chap00 1b performance measurement
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© 2011 Pearson Education, Inc. publishing as Prentice Hall
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
© 2011 Pearson Education, Inc. publishing as Prentice Hall
Break-Even Analysis
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
Assumptions
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Profit corridor
Loss
corridor
Break-Even AnalysisTotal revenue line
Total cost line
Variable cost
Fixed cost
Break-even pointTotal cost = Total revenue
–
900 –
800 –
700 –
600 –
500 –
400 –
300 –
200 –
100 –
–| | | | | | | | | | | |
0 100 200 300 400 500 600 700 800 900 1000 1100
Cost
in d
olla
rs
Volume (units per period)Figure S7.5
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Break-Even Analysis
BEPx =break-even point in unitsBEP$ =break-even point in dollarsP = price per unit (after all discounts)
x = number of units producedTR = total revenue = PxF = fixed costsV = variable cost per unitTC = total costs = F + Vx
TR = TCor
Px = F + Vx
Break-even point occurs when
BEPx =F
P - V
© 2011 Pearson Education, Inc. publishing as Prentice Hall
Break-Even Analysis
BEPx =break-even point in unitsBEP$ =break-even point in dollarsP = price per unit (after all discounts)
x = number of units producedTR = total revenue = PxF = fixed costsV = variable cost per unitTC = total costs = F + Vx
BEP$ = BEPx P
= P
=
=
F(P - V)/P
FP - V
F1 - V/P
Profit = TR - TC= Px - (F + Vx)= Px - F - Vx= (P - V)x - F
© 2011 Pearson Education, Inc. publishing as Prentice Hall
Break-Even Example
Fixed costs = $10,000 Material = $.75/unitDirect labor = $1.50/unit Selling price = $4.00 per unit
BEP$ = F1 -(V/P)
$10,0001 - [(1.50 + .75)/(4.00)]
© 2011 Pearson Education, Inc. publishing as Prentice Hall
Break-Even Example
Fixed costs = $10,000 Material = $.75/unitDirect labor = $1.50/unit Selling price = $4.00 per unit
BEP$ = =F
1 -(V/P)$10,000
1 - [(1.50 + .75)/(4.00)]
= $10,000
.4375
BEPx = F
P - V$10,000
4.00 - (1.50 + .75)
= $22,857.14
= = 5,714
© 2011 Pearson Education, Inc. publishing as Prentice Hall
Break-Even Example
50,000 –
40,000 –
30,000 –
20,000 –
10,000 –
–| | | | | |
0 2,000 4,000 6,000 8,000 10,000
Dol
lars
Units
Fixed costs
Total costs
Revenue
Break-even point
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Multiproduct Example
Annual ForecastedItem Price Cost Sales UnitsSandwich $5.00 $3.00 9,000Drink 1.50 .50 9,000Baked potato 2.00 1.00 7,000
Fixed costs = $3,000 per month
© 2011 Pearson Education, Inc. publishing as Prentice Hall
Multiproduct Example
Annual ForecastedItem Price Cost Sales UnitsSandwich $5.00 $3.00 9,000Drink 1.50 .50 9,000Baked potato 2.00 1.00 7,000
Fixed costs = $3,000 per month
Sandwich $5.00 $3.00 .60 .40 $45,000 .621 .248Drinks 1.50 .50 .33 .67 13,500 .186 .125Baked 2.00 1.00 .50 .50 14,000 .193 .096 potato
$72,500 1.000 .469
Annual WeightedSelling Variable Forecasted % of Contribution
Item (i) Price (P) Cost (V) (V/P) 1 - (V/P) Sales $ Sales (col 5 x col 7)
© 2011 Pearson Education, Inc. publishing as Prentice Hall
Multiproduct Example
Annual ForecastedItem Price Cost Sales UnitsSandwich $5.00 $3.00 9,000Drink 1.50 .50 9,000Baked potato 2.00 1.00 7,000
Fixed costs = $3,000 per month
Sandwich $5.00 $3.00 .60 .40 $45,000 .621 .248Drinks 1.50 .50 .33 .67 13,500 .186 .125Baked 2.00 1.00 .50 .50 14,000 .193 .096 potato
$72,500 1.000 .469
Annual WeightedSelling Variable Forecasted % of Contribution
Item (i) Price (P) Cost (V) (V/P) 1 - (V/P) Sales $ Sales (col 5 x col 7)
BEP$ =F
∑ 1 - x (Wi)Vi
Pi
= = $76,759$3,000 x 12
.469
Daily sales = = $246.02
$76,759312 days
.621 x $246.02$5.00 = 30.6 31
sandwichesper day
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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
-$90,000Market unfavorable (.6)
Market favorable (.4)$100,000
Large plant
Market favorable (.4)
Market unfavorable (.6)
$60,000
-$10,000
Medium plant
Market favorable (.4)
Market unfavorable (.6)
$40,000
-$5,000
Small plant
$0
Do nothing
© 2011 Pearson Education, Inc. publishing as Prentice Hall
Expected Monetary Value (EMV) and Capacity Decisions
-$90,000Market unfavorable (.6)
Market favorable (.4)$100,000
Large plant
Market favorable (.4)
Market unfavorable (.6)
$60,000
-$10,000
Medium plant
Market favorable (.4)
Market unfavorable (.6)
$40,000
-$5,000
Small plant
$0
Do nothing
EMV = (.4)($100,000) + (.6)(-$90,000)
Large Plant
EMV = -$14,000
© 2011 Pearson Education, Inc. publishing as Prentice Hall
Expected Monetary Value (EMV) and Capacity Decisions
-$90,000Market unfavorable (.6)
Market favorable (.4)$100,000
Large plant
Market favorable (.4)
Market unfavorable (.6)
$60,000
-$10,000
Medium plant
Market favorable (.4)
Market unfavorable (.6)
$40,000
-$5,000
Small plant
$0
Do nothing
-$14,000
$13,000
$18,000
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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)
where F = future valueP = present valuei = interest rate
N = number of years
P =F
(1 + i)N
F = P(1 + i)N
In general:
Solving for P:
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Net Present Value (NPV)
where F = future valueP = present valuei = interest rate
N = number of years
P =F
(1 + i)N
F = P(1 + i)N
In general:
Solving for P:
While this works fine, it is cumbersome for larger values of N
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NPV Using Factors
P = = FXF (1 + i)N
where X = a factor from Table S7.1 defined as = 1/(1 + i)N and F = future value
Portion of Table S7.1
Year 6% 8% 10% 12% 14%1 .943 .926 .909 .893 .8772 .890 .857 .826 .797 .7693 .840 .794 .751 .712 .6754 .792 .735 .683 .636 .5925 .747 .681 .621 .567 .519
© 2011 Pearson Education, Inc. publishing as Prentice Hall
Measuring Supply-Chain Performance
Table 11.6
Typical FirmsBenchmark
Firms
Lead time (weeks) 15 8
Time spent placing an order 42 minutes 15 minutes
Percentage of late deliveries 33% 2%
Percentage of rejected material 1.5% .0001%
Number of shortages per year 400 4
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Measuring Supply-Chain Performance
Assets committed to inventory
Percent invested in inventory = x 100
Total inventory investment
Total assets
Investment in inventory = $11.4 billionTotal assets = $44.4 billion
Percent invested in inventory = (11.4/44.4) x 100 = 25.7%
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Measuring Supply-Chain Performance
Table 11.7
Inventory as a % of Total Assets(with exceptional performance)
Manufacturing 15%(Toyota 5%)
Wholesale 34%(Coca-Cola 2.9%)
Restaurants 2.9%(McDonald’s .05%)
Retail 27%(Home Depot 25.7%)
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Measuring Supply-Chain Performance
Inventory turnover
Inventory turnover =
Cost of goods sold
Inventory investment
© 2011 Pearson Education, Inc. publishing as Prentice Hall
Measuring Supply-Chain Performance
Table 11.8
Examples of Annual Inventory Turnover
Food, Beverage, RetailManufacturingAnheuser Busch 15 Dell Computer 90Coca-Cola 14 Johnson Controls 22Home Depot 5 Toyota (overall) 13McDonald’s 112 Nissan (assembly) 150
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Measuring Supply-Chain Performance
Inventory turnover
Net revenue $32.5Cost of goods sold $14.2Inventory:
Raw material inventory $.74Work-in-process inventory $.11Finished goods inventory $.84
Total inventory investment $1.69
© 2011 Pearson Education, Inc. publishing as Prentice Hall
Measuring Supply-Chain Performance
Inventory turnover
Net revenue $32.5Cost of goods sold $14.2Inventory:
Raw material inventory $.74Work-in-process inventory $.11Finished goods inventory $.84
Total inventory investment $1.69
Inventory turnover = Cost of goods sold
Inventory investment
= 14.2 / 1.69 = 8.4
© 2011 Pearson Education, Inc. publishing as Prentice Hall
Measuring Supply-Chain Performance
Inventory turnover
Net revenue $32.5Cost of goods sold $14.2Inventory:
Raw material inventory $.74Work-in-process inventory $.11Finished goods inventory $.84
Total inventory investment $1.69
Inventory turnover = Cost of goods sold
Inventory investment
= 14.2 / 1.69 = 8.4Weeks of supply =
Inventory investmentAverage weekly cost of goods sold
= 1.69 / .273 = 6.19 weeks
Average weekly cost of goods sold = $14.2 / 52 = $.273