to stand and with a lever I will move the whole world”

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Operating Leverage

• Measure of the sensitivity of OI to % change in sales– Acts as a multiplier– Higher leverage: small change in sales leads to larger shift in

OI– Differs at any level of sales (i.e. valid at given X only), greatest

at break-even point and decreases as sales increases• Cost structure drives leverage

– More FC rather than VC yields greater leverage– Drive to automation?

Degree of Operating Leverage = CMOI

Leverage Graph: Cost Structure

Activity

$Case A: Total Expenses

Total Sales Revenue

Case B: Total Expenses

High FC

Low FC

Break-even Point

Lower FC results in a lower break-even point (Fixed expenses/unit CM), so less risk of losses when sales decrease

Leverage Graph: Cost Structure

Activity

$ Case A: Total Expenses

Total Sales Revenue

Case B: Total Expenses

High FC

Low FC

X

Which has a greater degree of operating leverage at point X: A or B?

Higher FC (higher CM) results in higher leverage (CM/OI), so better upside potential in profits when sales increases

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Per Unit Income IncomeRev $100 $100,000 $110,000VC $60 $60,000 $66,000CM $40 $40,000 $44,000FC $30,000 $30,000OI $10,000 $14,000

Units 1,000 1,100Degree of Leverage 4

Operating Leverage Example 1

Degree of Operating Leverage = CMOI

Sales increase by 10%

OI increases by 4 times (i.e., 40%)

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Per Unit Income IncomeRev $100 $100,000 $110,000VC $30 $30,000 $33,000CM $70 $70,000 $77,000FC $60,000 $60,000OI $10,000 $17,000

Units 1,000 1,100Degree of Leverage 7

Operating Leverage Example 2

Degree of Operating Leverage = CMOI

Sales increase by 10%

OI increases by 7 times (i.e., 70%)

Same total sales

Same total expenses, but greater proportion of FC

Higher FC (higher CM) results in higher leverage (CM/OI), so better upside potential in profits when sales increases

The critical assumption about leverage

• As fixed cost increases, variable cost will come down– More roads and infrastructure, people are more

productive because they spend less time on the travel

– Bigger class rooms, fewer instructors need to be hired

It is Clicker Time!!

Feel Free to Work Together on Clicker Questions

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Clicker Question #1

Green Company's variable expenses are 75% of sales. At a sales level of $400,000, the company's degree of operating leverage is 8. At this sales level, fixed expenses equal which of the following?

A) $87,500.B) $100,000.C) DogbertC) $12,500.D) $75,000.

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Clicker Question #1: Answer

Green Company's variable expenses are 75% of sales. At a sales level of $400,000, the company's degree of operating leverage is 8. At this sales level, fixed expenses equal which of the following?

Answer:

Clicker Question #2If two companies produce the same product and have the same total sales and same total expenses, operating leverage will be lower in the company with a higher proportion of fixed expenses in its cost structure.

A. TrueB. False

Leverage Graph: Cost Structure

Activity

$ A - Total Expenses

Total Sales Revenue

B - Total Expenses

High FC

Low FC

X

Which has a greater degree of operating leverage at point X: A or B?

Indifference Point(indifferent wrt profit between high FC vs. low FC)

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Indifference Point (P7-31)

Item Cost 1 Cost 2DM per unit $9.00 $7.50DL per unit 1.2 DLH @

$14/DLH0.75 DLH @ $18/DLH

Variable OH per unit 0.75 of DL costs 0.60 of DL costs

Fixed Man. Costs $1,108,000 $1,494,000Fixed S&A $1,685,000 $1,685,000Selling Price per unit $60.00 $60.00Variable Selling Cost per unit $4.00 $4.00

1) Find equations for both cost lines2) Set the two equations equal to each other and solve for X

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Cost 1 Equation …

Item Cost 1DM per unit $9.00DL per unit 1.2 DLH @

$14/DLHVariable OH per unit 0.75 of DL costs

Fixed Man. Costs $1,108,000Fixed S&A $1,685,000Selling Price per unit $60.00Variable Selling Cost per unit

$4.00

VC per Unit:= $9 + ($14*1.2) + ($14*1.2*0.75) + $4= $42.40 per unit

Fixed Costs:= ($1,108,000 +$1,685,000)= $2,793,000

Cost 1 EquationY = $2,793,000 + $42.40X

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Cost 2 Equation …Item Cost 2DM per unit $7.50DL per unit 0.75 DLH @

$18/DLHVariable OH per unit 0.60 of DL costs

Fixed Man. Costs $1,494,000Fixed S&A $1,685,000Selling Price per unit $60.00Variable Selling Cost per unit

$4.00

VC per Unit:= $7.50 + ($18*0.75) + ($18*0.75*0.60) + $4 = $33.10 per unit(Lower VC per unit)

Fixed Costs:= ($1,494,000 +$1,685,000)= $3,179,000(Higher Total FC)

Cost 2 EquationY = $3,179,000 + $33.10X

Cost 1 = Cost 2Set Cost 1 equation equal to Cost 2 equation to

determine the point of indifference:

Cost 1 = Cost 2$2,793,000 + $42.40X = $3,179,000 + $33.10X

$9.30X = $386,000X = 41,505 (rounded) units

The point of indifference in cost structure occurs when 41,505 units are produced and sold.

It is Clicker Time!!

Feel Free to Work Together on Clicker Questions

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Clicker Question #3

Company Y is considering two production technologies for producing its new product. The cost structures of the two technologies are as follows:

Bronze PlatinumSelling Price / Unit $ 150 $ 150Variable Production Costs / Unit $ 120 $ 50Total Fixed Production Costs $300,000 $1,210,000

Q: At what sales volume in units (rounded to the nearest whole unit) would Company Y be indifferent in technologies?

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Clicker Question #3

Q: At what sales volume in units (rounded to the nearest whole unit) would Company Y be indifferent in technologies?

A) 10,000 units.B) 12,100 units.C) 13,000 units.D) Infinite number of unitsE) Cannot be determined without additional

information.

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Sales Mix• Overall sales volume is very important to an

organization• The mix of sales also matters

– Low CM products? High CM products?• Relative proportions of product sales

– Expressed as a % of Total Sales• Sum across products

– Revenue– Variable Cost

• Fixed cost comes last

Budgeted Sales Mix (P7-20)Sinks Mirrors Vanities Total

% of Total 48% 20% 32% 100%Sales $240,000 $100,000 $160,000 $500,000VC 72,000 80,000 88,000 240,000CM $168,000 $20,000 $72,000 $260,000FC 223,600OI $36,400CMR 70% 20% 45% 52%

Q: What is Break-Even Sales Point given actual sales mix?

It is Clicker Time!!

Feel Free to Work Together on Clicker Questions

Clicker Question #4Sinks Mirrors Vanities Total

% of TotalSalesVCCMFC 223,600OICMR 70% 20% 45%

Q: Actual sales mix: Sinks: $160,000; Mirrors: $200,000; Vanities: $140,000. What is breakeven sales?

Clicker Question #4Q: Actual sales mix: Sinks: $160,000; Mirrors:

$200,000; Vanities: $140,000. What is breakeven sales?

A. That is a good questionB. $520,000C. $550,000D. $580,000E. $610,000

Important points

• Leverage: – Beyond the break even point, higher leverage means

that you receive higher profit per unit sold.– Higher leverage likely means higher fixed costs, so the

break even point is harder (more units) to reach• Indifference means given two cost structures, the

profits are equal at some activity level• In the real world, you would use a computer for

multi-product analysis because sales mixes will not remain equal

Summary• Today’s lecture …

– Cost Structure Choice and Leverage– Indifference analysis– Multi-product Settings

• Next lecture …– Prof Kelly returns to lecture (Hooray!!)– Introduction to Variable Costing (Chapter 8)