Transcript Break-Even Analysis

Break-Even Analysis
 Technique for evaluating process and
equipment alternatives
 Objective is to find the point in dollars
and units at which cost equals revenue
 Requires estimation of fixed costs,
variable costs, and revenue
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Break-Even Analysis
 Fixed costs are costs that continue even if
no units are produced
 Depreciation, taxes, debt, mortgage
payments
 Variable costs are costs that vary with the
volume of units produced
 Labor, materials, portion of utilities
 Contribution is the difference between
selling price and variable cost
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Break-Even Analysis
Assumptions
 Costs and revenue are linear
functions
 Generally not the case in the real
world
 We actually know these costs
 Very difficult to verify
 Time value of money is often
ignored
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Break-Even Analysis
–
Total revenue line
900 –
800 –
700 –
Cost in dollars
Total cost line
Break-even point
Total cost = Total revenue
600 –
500 –
Variable cost
400 –
300 –
200 –
100 –
–
0
Fixed cost
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100 200 300 400 500 600 700 800 900 1000 1100
Figure S7.5
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Volume (units per period)
Break-Even Analysis
BEPx = break-even point in units
BEP$ = break-even point in
dollars
P = price per unit (after all
discounts)
x = number of units produced
TR
F
V
TC
=
=
=
=
total revenue = Px
fixed costs
variable cost per unit
total costs = F + Vx
Break-even point occurs when
TR = TC
or
Px = F + Vx
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BEPx =
F
P-V
Break-Even Analysis
BEPx = break-even point in units
BEP$ = break-even point in
dollars
P = price per unit (after all
discounts)
BEP$ = BEPx P
F
=
P
P-V
F
=
(P - V)/P
F
=
1 - V/P
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x = number of units produced
TR
F
V
TC
=
=
=
=
total revenue = Px
fixed costs
variable cost per unit
total costs = F + Vx
Profit = TR - TC
= Px - (F + Vx)
= Px - F - Vx
= (P - V)x - F
Break-Even Example
Fixed costs = $10,000
Direct labor = $1.50/unit
BEP$ =
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Material = $.75/unit
Selling price = $4.00 per unit
F
1 -(V/P)
$10,000
1 - [(1.50 + .75)/(4.00)]
Break-Even Example
Fixed costs = $10,000
Direct labor = $1.50/unit
Material = $.75/unit
Selling price = $4.00 per unit
F
1 -(V/P)
BEP$ =
=
BEPx =
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=
$10,000
.4375
F
P-V
=
$10,000
1 - [(1.50 + .75)/(4.00)]
= $22,857.14
$10,000
4.00 - (1.50 + .75)
= 5,714
Break-Even Example
50,000 –
Revenue
40,000 –
Break-even
point
Dollars
30,000 –
Total
costs
20,000 –
Fixed costs
10,000 –
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0
2,000
4,000
6,000
8,000
10,000
Units
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Multiproduct Example
Fixed costs = $3,000 per month
Item
Sandwich
Drink
Baked potato
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Price
$5.00
1.50
2.00
Cost
$3.00
.50
1.00
Annual Forecasted
Sales Units
9,000
9,000
7,000
Multiproduct Example
Fixed costs = $3,000 per month
Item
Sandwich
Drink
Baked potato
Item (i)
Sandwich
Drinks
Baked
potato
Price
$5.00
1.50
2.00
Cost
$3.00
.50
1.00
Annual Forecasted
Sales Units
9,000
9,000
7,000
Annual
Selling Variable
Forecasted
Price (P) Cost (V) (V/P) 1 - (V/P) Sales $
$5.00
1.50
2.00
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$3.00
.50
1.00
.60
.33
.50
.40
.67
.50
% of
Sales
Weighted
Contribution
(col 5 x col 7)
$45,000
13,500
14,000
.621
.186
.193
.248
.125
.096
$72,500
1.000
.469
F
Multiproduct
Example
BEP =
V
∑ 1 - P x (W )
$
i
i
i
Fixed costs = $3,000 per month
Item
Sandwich
Drink
Baked potato
Item (i)
Sandwich
Drinks
Baked
potato
Price
$5.00
1.50
2.00
Selling Variable
Price (P) Cost (V) (V/P)
$5.00
1.50
2.00
$3.00
.50
1.00
.60
.33
.50
Annual
Forecasted
$3,000
x 12
Cost =
Sales=Units
$76,759
.469
$3.00
9,000
.50
9,000
$76,759
Daily
= $246.02
1.00
7,000
sales = 312 days
Annual
Weighted
Forecasted
.621
x $246.02 % of Contribution
= 30.6(col
 31
1 - (V/P) Sales
Sales
5 x col 7)
$5.00$
sandwiches
.40
$45,000
.621 per day.248
.67
13,500
.186
.125
.50
14,000
.193
.096
$72,500
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1.000
.469
Expected Monetary Value (EMV) and
Capacity Decisions
 Determine states of nature
 Future demand
 Market favorability
 Analyzed using decision trees
 Hospital supply company
 Four alternatives
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Expected Monetary Value (EMV) and
Capacity Decisions
Market favorable (.4)
Market unfavorable (.6)
Market favorable (.4)
Medium plant
Market unfavorable (.6)
Market favorable (.4)
Market unfavorable (.6)
$100,000
-$90,000
$60,000
-$10,000
$40,000
-$5,000
$0
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Expected Monetary Value (EMV) and
Capacity Decisions
Market favorable (.4)
Market unfavorable (.6)
Market favorable (.4)
Medium plant
Large Plant
EMV =
(.4)($100,000)
+ (.6)(-$90,000)
EMV = -$14,000
Market unfavorable (.6)
Market favorable (.4)
Market unfavorable (.6)
$100,000
-$90,000
$60,000
-$10,000
$40,000
-$5,000
$0
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Expected Monetary Value (EMV) and
Capacity Decisions
-$14,000
Market favorable (.4)
Market unfavorable (.6)
$100,000
-$90,000
$18,000
Market favorable (.4)
Medium plant
Market unfavorable (.6)
$60,000
-$10,000
$13,000
Market favorable (.4)
Market unfavorable (.6)
$40,000
-$5,000
$0
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Strategy-Driven Investment
 Operations may be responsible for
return-on-investment (ROI)
 Analyzing capacity alternatives
should include capital investment,
variable cost, cash flows, and net
present value
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Net Present Value (NPV)
In general:
F = P(1 + i)N
where
F
P
i
N
= future value
= present value
= interest rate
= number of years
Solving for P:
P=
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F
(1 + i)N
Net Present Value (NPV)
In general:
F = P(1 + i)N
where
F
P
i
N
= future value
= present value
While this works fine,
= interest rate
cumbersome for
= number ofis
years
larger values of N
Solving for P:
P=
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F
(1 + i)N
it
NPV Using Factors
F
P=
(1 + i)N
where
Portion of
Table S7.1
X =
Year
1
2
3
4
5
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6%
.943
.890
.840
.792
.747
= FX
a factor from Table S7.1 defined as =
1/(1 + i)N and F = future value
8%
.926
.857
.794
.735
.681
10%
.909
.826
.751
.683
.621
12%
.893
.797
.712
.636
.567
14%
.877
.769
.675
.592
.519
Measuring Supply-Chain
Performance
Typical Firms
Benchmark
Firms
15
8
Time spent placing an order
42 minutes
15 minutes
Percentage of late deliveries
33%
2%
Percentage of rejected material
1.5%
.0001%
400
4
Lead time (weeks)
Number of shortages per year
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Table 11.6
Measuring Supply-Chain
Performance
 Assets committed to inventory
Percent invested
in inventory
=
Total inventory
investment
x 100
Total assets
Investment in inventory = $11.4 billion
Total assets = $44.4 billion
Percent invested in inventory = (11.4/44.4) x 100 = 25.7%
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Measuring Supply-Chain
Performance
Inventory as a % of Total Assets
(with exceptional performance)
Manufacturing
(Toyota 5%)
15%
Wholesale
(Coca-Cola 2.9%)
34%
Restaurants
(McDonald’s .05%)
2.9%
Retail
(Home Depot 25.7%)
27%
Table 11.7
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Measuring Supply-Chain
Performance
 Inventory turnover
Cost of goods sold
Inventory
turnover
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=
Inventory investment
Measuring Supply-Chain
Performance
Examples of Annual Inventory Turnover
Food, Beverage, RetailManufacturing
Anheuser Busch
15
Dell Computer
90
Coca-Cola
14
Johnson Controls
22
Toyota (overall)
13
Home Depot
McDonald’s
5
112
Nissan (assembly)
150
Table 11.8
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Measuring Supply-Chain
Performance
 Inventory turnover
Net revenue
Cost of goods sold
Inventory:
Raw material inventory
Work-in-process inventory
Finished goods inventory
Total inventory investment
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$32.5
$14.2
$.74
$.11
$.84
$1.69
Measuring Supply-Chain
Performance
 Inventory turnover
Net revenue
$32.5
Cost
of
goods
sold
Cost of goods sold
$14.2
Inventory turnover =
Inventory:
Inventory investment
Raw material inventory
$.74
Work-in-process inventory
$.11
Finished goods inventory = 14.2 / 1.69 = 8.4 $.84
Total inventory investment
$1.69
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Measuring Supply-Chain
Performance
 Inventory turnover
Net revenue
$32.5
Cost
of
goods
sold
Cost of goods sold
$14.2
Average
weekly
cost
of
Inventory turnover =
Inventory:
Inventory
= $14.2
/ 52 =investment
$.273
goods sold
Raw material inventory
$.74
Work-in-process inventory
$.11
= 8.4 investment
Inventory
Finished goods inventory = 14.2 / 1.69
$.84
Weeks
of supply
=
Total
inventory
investment
$1.69
Average weekly cost of goods sold
= 1.69 / .273 = 6.19 weeks
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