Question

#8. Cost Volume Profit Analysis

Scenario

Mirabel Manufacturing is a small but growing company that manufactures and sells marine sonar equipment. They employee a national sales force and their primary customers are marine retailers and boat dealerships. The company has expanded over the last 5 years and Paul Mirabel, the founder and CEO has become concerned that he no longer has a clear picture of their cost structure. He calls his CFO, Mary Jane Montgomery in for a meeting.

“Mary Jane, I am concerned that I am not current on our cost structure and how that is impacting our bottom line,” Paul begins.

“Well, Paul, the company has grown considerably over the past 5 years, so I’m not surprised that you feel a little disconnected with how things are going,” Mary Jane replied. She continued “In fact, I’ve been meaning to talk to you about a couple of big items such as increasing the sales commission to 15%. We’ve lost two of our best account managers in the last 9 months. It seems like we are behind the curve paying only 12% on gross sales.”

“What do you mean we are behind the curve,” Paul replied angrily. “We have always been the leader in every aspect of our business.”

“Well, that may have been the case in the past, Paul, but frankly we need to step up our compensation package to stay competitive,” Mary Jane replied. She continued, “And that’s not everything. I met with Frank Jacobs from marketing and he said we need to have a bigger presence at the trade show in March. He told me he would need about $650,000 added to the marketing budget to support new marketing materials.”

“Come on, Mary Jane, how can we do that when we are going to have to increase commission?” He continued, “I spoke with Dan Clark in production and he indicated that we have two pieces of equipment that need to be replaced by the end of the quarter and that’s going to set us back almost $1.2 million.”

Mary Jane shook her head. “Paul, I hate to bring this up but while we are talking costs, but Bob in purchasing stopped by the office and dropped off some revised cost information – it looks like several of our suppliers are talking about significant price increases by the end of the year.”

Paul slumped in his chair. “This is a mess, Mary Jane. Increasing commissions, new equipment, materials price increases and marketing expenses all at once. Even if Frank Mallow is correct that we should see a 10% increase in sales for the coming year, I just don’t see how we can make this work. We have to maintain enough profit to keep the shareholders happy and I can’t sleep when we dip below that $2 million margin of safety.”

Mary Jane gathered up her papers. “Before you get too distressed, let me put together some figures and let’s see what this looks like on paper. I’ll get back to you by the end of the week. In the meantime, stay positive, we’ll find the best solution.”

The following income and cost data for Mirabel is provided:

Mirabel Manufacturing

Budgeted Income Statement

For the Year Ending December 31

Sales

$ 36,750,000

Cost of goods sold:

Variable

$ 13,300,000

Fixed

$ 9,300,000

Gross Margin

$ 14,150,000

Selling & Administrative

Commissions

$ 4,410,000

Fixed Marketing Expenses

$ 1,350,000

Fixed Administrative

$ 6,000,000

Net Operating Income

$ 2,390,000

Model 101

Model 201

Model 301

Normal Annual Sales Volume

16,000

19,000

11,000

Unit Selling Price

$ 650

$ 750

$ 1,100

Variable expense per unit

$ 250

$ 200

$ 500

Questions

(Note: Each of the following questions is independent of the others)

1. What is Mirabel’s over-all break-even point in sales dollars?

2. Assume that sales revenue remains constant, what is the impact on break-even and the margin of safety if Paul takes Mary Jane’s advice and increases sales commission to 15%?

3. If Mirabel purchases the new equipment for $1,200,000, it will increase fixed costs by 10% but will decrease the variable cost per unit for all 3 models by 5%. What will Mirabel’s new break-even point be?

4. If Mirabel invests the additional $650,000 in fixed marketing expenses, sales of the Model 301 are expected to increase by 8%. What is the break-even and margin of safety under these circumstances?

5. If the projection is that sales will increase by 10% in the coming year, can the company afford to also increase commission from 12% to 15%? Why or why not.

6. Assume that sales volume remains fixed but there is a 5% increase in variable expenses (materials cost) for the Model 101 and 301, and a 10% increase in variable expenses for Model 201. What is the new break-even?

Report

Prepare a report from Mary Jane to Don explaining how these changes will affect Mirabel’s overall cost structure. For those changes that are controllable, make a recommendation considering the uncontrollable cost changes. Be certain to consider not only the company’s break-even point, but also the desired margin of safety.

Answer 1

ANSWER (1)  Mirabel’s over-all break-even point in sales dollars is as follows:-

Mirabel Manufacturing
Budgeted income Statement
For the Year Ending Sales $ 36,750,000
Cost of goods sold: Variable $ 13,300,000 ,Fixed 34 9,300,000
Gross Margin $ 14,150,000
Selling & Administrative Commissions $ 4,410,000, Fixed Marketing Expenses $ 1,350,000, Fixed Administrative $ 6,000,000
Net Operating Income $ 2,390,000

Model 101 ,Model 201 ,Model 301 ,Normal Annual Sales Volume ,16,000 19,000 11,000
UnitSelling Price $ 650, $ 750, $ 1,100 Variable expense per unit $ 250, $ 200, $ 500 .

1) Over-all break-even point in sales dollars=$31,516,184

2)  The Over-all break-even point in sales dollars will increase by $1,897,422 while Margin of safety will decrease by $1,897,422

3) New Over-all break-even point in sales dollars=$33,617,481

4)  The Over-all break-even point in sales dollars will increase by $1,273,808 while Margin of safety will decrease by $1,273,808.

Explanation:Mirabel’s over-all break-even point in sales dollars is as follows:-

Over-all break-even point in sales dollars=Total Fixed costs/(W.A.C.M.R)

W.A.C.M.R( Weighted average contribution margin ratio)= W1.C.M.R1 + W2.C.M.R2 + W3.C.M.R3

W1,W2, andW3-Weights of Models 101, 201 and 301

C.M.R(Contribution margin ratio)= (Selling price-Total Variable cost per unit)/ Selling price

Commission is Variable expense therefore should be added to the stated variable expenses per unit ($1,248,000 +$1,710,000 +$1,452,000=$4,410,000)

Model 101=$650 x 16,000 x12%=$1,248,000; Per unit=$1,248,000/16,000=$78

Model 201=$750 x 19,000 x12%=$1,710,000; Per unit=$1,710,000/19,000=$90

Model 301=$1,100 x 11,000 x12%=$1,452,000; Per unit=$1,452,000/11,000=$132

C.M.R1 (Contribution margin ratio of Model 101)= ($650-$328)/$650=0.50

C.M.R2 (Contribution margin ratio of Model 201)=($750-$290)/$700=0.61

C.M.R3 (Contribution margin ratio of Model 301)=($1,100-$632)/$1,100=0.43

Weight of Model 101=16,000/46,000=0.35

Weight of Model 201=19,000/46,000=0.41

Weight of Model 301=11,000/46,000=0.24

(Total weights=16,000 +19,000 +11,000=46,000)

W.A.C.M.R( Weighted average contribution margin ratio)=(0.50 x0.35) + (0.61 x0.41) + (0.43 x0.24)

W.A.C.M.R( Weighted average contribution margin ratio)=0.175 +0.2501 +0.1032

W.A.C.M.R( Weighted average contribution margin ratio)=0.5283

Total Fixed costs=$9,300,000 +$1,350,000+$6,000,000=$16,650,000

Over-all break-even point in sales dollars=$16,650,000/0.5283

Over-all break-even point in sales dollars=$31,516,184.

ANSWER (2) the impact on break-even and the margin of safety if Paul takes Mary Jane’s advice and increases sales commission to 15% are as follows :-

Sales commission:

Model 101=$650 x 16,000 x15%=$1,560,000; Per unit=$1,560,000/16,000=$97.50

Model 201=$750 x 19,000 x15%=$2,137,500; Per unit=$2,137,500/19,000=$112.50

Model 301=$1,100 x 11,000 x15%=$1,815,000; Per unit=$1,815,000/11,000=$165

Total variable cost per unit for each model;

Model 101=$250 +$97.50=$347.5

Model 201=$200 +$112.50=$312.5

Model 301=$500 +$165=$665

C.M.R1 (Contribution margin ratio of Model 101)= ($650-$347.5)/$650=0.47

C.M.R2 (Contribution margin ratio of Model 201)=($750-$312.5)/$700=0.58

C.M.R3 (Contribution margin ratio of Model 301)=($1,100-$665)/$1,100=0.40

W.A.C.M.R( Weighted average contribution margin ratio)=(0.47 x0.35) + (0.58 x0.41) + (0.40 x0.24)

W.A.C.M.R( Weighted average contribution margin ratio)=0.1645 +0.2378 + 0.096

W.A.C.M.R( Weighted average contribution margin ratio)=0.4983

Over-all break-even point in sales dollars=$16,650,000/0.4983

Over-all break-even point in sales dollars=$33,413,606

The Over-all break-even point in sales dollars will increase by $1,897,422 ($33,413,606-$31,516,184)

Margin of safety before increase in Commission= $36,750,000-$31,516,184=$5,233,816

Margin of safety after increase in Commission= =$36,750,000-$33,413,606=$3,336,394

Margin of safety will decrease by $1,897,422 ($5,233,816-$3,336,394).

ANSWER (3) Mirabel’s new break-even point be as follows :-

Changes in Variable cost per unit( Decrease; 1-5%=95%

Model 101=$250 x 16,000 x95%=$3,800,000; Per unit=$3,800,000/16,000=$237.5

Model 201=$200 x 19,000 x95%=$3,610,000; Per unit=$3,610,000/19,000=$190

Model 301=$500 x 11,000 x95%=$5,225,000; Per unit=$5,225,000/11,000=$475

Model 101=$237.5 +$78=$315.5

Model 201=$190 +$90=$280

Model 301=$475 +$132=$607

C.M.R1 (Contribution margin ratio of Model 101)= ($650-$315.5)/$650=0.51

C.M.R2 (Contribution margin ratio of Model 201)=($750-$280)/$700=0.63

C.M.R3 (Contribution margin ratio of Model 301)=($1,100-$607)/$1,100=0.45

W.A.C.M.R( Weighted average contribution margin ratio)=(0.51 x0.35) + (0.63 x0.41) + (0.45 x0.24)

W.A.C.M.R( Weighted average contribution margin ratio)=0.1785 + 0.2583 + 0.108

W.A.C.M.R( Weighted average contribution margin ratio)=0.5448

Changes in Total Fixed costs=$16,650,000 x 110%=$18,315,000

New Over-all break-even point in sales dollars=$18,315,000/0.5448

New Over-all break-even point in sales dollars=$33,617,481.

ANSWER (4)  If Mirabel invests the additional $650,000 in fixed marketing expenses, sales of the Model 301 are expected to increase by 8% than the break-even and margin of safety under these circumstances are as follows :-

Changes in sales for Model 301; Increase in sales 100% + 8%=108%

Model 301=11,000 x 108%=11,880 units

Weight of Model 101=16,000/46,880=0.34

Weight of Model 201=19,000/46,880=0.41

Weight of Model 301=11,880/46,880=0.25

Commission; (Variable cost)

Model 101=$650 x 16,000 x12%=$1,248,000; Per unit=$1,248,000/16,000=$78

Model 201=$750 x 19,000 x12%=$1,710,000; Per unit=$1,710,000/19,000=$90

Model 301=$1,100 x 11,880 x12%=$1,568,160; Per unit=$1,568,160/11,880=$132

Model 101=$250 +$78=$328

Model 201=$200 +$90=$290

Model 301=$500 +$132=$632

C.M.R1 (Contribution margin ratio of Model 101)= ($650-$328)/$650=0.50

C.M.R2 (Contribution margin ratio of Model 201)=($750-$290)/$700=0.61

C.M.R3 (Contribution margin ratio of Model 301)=($1,100-$632)/$1,100=0.43

W.A.C.M.R( Weighted average contribution margin ratio)=(0.50 x0.34) + (0.61 x0.41) + (0.43 x0.25)

W.A.C.M.R( Weighted average contribution margin ratio)=0.17+0.2501 + 0.1075

W.A.C.M.R( Weighted average contribution margin ratio)=0.5276

Changes in Total fixed costs

Total Fixed costs=$9,300,000 +$1,350,000+$6,000,000 +$650,000=$17,300,000

New Over-all break-even point in sales dollars=$17,300,000/0.5276

New Over-all break-even point in sales dollars=$32,789,992

The Over-all break-even point in sales dollars will increase by $1,273,808 ($32,789,992-$31,516,184)

Margin of safety before fixed marketing expenses= $36,750,000-$31,516,184=$5,233,816

Margin of safety after increase in Commission= $36,750,000-$32,789,992=$3,960,008

Margin of safety will decrease by $1,273,808 ($5,233,816-$3,960,008).

ANSWER (5)  If the projection is that sales will increase by 10% in the coming year, can the company afford to also increase commission from 12% to 15% are  because it will result in an increase in the net income by $2,021,250($4,411,250 -$2,390,000)

Explanation:

Mirabel Manufacturing

Budgeted Income statement

For the year ended December 31

Sales($36,750,000 x 110%)-----------------------------------$40,425,000

Cost of Goods sold:

Variable------------------------------------------$13,300,000

Fixed Cost---------------------------------------$9,300,000

Cost of goods sold----------------------------------------------($22,600,000)

Gross profit--------------------------------------------------------$17,825,000

Selling & Administrative

Commission (15% x $40,425,000)----------$6,063,750

Fixed Marketing expenses--------------------$1,350,000

Fixed administrative----------------------------$6,000,000

Total Selling & Administrative expenses---------------------($13,413,750)

Net Income---------------------------------------------------------$4,411,250

ANSWER (6)  that sales volume remains fixed but there is a 5% increase in variable expenses (materials cost) for the Model 101 and 301, and a 10% increase in variable expenses for Model 201 than the new break-even are as follows:-

New Over-all break-even point in sales dollars=Total Fixed costs/(W.A.C.M.R)

W.A.C.M.R( Weighted average contribution margin ratio)= W1.C.M.R1 + W2.C.M.R2 + W3.C.M.R3

W1,W2, andW3-Weights of Models 101, 201 and 301

C.M.R(Contribution margin ratio)= (Selling price-Total Variable cost per unit)/ Selling price

Changes in Variable expenses per unit( Decrease; 100% + 5%=105%

Model 101=$250 x 105%=$262.50

Model 201=$200 x 105%=$210

Model 301=$500 xx105%=$525

Commission per unit:

Model 101=$650 x12%=$78

Model 201=$750 x12%=$90

Model 301=$1,100 x12%=$132

Total variable cost per unit:

Model 101=$262.50 +$78=$340.5

Model 201=$210 + $90=$300

Model 301=$525 + $132=$657

C.M.R1 (Contribution margin ratio of Model 101)= ($650-$340.5)/$650=0.48

C.M.R2 (Contribution margin ratio of Model 201)=($750-$300)/$700=0.60

C.M.R3 (Contribution margin ratio of Model 301)=($1,100-$657)/$1,100=0.40

Weight of Model 101=16,000/46,000=0.35

Weight of Model 201=19,000/46,000=0.41

Weight of Model 301=11,000/46,000=0.24

(Total weights=16,000 +19,000 +11,000=46,000)

W.A.C.M.R( Weighted average contribution margin ratio)=(0.48 x0.35) + (0.60 x0.41) + (0.40 x0.24)

W.A.C.M.R( Weighted average contribution margin ratio)=0.168 + 0.246 + 0.096

W.A.C.M.R( Weighted average contribution margin ratio)=0.51

Total Fixed costs=$9,300,000 +$1,350,000+$6,000,000=$16,650,000

New break-even point in sales dollars=$16,650,000/0.51

New break-even point in sales dollars=$32,647,059.