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Breakeven

Analysis

PS Homework 6 and 7

Due: Feb. 13, 2003

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In-class TEAM

Assignments The machinist who was hired at $20.00

per hour makes parts which are normallydistributed in size with a standard

deviation of .001 inches.s If your part requires an RC8 tolerance on

a diameter 1 hole and requires one hourto manufacture, what is the effective costof a part?

s Draw a break-even graph for this case.s Use the basic data shown on the next

slide.

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Basic Data

s Startup Costs are $125,000s Shipping is $10.00 per parts Materials $5.00 per part, fully

recoverable for a bad parts Sales price is $60.00 per parts

Inventory on hand required to be250 units

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Solution

s Find the actual limits on the size ofthe hole. For an RC8 diameter1.0 hole the limits are 1.0000 to1.0035.

s Assume a theoretical size in themiddle of that range, thus a size of1.00175 would be the expectedaverage size.

s Calculate the rejection fractionusing the standard deviation given.

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Solution (cont.)

s Find the z value associated with thelimits on the hole.x

Z+ = (1.0035-1.00175)/0.001 = 1.75x Z- = (1.0000-1.00175)/0.001 = -1.75s From the z table find the percentage

rejection for a z of 1.75

xAcceptable fraction is 2*(0.4599) =0.9198

x Rejection is therefore 0.0802

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Solution (cont.)

s Find the number which must bemanufactured to yield 1 sellable valuesx X * 0.9198 = 1X=1.0872

s Total cost is therefore:

(assuming material from rejected parts iscompletely recyclable)

x Shipping+Materials+Labor=

x $10.00*1.000 + $5.00*1.000 +$20.00*1.0872= $36.74 (per valve)

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Solution (cont.)

s Cost = 36.74*NAP + 125,000s Income = 60*NAP - 15,000

s Break-even:x Cost = Income

x NAP = 6,019 (number of acceptable parts

PRODUCED)x NAS = 6019 250 = 5,769 (number of

acceptable parts that must be SOLD)

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SolutionSolve in terms of

NASs Cost = 36.74*NAS + 125,000 + 250(36.74)s Income = 60*NASs

Break-even:x Cost = Income

x NAS = 5,769 (number of acceptable partsSOLD)

x NAP = 5,769 + 250 = 6,019 (number ofacceptable parts that must be PRODUCED)

s SAME AS BEFORE!!!!

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Further

Refinementss Inventory are never shipped so

that the cost of shipping for these

items should not be included in theanalysis.s On the previous slide, the effective

cost of the inventory parts is

$36.74 - $10.00 = $26.74.s See refined solution on next slide.

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Refined Solution

s Cost = 36.74*NAS + 125,000 + 250(26.74)s Income = 60*NASs

Break-even:x Cost = Income

x NAS = 5,662 (number of acceptable partsSOLD)

x NAP = 5,662 + 250 = 5,912 (number ofacceptable parts that must be PRODUCED)

Could also work in terms of NAP (next slide).

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Refined Solution

s Cost = 36.74*NAP + 125,000 - 250(10.00)s Income = 60*NAP 15,000s

Break-even:x Cost = Income

x NAP = 5,912 (number of acceptable partsPRODUCED)

x NAS = 5,912 - 250 = 5,662 (number ofacceptable parts that must be SOLD)

SAME AS BEFORE!!!

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Updated Graph

Breakeven Graph for Valve Production

$0.00

$50,000.00

$100,000.00

$150,000.00

$200,000.00

$250,000.00

$300,000.00

$350,000.00

$400,000.00

$450,000.00

0 1000 2000 3000 4000 5000 6000 7000 8000Number of Acceptable Valves PRODUCED, NAP

Worth($)

Cost

Income

750 27501750-250 77506750575047503750

Number of Acceptable Valves SOLD, NAS

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Assignment #6Due:02/13/2003

Team Assignments Evaluate the following situations and write

a memo to your supervisor (Ms. Jamison)with your recommendations and reasons.

s Clearly state which options you wouldrecommend the company to use and why.

s Include the effective cost of all six options.s Work problem in terms of parts SOLD.

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Assignment #6

(cont.)s Rather than hiring a machinist, you could

hire a Master Machinist at $30.00 perhour (i.e. Widget) her standard deviation

is only .0005 inchess You could hire an apprentice for only

$12.50 an hour with a standard deviationof .003 inches

s By spending an additional $50,000 youcan purchase better equipment which willreduce all standard deviations by 25%.

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Assignment #6(cont.)

Worker Std. Dev.without new

equip.

Std. Dev. withnew equip.

Apprentice .003 .00225

Machinist .001 .00075

MasterMachinist

.0005 .000375

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Assignment #7Due:

IndividualAssignmentsPrepare 1 page (12pt. Font, 1.5 linespacing ) for EACH industry presentation

you attended on February 6th

.(See web page for exact time andlocation for each company)