TM 661Engineering Economics

forManagers

Break Even &Sensitivity

MotivationSuppose 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.

MotivationSuppose 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.

1 2 3 4 5

100,000

25,000

i = 15%

MotivationSuppose 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.

1 2 3 4 5

100,000

25,000

NPW = -100 + 25(P/A,15,5) = -16,196

i = 15%

MotivationSuppose 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.

1 2 3 4 5

100,000

25,000

NPW = -100 + 25(P/A,15,5) = -16,196

i = 15%

MotivationBoss 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.

1 2 3 4 5

100,000

40,000

MotivationBoss 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.

1 2 3 4 5

100,000

40,000

NPW = -100 + 40(P/A,15,5) = 34,086

MotivationBoss 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.

1 2 3 4 5

100,000

40,000

NPW = -100 + 40(P/A,15,5) = 34,086

MotivationTell 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

1 2 3 4 5

100,000

32,000

MotivationTell 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

1 2 3 4 5

100,000

32,000

NPW = -100 + 32(P/A,15,5) = 7,269

MotivationTell 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

1 2 3 4 5

100,000

32,000

NPW = -100 + 32(P/A,15,5) = 7,269

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

MotivationTell 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 numbersyou want to use!

Motivation

1 2 3 4 5

100,000

A

NPW = -100 + A(P/A,15,5) > 0

Motivation

1 2 3 4 5

100,000

A

NPW = -100 + A(P/A,15,5) > 0

A > 100/(A/P,15,5) > 29,830

A < 29,830A > 29,830

Motivation

1 2 3 4 5

100,000

A

Break-Even Analysis

Site Fixed Cost/Yr Variable CostA=Austin $ 20,000 $ 50 S= Sioux Falls 60,000 40 D=Denver 80,000 30

TC = FC + VC * X

Break-Even (cont)Break-Even Analysis

0

50,000

100,000

150,000

200,000

250,000

0 500 1,000 1,500 2,000 2,500 3,000 3,500 4,000

Volume

Tota

l Cos

t AustinS. FallsDenver

Class Problem A firm is considering a new product line and the following data have been recorded:

Sales price $ 15 / unitCost of Capital $300,000Overhead $ 50,000 / yr.Oper/maint. $ 50 / hr.Material Cost $ 5 / unitProduction 50 hrs / 1,000 unitsPlanning Horizon 5 yrs.MARR 15%

Compute the break even point.

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

= $15 - 5 - $50 / hr

= $ 7.50 / unit

50 hrs1000 units

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

= $15 - 5 - $25 / hr

= $ 7.50 / unit

50 hrs1000 units

1 2 3 4 5

300,000

7.5X

50,000

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

= $15 - 5 - $25 / hr

= $ 7.50 / unit

50 hrs1000 units

1 2 3 4 5

300,000

7.5X

50,000

300,000(A/P,15,5) + 50,000 = 7.5X139,495 = 7.5XX = 18,600

Suppose we consider the following cash flow diagram:

NPW = -100 + 35(P/A,15,5) = $ 17,325

Sensitivity

1 2 3 4 5

100,000

35,000

i = 15%

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

Sensitivity

1 2 3 4 5

100,000

35,000(1+X) i = 15%

Then,

EUAW = -100(A/P,15,5) + 35(1+X) > 0 35(1+X) > 100(.2983)

X > -0.148

Sensitivity

1 2 3 4 5

100,000

35,000(1+X)

i = 15%

Sensitivity (cont.)NPV vs. Errors in A

(20,000)

(10,000)

0

10,000

20,000

30,000

40,000

50,000

-0.30 -0.20 -0.10 0.00 0.10 0.20

Error X

NPV

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

Sensitivity (Ao)

1 2 3 4 5

100,000(1+X)

35,000i = 15%

Sensitivity (Ao)NPV vs Initial Cost Errors

(20,000)

(10,000)

0

10,000

20,000

30,000

40,000

50,000

-0.30 -0.20 -0.10 0.00 0.10 0.20

Error X

NPV

Sensitivity (A & Ao)NPV vs Errors

(20,000)

(10,000)

0

10,000

20,000

30,000

40,000

50,000

-0.30 -0.20 -0.10 0.00 0.10 0.20

Error X

NPV

Errors in initial costErrors in Annual receipts

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

Sensitivity (PH)

1 2 3 4 5 6 7

100,000

35,000i = 15%

Sensitivity (PH)NPV vs Planning Horizon

(30,000)

(20,000)

(10,000)

0

10,000

20,000

30,000

40,000

50,000

0 1 2 3 4 5 6 7

NPV

PH

Sensitivity (Ind. Changes)

NPV vs Errors

(20,000)

(10,000)

0

10,000

20,000

30,000

40,000

50,000

-0.30 -0.20 -0.10 0.00 0.10 0.20

Error X

NPV

Errors in initial costErrors in Annual receipts

n=3

n=7

Planning HorizonMARR

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%).

1 2 3 4 5

100,000

50,000(1+X)

20,000(1+Y)

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%).

1 2 3 4 5

100,000

50,000(1+X)

20,000(1+Y)

Multivariable SensitivitySuppose our net revenue is compose of $50,000 in annualrevenues which have an error of X and $20,000 in annualmaint. costs which might have an error of Y.

1 2 3 4 5

100,000

50,000(1+X)

20,000(1+Y)You S olve I t!! !

You Solve It!!!

Multivariable Sensitivity

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

1 2 3 4 5

100,000

50,000(1+X)

20,000(1+Y)

Multivariable Sensitivity

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

1 2 3 4 5

100,000

50,000(1+X)

20,000(1+Y)

Multivariable Sensitivity

Simultaneous Errors (Rev. vs. Cost)

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

-0.15 -0.1 -0.05 0 0.05 0.1 0.15

Error X

Erro

r Y

Unfavorable

Favorable

+ 10%

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 A1t A2t A3t

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

Mutually Exclusive Alt.t A1t A2t A3t

0 (50,000) (75,000) (100,000)1 18,000 25,000 32,000 2 18,000 25,000 32,000 3 18,000 25,000 32,000 4 18,000 25,000 32,000 5 18,000 25,000 32,000 MARR = NPV1 NPV2 NPV34.0% 30,133 36,296 42,458 6.0% 25,823 30,309 34,796 8.0% 21,869 24,818 27,767 10.0% 18,234 19,770 21,305 12.0% 14,886 15,119 15,353 14.0% 11,795 10,827 9,859 16.0% 8,937 6,857 4,777 18.0% 6,289 3,179 69 20.0% 3,831 (235) (4,300)

Mutually Exclusive Alt.

NPV vs. MARR

(10,000)

0

10,000

20,000

30,000

40,000

50,000

0.0% 5.0% 10.0% 15.0% 20.0%

MARR

NPV

NPV1

NPV2

NPV3