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BEP :A REFRESHER AS EVERYONE SEES IT
Given overleaf is a recap note on Break Even Point analysis, as relevant to Service
Operations Management.
As I am sure, you would have already dealt with this topic as part of other subjects.
Hence go through this recap to avoid duplication prior to class.
We will discuss only specific issues of relevance to us service operations professionals.
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Recap notes on break even point concept as relevant to Operations Management
Different ways of classifying cost:
Costs involved in the a manufacturing or service process can be classified invarious
ways: For example as:
o Fixed costs and variable costs
o Direct costs and indirect costs
o Average costs and marginal costs
o Standard costs
Fixed and Variable cost
Fixed costsdo not change when production is higher or lower.
Examples of fixed costs:
Lighting, heating and power of factory
Wages and salaries of workers
Rent of building
Insurance on vehicles or fire insurance
Variable costschange in direct relation to the level of production.
Examples of variable costs:
More raw materials will be used when production levels increase.
You might need to employ more workers, and hence more wages when
production level is increased.
Increased production can also lead to workers having to work overtime.
Direct & Indirect Cost
Direct costscan be directly linked with the product that is produced. Example :The raw
material used for a product is a direct cost.
Indirect costsare not directly linked to the product or the production process. Example :
rent of the factory, administration cost of the business, the wages and salaries of the
administration staff.
Average Cost & Marginal Cost
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Average cost of producing an articleis found by dividing the total number of units
manufactured by total cost. If production levels increase, the unit cost of an article will
decrease. This is because the fixed cost stays the same although the variable costs
increase in direct relation to the increased production.
Marginal costis the cost of making one product. It is calculated by looking at the
difference in total costs if one extra item is produced.
Example:
o To produce 50 chairs costs $2000.
o If 51 chairs are produced the total cost will increase to $2020.
o Average Cost:
The averagecost of one chair if 50chairs are produced: $2000 / 50 =
$40.
The averagecost of one chair if 51chairs are made: $2020 / 51 = $39.6.
o Note: Production costs can go down when more units are produced, because the
fixed costs stay the same only variable might be incurred.
Marginal Cost
The marginal cost to make an extra chair is $20.
The average cost of making 51 chairs is $39.6. The average cost per
chair decreases because the fixed costs stay the same.
o Another Example
o In a Photocopy shop
Output in
pages
photocopied
Fixed costs
in $ [ rental for
place and
machine]
Total Variable
costs $ ( of
manpower and
consumable)
Total cost
incurred $
0
1,000
2,000
1,500
1,500
1,500
0
500
1,000
1,500
2,000
2,500
When 1,000 units are produced the unit cost is $2 Total cost/number of units
When 2,000 units are produced the unit cost decreases to $1.25 2,500/2,000.From
the example you can see that when more units are produced the cost of producing one
unit decreases.
BEP AS WE KNOW
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A business reaches the break-even point in production when the total sales value equals the total
cost incurred to produce the item. At this point no profit or loss is made
Example of working out the break-even point
Consider a haircutting saloon. The fixed cost of a business is $10,000 and the variable
cost of each persons hair cut unit is $8. The firm charges $12 per p
Calculate the break-even point:
Number of
customers
Fixed
costs $
Variable
costs $
Total
costs $
Revenue @
$12 per unit
Profit/
(Loss) $
0
1,0002,000
2,500
3,000
10,000
10,00010,000
10,000
10,000
0
8,00016,000
20,000
24,000
10000
18,00026,000
30,000
34,000
.0
12,00024,000
30,000
36,000
(10,000)
(6,000)(2,000)
Break even
2,000
Any unit produced over 2,500 will result in a profit
One formula to calculate the break-even point
Fixed cost-------------------------------------------------------
selling price per unit less variable cost per unit
= 10,000 / (12 - 8) = 10,000 / 4 = 2,500 units
BEP CHART:
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When we put this on a graph we need to look at:
Sales Revenue -this is plotted against units sold. [The higher the price the steeper the
gradient line. The lower the price the less steep is the gradient line.] This is the line marked
sales revenue in the diagram below.
Fixed Cost line -Before commencing production a firm must buy what are known as its
FIXED ASSETS. As such they have to be paid for regardless of output. Let's say that in our
example the fixed costs are $10,000 whether we fully produce or make a complete zero
amount of whatever it is we are producing. We can see in the diagram below that the fixed
costs line is horizontal.
Variable Cost line:Next we need to look at our variable costs, which do vary with changes
in output. Therefore the line on the diagram is upward-sloping. At zero production we will not
incur any variable costs but as we expand production for each successive unit made we incur
additional cost of say 3$.
Total Cost line: When we add the fixed costs to the variable costs we get total costs line.
With fixed costs needing to be paid for regardless of sales, we can predict that in most
companies low levels of sales will not result in profits.
However, as sales increase so the fixed costs are being spread over a larger output and will
reduce per unit sold. To put this in more technical language the average fixed cost will start to
fall. So, if for example output is 100 units, fixed costs are $100 per unit produced, then if
output rises to 2000 units the average fixed cost will be $5 per unit produced.
The output required to break even is 2000 units (as marked break-even on the diagramabove), at which level the total sales revenue and costs equate at $16000.
It is always sensible to leave some room for change and so we introduce the concept of
margin of safety. This is the difference between the actual output and the break-even output.
So, if this company couldroduce 3000 items its margin of safety is 1000 units.
Mini caselet Dog Grooming & BEP: Linear
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After working for ten years as a dog groomer, youre thinking of starting your own dog grooming
business. You found a place you could rent thats right next to a popular shopping center, and two
of your friends (who are also dog groomers) have agreed to work for you. The problem is that you
need to borrow money to start the business and your banker has asked for a breakeven analysis.
You have prepared the following cost estimates for your first year of operations:
Fixed Costs
Salaries $105,000
Rent and utilities $36,000
Advertising $2,000
Equipment $3,000
Variable Cost per Dog
Shampoo $2.00
Coat conditioner $1.50
Pet cologne $0.75
Dog treats $1.25
Hair ribbons $0.50
You went online and researched grooming prices in your area. Based on your review, you
have decided to charge $32 for each grooming.
Q 1:o Whats the breakeven point in unitshow many dogs will you need to groom in
the first year to break even?
o If you and your two employees groomed dogs five days a week, seven hours a
day, fifty weeks a year, how many dogs would each of you need to groom
each day? Is this realistic given that it takes one hour to groom a dog?
Q 2:
o If you raised your grooming fee to $38, how many dogs would you need to
groom to break even?
o At this new price, how many dogs will each of you have to groom each day
(assuming working as in Q1.)? Q 3:
o Would you start this business? What price would you charge to groom a dog?
o How could you lower the breakeven point and make the business more
profitable?
BEP As an Operation manager see it
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Example situation- Non Linear cost / price Jeanie In 2008
Brian plans to start a tailoring shop wherein he will stitch Denim Jeans to customers
measurement. The business model he plans to follow is:
-
The customers will bring their own cloth and Jeanie the Tailors will stitch custom fit
pants.
He understands that the demand for their product Designer Jeans is strongly influenced
by the price. To assess the price at which he can offer his stitching services and hence
establish price to demand relationship Brian decides to conduct a !ar"et #esearch . He
surveys among $%%% visitors to a shopping mall by showing a sample stitched &eans how
much they are willing to pay for the stitching alone.
The research shows the following estimate of sales at different prices.
'T(T)H(*+ ,#() 'T(!TD /T0
11.2-13.2 4%%
13.2-51.2 32%
51.2-23.2 6%%
Brian has already fi7ed up a shop in Bugis.
He now estimates the costs he is li"ely to incur to include the following for the first few
months of operation:
a8
a fi7ed monthly rental of 9 62%%
b8
a counter staff with a fi7ed salary of 9 $2%%
c8
!onthly electricity etc. will be appro7imately 9 2%%
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d8
,art time tailors will be employed who will be paid 9 $1 for every pant they
cut and stitch
e8
The consumables for the pant- vi. ip ; button thread etc. would cost
appro7imately 9 6 per pant.
Brian wonders what price he should charge how much orders he should get per month
to brea" even and how much for a profit which he can ta"e home of 9 1%%% at least
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Price sales qty sale Rev fixed cost var cost TC profit
1.0 1475 1475 6500 23600 30100 -28625
2.0 1450 2900 6500 23200 29700 -26800
3.0 1426 4278 6500 22816 29316 -25038
4.0 1401 5604 6500 22416 28916 -23312
5.0 1377 6885 6500 22032 28532 -216476.0 1352 8112 6500 21632 28132 -20020
7.0 1327 9289 6500 21232 27732 -18443
8.0 1303 10424 6500 20848 27348 -16924
9.0 1278 11502 6500 20448 26948 -15446
10.0 1254 12540 6500 20064 26564 -14024
11.0 1229 13519 6500 19664 26164 -12645
12.0 1204 14448 6500 19264 25764 -11316
13.0 1180 15340 6500 18880 25380 -10040
14.0 1155 16170 6500 18480 24980 -8810
15.0 1131 16965 6500 18096 24596 -7631
16.0 1106 17696 6500 17696 24196 -6500
17.0 1081 18377 6500 17296 23796 -541918.0 1057 19026 6500 16912 23412 -4386
19.0 1032 19608 6500 16512 23012 -3404
20.0 1008 20160 6500 16128 22628 -2468
21.0 983 20643 6500 15728 22228 -1585
22.0 958 21076 6500 15328 21828 -752
23.0 934 21482 6500 14944 21444 38
24.0 909 21816 6500 14544 21044 772
25.0 885 22125 6500 14160 20660 1465
26.0 860 22360 6500 13760 20260 2100
27.0 835 22545 6500 13360 19860 2685
28.0 811 22708 6500 12976 19476 3232
29.0 786 22794 6500 12576 19076 3718
30.0 762 22860 6500 12192 18692 4168
31.0 737 22847 6500 11792 18292 4555
32.0 712 22784 6500 11392 17892 4892
33.0 688 22704 6500 11008 17508 5196
34.0 663 22542 6500 10608 17108 5434
35.0 639 22365 6500 10224 16724 5641
36.0 614 22104 6500 9824 16324 5780
37.0 589 21793 6500 9424 15924 5869
38.0 565 21470 6500 9040 15540 5930
39.0 540 21060 6500 8640 15140 5920
40.0 516 20640 6500 8256 14756 5884
41.0 491 20131 6500 7856 14356 5775
42.0 466 19572 6500 7456 13956 561643.0 442 19006 6500 7072 13572 5434
44.0 417 18348 6500 6672 13172 5176
45.0 393 17685 6500 6288 12788 4897
46.0 368 16928 6500 5888 12388 4540
47.0 343 16121 6500 5488 11988 4133
48.0 319 15312 6500 5104 11604 3708
49.0 294 14406 6500 4704 11204 3202
50.0 270 13500 6500 4320 10820 2680
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-35000
-30000
-25000
-20000
-15000
-10000
-5000
0
5000
10000
0.0 10.0 20.0 30.0 40.0 50.0 60.0
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-40000
-30000
-20000
-10000
0
10000
20000
30000
40000
0 200 400 600 800 1000 1200 1400 1600
sale Rev
fixed cost
var cost
TC
profit
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The vertical axis of this logarithmic graph is the real unit cost of adding value, adjusted
for inflation. It includes the cost that the firm incurs to add value to the starting materials,
but excludes the cost of those materials themselves, which are subject the experience
curves of their suppliers.
Note that the experience curve differs from the learning curve. The learning curve
describes the observed reduction in the number of required direct labor hours as
workers learn their jobs. The experience curve by contrast applies not only to labor
intensive situations, but also to process oriented ones.
The experience curve, like the half-life, is also an empirical observation. It states that for
each doubling of cumulative experience (total units produced from the very beginning,
not just this year), real unit cost drops by a constant percent, for example 20%. If your
first million units cost $10 each, then your next million units should cost $8 each, the
next two million units, $6.40, the next four million units, $5.12, etc. Because cost is
driven by cumulative units produced (1+1+2+4 million in our example), the rate of
decline of cost drops over time unless unit volume grows at a sufficiently high
exponential rate.
Research has shown that as the cumulative number of units of a product rises
(cumulative means the total number of units produced since the business was formed,)
the cost of producing a unit drops at a predictable rate. For example, as shown in Figure
1, every time production doubles (from 1X to 2X and from 2X to 4X), the cost of making
a unit drops by 40 percent (C1 to C2 and from C2 to C4).
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Figure 1: 40 Percent Experience Curve
To provide a numeric example, with a 40 percent experience curve the cost per unit
declines from $20.00 per unit at 10,000 units of cumulative production to $12.00 ($20 x
40% = $8, $20 - $8 = $12) at a cumulative production of 20,000 units (2 x 10,000 units.)
As can be observed, the experience curve concept is more applicable to some productsthan to others, and the rate of reduction varies greatly depending on the product and the
business.
The experience curve concept is not the same as Economies of Size. Economies of
size involve spreading a fixed amount of cost (e.g. facility cost, administration cost, etc.)
over an increasing number of units of production. Conversely, the experience curve
involves improving skills expertise, and finding new ways of doing things. Also, the
experience curve analysis is based on the number of units produced since the business
was started. Economies of size is based on the number of units produced during a
production period such as a calendar year.
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The experience curve relationship holds over a wide range industries. In fact, its
absence would be considered by some to be a sign of possible mismanagement. Cases
in which the experience curve is not observed sometimes involve the withholding of
capital investment, for example, to increase short-term ROI. The experience curve can
be explained by a combination of learning (the learning curve), specialization, scale, and
investment.
Implications for Strategy
The experience curve has important strategic implications. If a firm is able to gain market
share over its competitors, it can develop a cost advantage. Penetration pricing
strategies and a significant investment in advertising, sales personnel, production
capacity, etc. can be justified to increase market share and gain a competitive
advantage.
When evaluating strategies based on the experience curve, a firm must consider the
reaction of competitors who also understand the concept. Some potential pitfalls include:
The fallacy of composition holds: if all other firms equally pursue the strategy,
then none will increase market share and will suffer losses from over-capacity
and low prices. The more competitors that pursue the strategy, the higher the
cost of gaining a given market share and the lower the return on investment. Competing firms may be able to discover the leading firm's proprietary methods
and replicate the cost reductions without having made the large investment to
gain experience.
New technologies may create a new experience curve. Entrants building new
plants may be able to take advantage of the latest technologies that offer a cost
advantage over the older plants of the leadingfirm.
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Based on the principle:More we do a job quicker we do it
Noticed in 1930-40s during World War
Shortage of manufacturing capacity
Record of manufacturing time showed interestingtrend
Same concept honed later on y !"# in
19$0s as %&perience "ur'e(
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)t the start of production runs* Wor+ers are unfamiliar with their tas+s
,ime it ta+es to produce the first few units is high)s the wor+ers learn their tas+s* ,heir output per day increases up to a point
,hen their output le'els off to a rather constantrate
As the quantity doubled the
time required for the piece wasimpacted by the learning rate
factor
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Most aircraft manufacturing tasks experience an!" learning rate#
$f the production quantity doubles % labor&hoursrequired to assemble an aircraft is !# times originaltime#
$f 'st aircraft assembled requires '!!!! labor&hours
(nd aircraft would require !!! labor&hours
)th
aircraft would require *)!! labor&hours th aircraft would require +'(! labor&hours, and so on
10 20 30 40 50 60 70 80 90 100 110 120 130
20
80
40
100
60
Unit Number (n)
120
Labor-Hours for nth
UnitAircraft Assembly
80% Learning
Curve
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!y analying wor+ers learning situations. weare ale to estimate*
,he exact labor&hours re/uired to produce thenth unit of a production run
,he total labor&hours re/uired to produce Nunits in a production run
,he a-erage labor&hours re/uired per unit for N
units in a production run
.earning /ur-e 0 1stimating learning rate% achine Shop has a contract to manufacture 100 turines(
,he first 20 turines ha'e een completed( ,he laor-hoursre/uired for a portion of the completed turines are listed elow(se this data to estimate the shops learning rate in manufacturingthe turines(
2nit 3o# .abor&4ours 2nit 3o# .abor&4ours1 140 9
2 115 10 51
3 109 1 6
4 102 20 $5
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7earning "ur'e - )rithmetic )nalysis
"ompute the learning rate for each of the 8doules(
nits 1 and 2 115:140 ; (5429nits 2 and 4 102:115 ; (5$44nits and 10 51:9 ; (52$nits 10 and 20 $5:51 ; (539
:4 ; (5499
,he appro&imate learning rate is 5?(
,hree approaches to learning-cur'e prolems
are*
)rithmetic analysis
7ogarithmic analysis
7earning cur'e tales
%&cel calculations
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Arithmetic Analysis ,he simplest approach to learning-cur'e
prolems @f we wish to find the laor-hours re/uired to
produce nth unit. and nAust happens to e anumer that is one of the douled 'alues.then this approach wor+s(
Bor e&le if 20th
unit ta+es $5 hours . 40th
unit will ta+e (5 & $5 hours(
) tale of learning cur'e coefficients allows usto compute*
,he laor-hours for the nth unit in a
production run ,he total laor-hours for the entire
production run. where the nth unit is the lastunit in the run
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,he manager of % achine Shop wants a goodestimate of the total laor-hours re/uired tomanufacture the entire 100 turines(
)lso. he is curious aout how many laor-hourswill e needed for the last unit(
se the oser'ed 5? learning rate and 140laor-hours re/uired for the first turine tocompute your estimates(
,otal time for 100 units*
,otal 7aor-Cours Re/uired for 100 nits;
@n ,ale locate the line for the 100th unit and read across tothe ,otal ,ime column under the 5? learning rate( ,he
'alue is 43(6(
,otal 7aor-Cours Re/uired for 100 nits; 140 ; $.12 laor-hours
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7ogarithmic )nalysis"ompute. using logarithmic analysis. the laor-hours
re/uired for the 0th turine (
; log :log ; - 0(2344$23
,0 ; 140
; (399$23 or (400E140; $
Selecting a learning rate
@ndustry Aournals
Cistorical e&perience
ses and limitations
Froducts and ser'ices tend to e custom designed
!atches tend to e small Froduct:ser'ices tend to e comple&(((( learning
occurs /uic+ly
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Learning curve: 80%
0.000
10.000
20.000
30.000
40.000
50.000
60.000
0 100 200 300 400 500 600
Batch Number
CAT
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Learning curve: 90%
0.000
10.000
20.000
30.000
40.000
50.000
60.000
0 100 200 300 400 500 600
Batch Number
CAT
Learning curve: 60%
0.000
10.000
20.000
30.000
40.000
50.000
60.000
0 100 200 300 400 500 600
Batch Number
CAT
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80% Learning Rate
Batches Total Time CAT
1 50.00 50.00
2 80.00 40.00
4 128.00 32.00
8 204.80 25.60
128 1,342.18 10.49
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No Learning
Batches Total Time CAT
1 50.00 50.00
2 100.00 50.00
4 200.00 50.00
8 400.00 50.00
128 6,400.00 50.00
Implications of leanin! ta"in! place as oppose#to no leanin! ta"in! place if the cost is $ 1 peho% an# each &atch has 5 pieces.
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Average Cost/unit
'nits 80( )eanin! *o )eanin!
5 10.00 10.00
10 16.00 20.00
20 25.60 40.00
40 40.96 80.00
+ +640 268.44 1,280.00
80% Learning Rate
Batches Total Time Aea!etime
1 50.00 50.00
2 80.00 40.00
4 128.00 32.008 204.80 25.60
128 1,342.18 10.49
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No Learning
Batches Total Time Aea!etime
1 50.00 50.00
2 100.00 50.00
4 200.00 50.00
8 400.00 50.00
128 6,400.00 50.00
in#%st- aea!es
Aeospace 85(
/hip&%il#in! 80 85(
a mateials 93 96(
%chase# pats 85 88(
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Problems & caselets on Learning curve
1. An assembly line for making trays of cup cakes has a 90% learning curve. The line has
begun to work on the first tray and it takes 2 minutes for the first piece. !stimate"
The time needed for the first # trays The time taken for the 20
thto 2#thtray
2.
$illing up of a form is supposed to have a learning rate of 2%. Time for the first units
are &0.#' 2.' 2(.2 and 2(.0 )oes the assumption look realistic*
&.
The company wants to identify which of the following trainees will reach the set target
of reaching + hours or less by the time they manufacture the +thpiece.
Arun took 10 hours and 9 hours for the first and second piece.
,askar took 10 hours and hours for the first and second piece.
-harles took 12 hours and 9 hours for the first and second piece.
hich trainee / trainees will make the standard* !plain your reasoning.
. A has received a pilot order for setting 20 AT3 3achines ,ased on their eperience
of setting up the first two AT34s they will be 5uoting for additional 1 such AT34s. The
contract envisages that they will be paid separately for 6abour and material costs at the
rate of cost 7 10%. They are negotiating a learning rate with the material supplier as well
The first AT3 took 0 hours to complete and cost 8 &00 in materials and e5uipment
usage. The second took &2 hours and 8 210 in material. 6abour cost is charged at 8 1
per hour.
a
!stimate the total manhours re5uired for total of 20 AT34s.
b
hat will be the average total cost for the 20 AT34s in the contract.
c
ork out the financial advantage to the customer by not estimating based on 1st
AT3 alone and basing cost based on eperience curve principle.
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#.
A customer has offered you the contract for cutting and packing vegetables for salad and
supply to :TA:. The raw material will be supplied by the customer. As per the customer
each packet of cut vegetable should be ready in an average time of 1.# minutes and
they are willing to reimburse your cost at the rate of 80.#0 per minute for the labour.
The contract is for 1000 sets. ;our first test took minutes and the second &.+ minutes.
ould you take the contract*
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3ini -aselets
6.
What should Bus Chair do?
,us -hair has developed a new chair.
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Supply of Coffee Vending Consumables
Messrs Cofco , is in the business of supplying coffee vending machine consumables. On
1stSeptember 200, as the ne! C"O !ho has ta#en charge, Mr. Symonds has as#ed for a
briefing on the company$s operations as !ell as an opportunity to ta#e stoc# of their
operations. %he company$s business is to supply #its comprising of all the relevant
consumables & li#e mil# po!der, coffee po!der and sugar as re'uired to be put in thecoffee ma#ing machines. %hey procure these ra! materials in bul#, re pac# and deliver
as #it set for the coffee vending machine.
Mar#eting (rief)
*n the meeting, Mr. Mar# the Mar#eting chief has informed the C"O that)
%heir analysis sho!s they cater to 2 distinctly clear mar#ets )
a+ estaurants
b+ Corporate offices
%heir last year sales !ere -00,000 #its, 0/ being sold to restaurants.
%he company mar#ets the #it at a differential pricing to the t!o mar#ets i.e. at
- for the restaurants at - for the offices.
Obviously the office #it is pac#aged nicer and delivered in smaller lots for easy
usage by individuals. %he delivery to offices is aimed at ensuring delivery !ithin
one hour of receiving the call in at least 0/ cases.
%he restaurants have a regular delivery schedule. %hey are supplied !ee#ly and
on designated days. the van from the company visits the outlets and delivers the
goods. %hey stoc# typically 2 !ee#s re'uirement
%he Mar#eting manager also e3presses his concern about the estaurant business
!herein he is e3periencing stiff competition from a ne! entrant. 4s a result he feels
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they should reduce their sales price to restaurants by at least 1 per #it. 5e feels
other!ise he might lose his mar#et share to the competitively priced ne! entrant.
%he 4ccounts head Ms. Maria brief)
%he basic cost of material in each #it is 10 per pac#.
%he labour content involved in pac#ing is 6 per pac#.
%he company$s annual costs comprise of)
o Sales commission paid at - per #it.
o 7elivery related cost 2.8 million
o Mar#eting and advertising costs 1.6 million
o 9roduct management teams cost 0. million
o
4dministration 0.6 million
%he company the overheads : not directly allotted costs given above based on the
#its sold to each mar#et segment.
7ata 4nalysis)
Mr Symond the C"O carries out basic cost calculations in the meeting to determine)
a+
Margin for both mar#et segmentsb+ the net profit for each product segment.
c+ ;hat is the assessment of the business< ;hat should he dopac#ing
and organi?ing all deliveries intervene. 5o! can the operations professional
interfere in this situation