TM 661 Engineering Economics for Managers

Transcript TM 661 Engineering Economics for Managers

IENG 217 Cost Estimating for Engineers

Break Even & Sensitivity

Motivation

Suppose that by investing in a new information system, management believes they can reduce inventory costs. Your boss asks you to figure out if it should be done.

Motivation

Suppose that by investing in a new information system, management believes they can reduce inventory costs. After talking with software vendors and company accountants you arrive at the following cash flow diagram. 25,000 i = 15% 1 2 3 4 5 100,000

Motivation

Boss indicates $25,000 per year savings is too low & is based on current depressed market. Suggests that perhaps $40,000 is more appropriate based on a more aggressive market.

40,000 1 2 3 4 5 100,000

Motivation

Boss indicates $25,000 per year savings is too low & is based on current depressed market. Suggests that perhaps $40,000 is more appropriate based on a more aggressive market.

40,000 1 2 3 4 5 100,000 NPW = -100 + 40(P/A,15,5) = 34,086

Motivation

Boss indicates $25,000 per year savings is too low & is based on current depressed market. Suggests that perhaps $40,000 is more appropriate based on a more aggressive market.

40,000 1 2 3 4 5 100,000 NPW = -100 + 40(P/A,15,5) = 34,086

Motivation

Tell your boss, new numbers indicate a go. Boss indicates that perhaps he was a bit hasty. Sales have fallen a bit below marketing forecast, perhaps a 32,000 savings would be more appropriate 32,000 1 2 3 4 5 100,000

Motivation

Tell your boss, new numbers indicate a go. Boss leans back in his chair and says, you know . . . .

Motivation

Tell your boss, new numbers indicate a go. Boss leans back in his chair and says, you know . . . . I’ll do anything, just tell me what numbers you want to use!

Motivation

A 1 2 3 4 5 100,000 NPW = -100 + A(P/A,15,5) > 0

Motivation

A 1 2 3 4 5 100,000 NPW = -100 + A(P/A,15,5) > 0 A > 100(A/P,15,5) > 29,830

Motivation

A 1 2 3 4 5 100,000 A > 29,830 A < 29,830

Fixed vs Variable

 Fixed - do not vary with production  general admin., taxes, rent, depreciation Variable - costs vary in proportion to the quantity of output material, direct labor, material handling

Fixed vs Variable

 Fixed - do not vary with production  general admin., taxes, rent, depreciation Variable - costs vary in proportion to the quantity of output material, direct labor, material handling TC(x) = FC + VC(x)

Fixed vs Variable

TC VC FC

TC(x) = FC + VC(x)

Break Even

Profit = R(x) - FC - VC(x)

R TC FC

Break-Even Analysis

Site Fixed Cost/Yr A=Austin S= Sioux Falls D=Denver $ 20,000 60,000 80,000 Variable Cost $ 50 40 30 TC = FC + VC * X

250,000

Break-Even (cont)

Break-Even Analysis

200,000 150,000 100,000 50,000 0 0 500 1,000 1,500 2,000

Volume

2,500 3,000 3,500 4,000 Austin S. Falls Denver

Example

 Company produces crude oil from a field where the basis of decision is the number of barrels produced. Two methods for production are:  automated tank battery  manually operated tank battery

Example

 Automated tank battery  annual depreciation = $3,200  annual maintenance = $5,200  Other fixed & variable costs

Automated Tank Battery

Automatic Tank Battery Operations Fixed Cost / day Control panel power Circulating pump Maintenance Meter calibration Chemical pump power Total 2.69/day or $982/yr Variable Cost / day Pipeline pump (5 hsp @ 50% util) Chemical additives (7.5 qts/day) Inhibitor (2 qts/day) Gas (10.8 MCF/day x 0.0275/MCF) Total 5.68/day / 500 barrels = $0.01136 / barrel $0.15

0.82

1.00

0.40

0.32

$2.69

$0.63

3.75

1.00

0.30

$5.68

TC(x) = (982 + 3,200 + 5,200) + 0.01136 X

Example

 Manual Tank Battery  annual depreciation = $2,000  annual maintenance = $7,500  other costs

Manual Tank Battery

Automatic Tank Battery Operations Fixed Cost / day Chemical pump power Circulating pump Total 0.98/day or $358/yr Variable Cost / day Chemical additives (7.5 qts/day) Gas (10.8 MCF/day x 0.0275/MCF) Total 4.05/day / 500 barrels = $0.00810 / barrel $0.16

0.82

$0.98

3.75

0.30

$4.05

TC(x) = (2,000 + 7,500 + 358) + 0.00810 X

BreakEven

TC A (x) = TC M (x)

BreakEven

TC A (x) = TC M (x) 9,382 + 0.01136 x = 9,858 + 0.0081 x

BreakEven

TC A (x) = TC M (x) 9,382 + 0.01136 x = 9,858 + 0.0081 x 0.0033 x = 476

BreakEven

TC A (x) = TC M (x) 9,382 + 0.01136 x = 9,858 + 0.0081 x 0.0033 x = 476 x * = 145,000

Example

Automatic vs Manual

12,000 11,000 10,000 9,000 8,000 50,000 100,000 150,000 200,000

Barrels per Year

Automatic Manual

Average vs Marginal Cost

(

) =

(

)

x MC

(

) = 

(

) 

Example

 Cost of running an automobile is TC(x) = $950 + 0.20 x where $950 covers annual depreciation and maintenance and x is the number of miles driven per year

Example

(

)

(

)

950 0 .

20

(

) = 



(

) =  ( 950 + 

0 .

) = 0 .

Example

Average vs Marginal Cost (Automobile)

1.5

1.0

0.5

0.0

0 10,000 20,000

Miles per year

30,000 Average Marginal

Marginal Returns

Example

 Small firm sells garden chemicals. x = number of tons sold per year SP(x) = selling price per ton (to sell x tons) = $(800 - 0.8x) TR(x) = total revenue at x tons = $(800 - 0.8x) x TC(x) = total production cost for x tons = $(8,000 + 400x)

Example

TP(x) = total profit at x tons = TR(x) - TX(x) = (800x - 0.8x

2 ) - (8,000 + 400x) = -0.8x

2 + 400x - 8,000 Compute a. x at which revenue is maximized b. marginal revenue at max revenue c. x at which profit is maximized d. average profit at max profit

Example

TR(x) = -0.8x

2 + 800x a. max R 

( 

x x

) = 0 =  ( 0 .

2 

+ 800

) = 1 .

+ 800

= 500

tons

Example

TR(x) = -0.8x

2 + 800x b. Marginal Revenue MR(500) = -1.6(500) + 800 = $0

Example

TP(x) = -0.8x

2 + 400x - 8,000 c. max profit 

(

) 

= 0 =  ( .

2 + 400



+ 8 , 000 ) = 1 .

+ 400

= 250

Example

TP(x) = -0.8x

2 + 400x - 8,000 c. average profit

(

) = 0 .

2 + 400

8 , 000

= 0 .

+ 400 8 , 000 /

x AP

( 250 ) = $ 168 /

ton

Break-Even Analysis

Site Fixed Cost/Yr A=Austin S= Sioux Falls D=Denver $ 20,000 60,000 80,000 Variable Cost $ 50 40 30 TC = FC + VC * X

Break-Even (cont)

Break-Even Analysis

250,000 200,000 150,000 100,000 50,000 0 0 500 1,000 1,500 2,000

Volume

2,500 3,000 3,500 4,000 Austin S. Falls Denver

Class Problem

A firm is considering a new product line and the following data have been recorded: Sales price Cost of Capital Overhead Oper/maint.

Material Cost Production Planning Horizon MARR $ 15 / unit $300,000 $ 50,000 / yr.

$ 50 / hr.

$ 5 / unit 50 hrs / 1,000 units 5 yrs.

15% Compute the break even point.

Class Problem

Profit Margin = Sale Price - Material - Labor/Oper.

= $15 - 5 50 hrs 1000 units $50 / hr = $ 7.50 / unit

Class Problem

Profit Margin = Sale Price - Material - Labor/Oper.

= $15 - 5 50 hrs 1000 units $25 / hr = $ 7.50 / unit 7.5X

1 2 3 4 5 50,000 300,000

Class Problem

Profit Margin = Sale Price - Material - Labor/Oper.

= $15 - 5 50 hrs 1000 units $25 / hr = $ 7.50 / unit 7.5X

1 2 3 4 5 50,000 300,000 300,000(A/P,15,5) + 50,000 = 7.5X

139,495 = 7.5X

X = 18,600

Sensitivity

Suppose we consider the following cash flow diagram: 35,000 i = 15% 1 2 3 4 5 100,000 NPW = -100 + 35(P/A,15,5) = $ 17,325

Sensitivity

Suppose we don’t know A=35,000 exactly but believe we can estimate it within some percentage error of + X.

35,000(1+X) i = 15% 1 2 3 4 5 100,000

Then,

Sensitivity

35,000(1+X) i = 15% 1 2 3 4 5 100,000 EUAW = -100(A/P,15,5) + 35(1+X) > 0 35(1+X) > 100(.2983) X > -0.148

Sensitivity (cont.)

-0.30

-0.20

NPV vs. Errors in A

50,000 40,000 30,000 20,000 10,000 -0.10

0 (10,000) 0.00

(20,000)

Error X

0.10

0.20

Sensitivity (A

)

Now suppose we believe that the initial investment might be off by some amount X.

35,000 i = 15% 1 2 3 4 5 100,000(1+X)

Sensitivity (A

)

NPV vs Initial Cost Errors

-0.30

-0.20

50,000 40,000 30,000 20,000 10,000 -0.10

0 (10,000) 0.00

(20,000)

Error X

0.10

0.20

Sensitivity (A & A

)

-0.30

NPV vs Errors

-0.20

50,000 40,000 30,000 20,000 10,000 -0.10

0 (10,000) 0.00

(20,000)

Error X

Errors in initial cost Errors in Annual receipts 0.10

0.20

Sensitivity (PH)

Now suppose we believe that the planning horizon might be shorter or longer than we expected.

35,000 i = 15% 1 2 3 4 5 6 7 100,000

Sensitivity (PH)

NPV vs Planning Horizon

50,000 40,000 30,000 20,000 10,000 0 (10,000) 0 (20,000) (30,000) 1 2 3 4

NPV

5 6 7

Sensitivity (Ind. Changes)

-0.30

NPV vs Errors

-0.20

n=3 50,000 40,000 30,000 20,000 10,000 -0.10

0 (10,000) 0.00

(20,000)

Error X

Errors in initial cost Errors in Annual receipts 0.10

n=7 0.20

Planning Horizon MARR

Multivariable Sensitivity

Suppose our net revenue is composed of $50,000 in annual revenues which have an error of X and $20,000 in annual maint. costs which might have an error of Y (i=15%).

50,000(1+X) 1 2 3 4 5 20,000(1+Y) 100,000

Multivariable Sensitivity

Suppose our net revenue is compose of $50,000 in annual revenues which have an error of X and $20,000 in annual maint. costs which might have an error of Y (i=15%).

50,000(1+X) 1 2 3 4 5 20,000(1+Y) 100,000 Multivariable Sensitivity Suppose our net revenue is compose of $50,000 in annual revenues which have an error of X and $20,000 in annual maint. costs which might have an error of Y.

50,000(1+X) 1 2 3 4 5 20,000(1+Y) 100,000 You Solve It!!!

You Solve It!!!

Multivariable Sensitivity

50,000(1+X) 1 2 3 4 5 20,000(1+Y) 100,000 EUAW = -100(A/P,15,5) + 50(1+X) - 20(1+Y) > 0 50(1+X) - 20(1+Y) > 29.83

Multivariable Sensitivity

50,000(1+X) 1 2 3 4 5 20,000(1+Y) 100,000 EUAW = -100(A/P,15,5) + 50(1+X) - 20(1+Y) > 0 50(1+X) - 20(1+Y) > 29.83

50X - 20Y > -0.17

X > 0.4Y - 0.003

Multivariable Sensitivity

-0.15

Simultaneous Errors (Rev. vs. Cost)

Unfavorable -0.1

-0.05

0.4

0.3

0.2

0.1

0 -0.1

0 -0.2

-0.3

-0.4

Error X

+ 10% 0.05

Favorable 0.1

0.15

Mutually Exclusive Alt.

Suppose we work for an entity in which the MARR is not specifically stated and there is some uncertainty as to which value to use. Suppose also we have the following cash flows for 3 mutually exclusive alternatives.

t 0 1 2 3 4 5 A 1t (50,000) 18,000 18,000 18,000 18,000 18,000 A 2t (75,000) 25,000 25,000 25,000 25,000 25,000 A 3t (100,000) 32,000 32,000 32,000 32,000 32,000

Mutually Exclusive Alt.

t 0 1 2 3 4 5 A 1t (50,000) 18,000 18,000 18,000 18,000 18,000 MARR = NPV 1 4.0% 30,133 6.0% 8.0% 10.0% 12.0% 14.0% 16.0% 18.0% 20.0% 25,823 21,869 18,234 14,886 11,795 8,937 6,289 3,831 A 2t (75,000) 25,000 25,000 25,000 25,000 25,000 NPV 2 36,296 30,309 24,818 19,770 15,119 10,827 6,857 3,179 (235) A 3t (100,000) 32,000 32,000 32,000 32,000 32,000 NPV 3 42,458 34,796 27,767 21,305 15,353 9,859 4,777 69 (4,300)

Mutually Exclusive Alt.

NPV vs. MARR

50,000 40,000 30,000 20,000 10,000 0 (10,000) 0.0% 5.0% 10.0%

MARR

15.0% 20.0% NPV1 NPV2 NPV3