ENGM 661 Engineering Economics for Managers Financial Statements.
TM 661 Engineering Economics for Managers
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Transcript of TM 661 Engineering Economics for Managers
TM 661Engineering Economics
forManagers
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.
1 2 3 4 5
100,000
25,000
i = 15%
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.
1 2 3 4 5
100,000
25,000
NPW = -100 + 25(P/A,15,5) = -16,196
i = 15%
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.
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
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, justtell 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 < 29,830
A > 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
To
tal
Co
st
Austin
S. Falls
Denver
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 = 7.5X
139,495 = 7.5X
X = 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
NP
V
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)
35,000
i = 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
NP
V
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
NP
V
Errors in initial cost
Errors 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
NP
V
Errors in initial cost
Errors in Annual receipts
n=3
n=7
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%).
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 Solve It!!!
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
Err
or 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 NPV3
4.0% 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
NP
V
NPV1
NPV2
NPV3