Breakeven Analysis

1
Breakeven Analysis

• Class 19.2 Using Tolerances and Statistics

2
Learning Objectives

• Be able to draw a break-even graph, ignoring the
  time value of money
• Calculate the effective cost of manufacturing a
  part

3
Readiness Assessment Test 19.2.1

• Individually respond to the following question.
  You will have 4 minutes.

4
Readiness Assessment Test 19.2.1

• Individually respond to the following question.
  You will have 4 minutes.
• If a part is toleranced such that it must be
  between 1.000 and 1.020 inches and the process
  has a standard deviation of 0.005 inches and an
  average of 1.010 inches, how many parts would be
  rejected from a batch of 1000?

5
RAT Soln 19.2.1

• Xmin 1.000 in
• Xmax 1.020 in
• s 0.005 in
• m 1.010 inches
• zmin (1.000-1.010)/0.005 -2.0
• zmax (1.020-1.010)/0.005 2.0
• Aacceptable 0.4772 0.4772 0.9544
• Aunacceptable 1- 0.9544 0.0456
• Reject 0.0456 1000 45.6 46

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Break-even Graphs

• Break-even graphs are a graphics method to
  represent profit or loss and show the number of
  units which must be manufactured and sold to
  recover the initial investment.

7
Starting a Business

• Your team has decided that you all want to begin
  your own business on the side manufacturing
  pressure valves.
• As a team spend 3 minutes discussing what costs
  you will have if you plan on mass producing
  (maybe 100,000) these pressure valves.

8
Possible Costs

• Startup
• Initial building and land
• Equipment
• Engineering Design Cost
• Material
• Labor
• Shipping
• Others??

9
Putting Some Numbers to These

• Startup
• Initial building and land (50,000)
• Equipment (30,000)
• Engineering Design (20,000)
• Material (5.00 per valve)
• Labor (20.00 per valve)
• Shipping (5.00 per valve)
• Others??

10
Plotting Expense

• Generate a graph which shows your capital outlay
  as a function of number of pressure valves
  PRODUCED. Plot this on the range of 0 to 10,000
  valves.
• Cost 30NOV 100,000

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Expense Graph
Expense to Produce Valves
500,000
400,000
300,000
Cost ()
200,000
100,000
0
0
2000
4000
6000
8000
10000
12000
Number of Valves PRODUCED
12
Income

• If pressure valves can be sold for 50.00, draw a
  graph which indicated your income as a function
  of number of valves SOLD.
• Income 50NOV

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Income Graph
Income
500,000
400,000
300,000
Income ()
200,000
100,000
0
0
2000
4000
6000
8000
10000
12000
Number of Valves SOLD
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Generating the Breakeven Graph

• Combine these two graphs to obtain a break-even
  graph.
• How many pressure valves should be PRODUCED AND
  SOLD to break-even?
• Cost Income
• 30NOV 100,000 50NOV
• NOV 5000

15
Generating the Breakeven Graph

• What is the profit if you produce and sell 7,000
  pressure valves?
• Profit Income - Cost
• Profit 50(7,000)-30(7,000)100,000
• Profit 40,000

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Break-even Graph
Breakeven Graph for Valve Production
600,000
500,000
400,000
profit
Worth ()
300,000
200,000
100,000
0
0
2000
4000
6000
8000
10000
12000
Number of Valves PRODUCED AND SOLD
17
Looking deeper

• As a team, spend 5 minutes discussing the
  problems and limitations of this approach.
• Generate a list of the concerns you all have
  about this analysis.

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Possible Problems

• Not all parts produced will meet Quality
  guidelines and so they must be rejected
• Not all parts that meet quality guidelines are
  sold immediately, some stay in stock.

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Accounting for Inventory

• How could you modify your break-even graph to
  account for an inventory of 1000 pressure valves?
• Number of Valves SOLD Number of Valves PRODUCED
  Number of Valves in Inventory
• NS NP - Inventory
• THUS
• Income 50(NP 1000)
• Income 50NP - 50,000
• where NP number of valves PRODUCED
• NS number of valves SOLD

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Modified Graph
Breakeven Graph for Valve Production
500,000
450,000
400,000
350,000
300,000
Worth ()
250,000
200,000
150,000
100,000
50,000
0
0
2000
4000
6000
8000
10000
12000
Number of Valves PRODUCED, NP
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Accounting for Rejects

• For a rejected part you
• Lose the cost of labor
• May lose the cost of materials
• You can find the effective cost of manufacturing,
  if you know the fraction of parts which will be
  rejected

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Example

• As a team spend 5 minutes to find the cost of
  manufacturing 1000 sellable pressure valves
• Assume the limiting feature is a diameter 0.5000
  inch hole which must have an RC6 tolerance.
• The standard deviation of the machinist will be
  0.0005 inches.

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Solution

• Find the actual limits on the size of the hole.
  For an RC6 diameter 0.5 hole the limits are
  0.5000-0.5016.
• Assume a theoretical size in the middle of that
  range, thus a size of 0.5008 would be the
  expected average size.
• Calculate the rejection fraction using the
  standard deviation given.

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Solution (cont.)

• Find the z value associated with the limits on
  the hole.
• Z (0.5016-0.5008)/0.0005 1.6
• Z- (0.5000-0.5008)/0.0005 -1.6
• From the z table find the percentage rejection
  for a z of 1.6
• Acceptable fraction is 2(0.4452) 0.8904
• Rejection is therefore 0.1096

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Solution (cont.)

• Find the number which must be manufactured to
  yield 1 sellable values
• X 0.8904 1 ? X1.123
• Total cost is therefore
• (assuming material from rejected parts is
  completely recyclable)
• ShippingMaterialsLabor
• 5.001.000 5.001.000 20.001.123 32.46
  (per valve)

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Update graph

• Update your graph and re-answer the following
  questions
• How many ACCEPTABLE pressure valves should be
  PRODUCED to break-even?
• Cost 32.46NAP100,000
• Income 50NAP-50,000
• Break-even IncomeCost
• NAP 8,552 (number of ACCEPTABLE VALVES
  PRODUCED)
• NAS 8552 1000 7,552 (number of ACCEPTABLE
  VALVES THAT MUST BE SOLD)

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Update graph

• What is the profit if you SOLD 6,000 acceptable
  valves?
• NAP NS Inventory
• NAP 6,000 1000 7000
• (the number of acceptable valves PRODUCED)
• Profit Income-Cost
• Profit 50(7,000)-50,000 - 32.46(7,000)100,000
  
• Profit -27,220

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Updated Graph
Breakeven Graph for Valve Production
Number of Acceptable Valves SOLD, NAS
1000
3000
5000
7000
9000
11000
-1000
500,000
450,000
400,000
350,000
300,000
Worth ()
250,000
200,000
150,000
100,000
50,000
0
0
2000
4000
6000
8000
10000
12000
Number of Acceptable Valves PRODUCED, NAP
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In-class TEAM Assignment

• The machinist who was hired at 20.00 per hour
  makes parts which are normally distributed in
  size with a standard deviation of .001 inches.
• If your part requires an RC8 tolerance on a
  diameter 1 hole and requires one hour to
  manufacture, what is the effective cost of a
  part?
• Draw a break-even graph for this case.
• Use the basic data shown on the next slide.

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Basic Data

• Startup Costs are 125,000
• Shipping is 10.00 per part
• Materials 5.00 per part, fully recoverable for a
  bad part
• Sales price is 60.00 per part
• Inventory on hand required to be 250 units

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Solution

• Find the actual limits on the size of the hole.
  For an RC8 diameter 1.0 hole the limits are
  1.0000 to 1.0035.
• Assume a theoretical size in the middle of that
  range, thus a size of 1.00175 would be the
  expected average size.
• Calculate the rejection fraction using the
  standard deviation given.

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Solution (cont.)

• Find the z value associated with the limits on
  the hole.
• Z (1.0035-1.00175)/0.001 1.75
• Z- (1.0000-1.00175)/0.001 -1.75
• From the z table find the percentage rejection
  for a z of 1.75
• Acceptable fraction is 2(0.4599) 0.9198
• Rejection is therefore 0.0802

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Solution (cont.)

• Find the number which must be manufactured to
  yield 1 sellable values
• X 0.9198 1 ? X1.0872
• Total cost is therefore
• (assuming material from rejected parts is
  completely recyclable)
• ShippingMaterialsLabor
• 10.001.000 5.001.000 20.001.0872
  36.74 (per valve)

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Solution (cont.)

• Cost 36.74NAP 125,000
• Income 60NAP - 15,000
• Break-even
• Cost Income
• NAP 6,019 (number of acceptable parts PRODUCED)
• NAS 6019 250 5,769 (number of acceptable
  parts that must be SOLD)

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Alternate Solution Solve in terms of NAS

• Cost 36.74NAS 125,000 250(36.74)
• Income 60NAS
• Break-even
• Cost Income
• NAS 5,769 (number of acceptable parts SOLD)
• NAP 5,769 250 6,019 (number of acceptable
  parts that must be PRODUCED)
• SAME AS BEFORE!!!!

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Further Refinements

• Inventory are never shipped so that the cost of
  shipping for these items should not be included
  in the analysis.
• On the previous slide, the effective cost of the
  inventory parts is 36.74 - 10.00 26.74.
• See refined solution on next slide.

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Refined Solution

• Cost 36.74NAS 125,000 250(26.74)
• Income 60NAS
• Break-even
• Cost Income
• NAS 5,662 (number of acceptable parts SOLD)
• NAP 5,662 250 5,912 (number of acceptable
  parts that must be PRODUCED)
• Could also work in terms of NAP (next slide).

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Refined Solution

• Cost 36.74NAP 125,000 - 250(10.00)
• Income 60NAP 15,000
• Break-even
• Cost Income
• NAP 5,912 (number of acceptable parts PRODUCED)
• NAS 5,912 - 250 5,662 (number of acceptable
  parts that must be SOLD)
• SAME AS BEFORE!!!

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Updated Graph
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Other Considerations

• How would this problem change if none of the
  material costs for the rejected valves could be
  recovered?
• How would this problem change if there was a
  1.00 fee to recycle the material for rejected
  valves?

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Assignment 6Due Team Assignment

• Evaluate the following situations and write a
  memo to your supervisor (Ms. Jamison) with your
  recommendations and reasons.
• Clearly state which options you would recommend
  the company to use and why.
• Include the effective cost of all six options.
• Work problem in terms of parts SOLD.

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Assignment 6 (cont.)

• Rather than hiring a machinist, you could hire a
  Master Machinist at 30.00 per hour (i.e. Widget)
  her standard deviation is only .0005 inches
• You could hire an apprentice for only 12.50 an
  hour with a standard deviation of .003 inches
• By spending an additional 50,000 you can
  purchase better equipment which will reduce all
  standard deviations by 25.

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Assignment 6 (cont.)
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Assignment 7Due Individual Assignment

• Prepare 1 page (12pt. Font, 1.5 line spacing )
  for EACH industry presentation you attended on
  February 6th.
• (See web page for exact time and location for
  each company)