Present Value
Single Sum Future Worth Interest Periods PW Total PW
P/F 0 0.00% 0 0.00
0 0.00% 0 0.00
0 0.00% 0 0.00
0 0.00% 0 0.00
F/P PW Periods
Interest FW Total FW
3,000 10.00% 35 84,307.31
40000 10.00% 35 1,124,097.47
0 0.00% 0 0.00
0 0.00% 0 0.00
P/A Period Amt A Periods
Interest PW Total PW
0 0.00% 0 0.00
0 0.00% 0 0.00
0 0.00% 0 0.00
0 0.00% 0 0.00
F/A Period Amt A Periods
Interest FW Total FW
70 10.00% 35 18,971.71
120 10.00% 35 32,522.92
10,000 10.00% 35 2,710,243.68
0 0.00% 0 0.00
Combined A and F Cash Flows
Period Amt A Interest Periods F1 N1 F2
1,000 8.00% 9 -1000 1 -1000
Interest Period Factor
A/P Factor 8.00% 8 0.17401
A/F 8.00% 8 0.09401
Arithmetic Gradient
Interest Periods P/G
6.00% 5 7.9345
Geometric Gradient
Interest Periods Gradient %
6.00% 5 5.00%
Interest Periods A n for A PV FV Interest
20 0.00 0 6,000.00 50,000.00 11.18%
Periods Interest A n for A PV FV Periods
8.00% 8,000.00 4 26,497.01 100,000.00 17.26
Search
F wanted n for F A n for A Interest FV Calc
100,000.00 17.258 8,000.00 4 8.00% 100,005.55
N2 PW
2 4,463.62
P or F A
A/P 2,000,000 348029.5
A/F 2,000,000 188029.5
A/G
1.8836
P/G
4.63
Interest 6.80% Period 17 IRR with Solver
Period 15,779.98 PW FW 48,285.61 Period
0 500.00 Period 10 0 -27,000.00
1 640.00 AW 2,225.99 1 1,019.00
2 780.00 2 2,019.00
3 920.00 3 2,499.20
4 1,060.00 4 4,019.00
5 1,200.00 5 5,019.00
6 1,340.00 6 6,019.00
7 1,480.00 7 7,019.00
8 1,620.00 8 8,019.00
9 1,760.00 9 7,497.60
10 1,900.00 10 0.00
11 2,040.00 11 0.00
12 2,180.00 12 0.00
13 2,320.00 13 0.00
14 2,460.00 14 0.00
15 2,600.00 15 0.00
16 2,740.00 16 0.00
17 2,880.00 17 0.00
18 0.00 18 0.00
19 0.00 19 0.00
20 0.00 20 0.00
21 0.00 21 0.00
22 0.00 22 0.00
23 0.00 23 0.00
24 0.00 24 0.00
25 0.00 25 0.00
26 0.00 26 0.00
27 0.00 27 0.00
28 0.00 28 0.00
29 0.00 29 0.00
30 0.00 30 0.00
31 0.00 31 0.00
32 0.00 32 0.00
33 0.00 33 0.00
34 0.00 34 0.00
35 0.00 35 0.00
IRR 8.00%
Test Score Weight Weighted Extra
1 96.000 0.167 16.000 0.000
2 87.000 0.167 14.500 0.000
3 78.000 0.167 13.000 10.000
4 100.000 0.167 16.667 10.000
5 100.000 0.250 25.000 10.000
6 57.037 0.090 7.833 0.000
ENGR ECON AVERAGE 93.000
Nominal per Period 0.55% Nominal per Year 8.35%
Periods per Year 12 Compound Periods per Year 4
Nominal per Year 6.60% Effective Interest Rate 8.62%
Effective per Year 6.80%
Effective Sub Periods Sub Periodic or Sub Periodic Sub Periods Effective
10.00% 365 0.026% 1.53% 4 6.262%
Options A B C D Interest
Salvage 1,600.00 2,200.00 1,800.00 2,400.00 5.50%
Salvage Life 3 4 5 4
0 -8,000.00 -9,500.00 -11,000.00 -12,000.00
1 -3,500.00 -3,300.00 -3,000.00 -2,200.00
2 -3,500.00 -3,300.00 -3,000.00 -2,200.00
3 -3,500.00 -3,300.00 -3,000.00 -2,200.00
4 0.00 -3,300.00 -3,000.00 -2,200.00
5 0.00 0.00 -3,000.00 0.00
6 0.00 0.00 0.00 0.00
7 0.00 0.00 0.00 0.00
8 0.00 0.00 0.00 0.00
9 0.00 0.00 0.00 0.00
10 0.00 0.00 0.00 0.00
PW/PWC -16,080.18 -19,291.12 -22,433.61 -17,774.01
NAW/AWC -5,960.19 -5,503.65 -5,253.42 -5,070.83
FW/FWC -18,882.02 -23,898.31 -29,319.83 -22,018.88
DO NOT TOUCH
Options A B C D Interest
Salvage 1,600.00 2,400.00 3,800.00 0.00 16.00%
Salvage Life 4 5 7 0
0 -15,000.00 -21,000.00 -28,000.00 0.00
1 -8,000.00 -6,000.00 -4,600.00 0.00
2 -8,400.00 -6,500.00 -4,840.00 0.00
3 -8,800.00 -7,000.00 -5,080.00 0.00
4 -7,600.00 -7,500.00 -5,320.00 0.00
5 0.00 -5,600.00 -5,560.00 0.00
6 0.00 0.00 -5,800.00 0.00
7 0.00 0.00 -2,240.00 0.00
8 0.00 0.00 0.00 0.00
9 0.00 0.00 0.00 0.00
10 0.00 0.00 0.00 0.00
PW/PWC -37,974.32 -42,295.99 -47,575.49 0.00
NAW/AWC -13,571.08 -12,917.59 -11,780.29 #DIV/0!
FW/FWC -68,757.80 -88,836.03 -134,458.78 0.00
A B Interest A B C
Purchase 25,000.00 12,000.00 12.00% Purchase 14,000.00 26,000.00 29,500.00
Annual OC 4,000.00 900 Annual OC 6,000.00 5,500.00 5,000.00
Salvage 3,000.00 2,500.00 Salvage 2,000.00 3,500.00 4,500.00
Life 5 6 Life 5 10 10
Period Interest 6.00% 6.00% 6.00%
0 25,000.00 12,000 NAW/AWC 8,968.76 8,767.03 8,666.70
1 4,000.00 900 PW/PWC 66,010.83 64,526.10 63,787.66
2 4,400.00 900 DO NOT TOUCH
3 4,800.00 900
4 5,200.00 900 A B C
5 5,600.00 900 Purchase 14,000.00 26,000.00 29,500.00
6 0.00 10,400.00 Annual OC 6,000.00 5,500.00 5,000.00
7 0.00 900 Salvage 2,000.00 3,500.00 4,500.00
8 0.00 900 Life 5 10 10
PW 41,977.91 21,283.87 Interest 6.00% 6.00% 6.00%
NAW/AWC 11,645.08 5,176.78 NAW/AWC 8,968.76 8,767.03 8,666.70
PW/PWC 66,010.83 64,526.10 63,787.66
Year Amount
0 -$18,000.00 Bond Face Value 25,000.00
1 $1,853.63 Bond Interest Rate 7.20%
2 $1,853.63 Bond Interest/half year $900.00
3 $1,853.63 FV (or PW) of bond interest/year $1,853.63
4 $1,853.63 Beware of PV vs. FV
5 $1,853.63
6 $1,853.63
7 $1,853.63
8 $1,853.63
9 $1,853.63
10 $1,853.63
11 $1,853.63
12 $26,853.63
ROR 11.917%
Single Sum ROR Calculation
PV -10,000 FV 18,000 n 6 ROR 10.29%
10.29%
Single Sum & Uniform Amount ROR
PV -10,000 FV 18,000 n 6 A uniform 1,000 ROR 18.39%
General Pattern Cash Flow ROR
Period A B C
0 -110,000 0 0
1 19,000 0 0
2 19,000 4,000 4,000
3 19,000 4,000 4,000
4 19,000 4,000 4,000
5 19,000 4,000 4,000
6 19,000 4,000 4,000
7 19,000 4,000 4,000
8 19,000 104,000 104,000
9 19,000
10 25,500
11
12
13
14
15
ROR ROR ROR
11.88% #NUM! #NUM!
Incremental ROR
A B C
P -14,000 -26,000 -29,500
A -6,000 -5,500 -5,000
n 5 10 10
MARR 6.00% 6.00% 6.00%
Period B-A C-A
0 -14,000 -26,000 -12,000 -29,500 -15,500
1 -6,000 -5,500 500 -5,000 1,000
2 -6,000 -5,500 500 -5,000 1,000
3 -6,000 -5,500 500 -5,000 1,000
4 -6,000 -5,500 500 -5,000 1,000
5 -18,000 -5,500 12,500 -5,000 13,000
6 -6,000 -5,500 500 -5,000 1,000
7 -6,000 -5,500 500 -5,000 1,000
8 -6,000 -5,500 500 -5,000 1,000
9 -6,000 -5,500 500 -5,000 1,000
10 -4,000 -2,000 2,000 -500 3,500
11 0 0
12 0 0
13 0 0
14 0 0
15 0 0
ROR 8.37% ROR 8.69%
C-B
-3,500
500
500
500
500
500
500
500
500
500
1,500
0
0
0
0
0
9.75%
Interest Rate 12.00% Note: make sure that AO Cashflow after life of project is a large negative number!!
First Cost 7,000
Defender Market
Year Value AO Cashflow Capital Recovery AW of AOC Total AW
1 3,500 -16,000 -4,340 -16,000 -20,340 1
2 100 -20,000 -4,095 -17,887 -21,982 2
3 0 -100,000 -2,914 -42,221 -45,135 3
4 0 -100,000 -2,305 -54,310 -56,615 4
5 0 -100,000 -1,942 -61,502 -63,444 5
6 0 -100,000 -1,703 -66,246 -67,949 6
7 0 -100,000 -1,534 -69,592 -71,126 7
8 0 -100,000 -1,409 -72,064 -73,473 8
Least Cost AW -20,340
Economic Service Life 1
project is a large negative number!!!! Interest Rate 12.00%
First Cost 21,000
Challenger Market
Year Value AO Cashflow Capital Recovery AW of AOC Total AW
1 13,000 -11,000 -10,520 -11,000 -21,520
2 7,000 -13,000 -9,124 -11,943 -21,067
3 0 -19,000 -8,743 -14,035 -22,778
4 0 -100,000 -6,914 -32,022 -38,935
5 0 -100,000 -5,826 -42,722 -48,548
6 0 -100,000 -5,108 -49,780 -54,888
7 0 -100,000 -4,601 -54,758 -59,359
8 0 -100,000 -4,227 -58,436 -62,663
Least Cost AW -21,067
Economic Service Life
1
2
3
4
5
6
7
8
2
Depreciation Not the initial cost, it is the
Straight Line Price (Cost) 69,000 Salvage 0 Life (n) 6 Depends on whether or not
Depreciation 11,500 Depreciation outside of Life
Declining Balance Price (Cost) 80,000 Salvage 12,000 Life (n) 10
Period 1 2 3 4 5 6
Depreciation $16,000.00 $12,800.00 $10,240.00 $8,192.00 $6,553.60 $5,242.88
Sum $53,785.60
Sum of Years Digits Price (Cost) 50,000 Salvage 0 Life (n) 6
Period 1 2 3 4 5 6
Depreciation $14,285.71 $11,904.76 $9,523.81 $7,142.86 $4,761.90 $2,380.95
Sum $50,000.00
MACRS Tax Depreciation Price (Cost) 45,000 Salvage 0 Life (N) 8
Period 1 2 3 4
3 years Depr % 33.33% 44.45% 14.81% 7.41%
Depr Amt 14,999 20,003 6,665 3,335
Period 1 2 3 4 5 6
5 years Depr % 20.00% 32.00% 19.20% 11.52% 11.52% 5.76%
Depr Amt 9,000 14,400 8,640 5,184 5,184 2,592
Period 1 2 3 4 5 6
7 years Depr % 14.29% 24.49% 17.49% 12.49% 8.93% 8.92%
Depr Amt 6,431 11,021 7,871 5,621 4,019 4,014
Period 1 2 3 4 5 6
10 years Depr % 10.00% 18.00% 14.40% 11.52% 9.22% 7.37%
Depr Amt 4,500 8,100 6,480 5,184 4,149 3,317
Period 1 2 3 4 5 6
15 years Depr % 5.00% 9.50% 8.55% 7.70% 6.93% 6.23%
Depr Amt 2,250 4,275 3,848 3,465 3,119 2,804
Period 1 2 3 4 5 6
20 years Depr % 3.75% 7.22% 6.68% 6.18% 5.71% 5.29%
Depr Amt 1,688 3,249 3,006 2,781 2,570 2,381
Not the initial cost, it is the purchase price
Depends on whether or not it is at the beginning of a year or at the end of the year (which includes depreciation of that year)
Depreciation outside of Life is 0
7 8 9 10
$4,194.30 $3,355.44 $1,421.77 $0.00
7 8 9 10
#NUM! #NUM! #NUM! #NUM!
p.546 & p.542
7 8
8.93% 4.46%
4,019 2,007
7 8 9 10 11
6.55% 6.55% 6.56% 6.55% 3.28%
2,948 2,948 2,952 2,948 1,476
7 8 9 10 11 12 13 14 15
5.90% 5.90% 5.91% 5.90% 5.91% 5.90% 5.91% 5.90% 5.91%
2,655 2,655 2,660 2,655 2,660 2,655 2,660 2,655 2,660
7 8 9 10 11 12 13 14 15
4.89% 4.52% 4.46% 4.46% 4.46% 4.46% 4.46% 4.46% 4.46%
2,201 2,034 2,007 2,007 2,007 2,007 2,007 2,007 2,007
on of that year)
16
2.95%
1,328
16 17 18 19 20 21
4.46% 4.46% 4.46% 4.46% 4.46% 2.23%
2,007 2,007 2,007 2,007 2,007 1,004
State Taxes Fed Taxes
State Tax 7.50% 31.00%
Period Revenues Expenses Depr % State Income State Tax Depr % Fed Income Fed Tax
0 10
1 2 1 20.00% -1 -0.075 20.00% -0.925 -0.287
2 2 1 20.00% -1 -0.075 32.00% -2.125 -0.659
3 2 1 20.00% -1 -0.075 19.20% -0.845 -0.262
4 2 1 20.00% -1 -0.075 11.52% -0.077 -0.024
5 2 1 20.00% -1 -0.075 11.52% -0.077 -0.024
6 2 1 0.00% 1 0.075 5.76% 0.349 0.108
7 2 1 0.00% 1 0.075 0.00% 0.925 0.287
8 2 1 0.00% 1 0.075 0.00% 0.925 0.287
9 2 1 0.00% 1 0.075 0.00% 0.925 0.287
10 2 1 0.00% 1 0.075 0.00% 0.925 0.287
DO NOT TOUCH!
MARR 14%
State Taxes
Total Cash Flow State Tax 0.00%
Taxes After Tax Period Revenues Expenses Depr % State Income State Tax
-10.00 0 40,000
-0.36 1.36 1 20,000 0 0.00% 20,000.00 0
-0.73 1.73 2 24,000 0 0.00% 24,000.00 0
-0.34 1.34 3 0 0 0.00% 0.00 0
-0.10 1.10 4 0 0 0.00% 0.00 0
-0.10 1.10 5 0 0 0.00% 0.00 0
0.18 0.82 6 0 0 0.00% 0.00 0
0.36 0.64 7 0 0 0.00% 0.00 0
0.36 0.64 8 0 0 0.00% 0.00 0
0.36 0.64 9 0 0 0.00% 0.00 0
0.36 0.64 10 0 0 0.00% 0.00 0
ROR 0.000%
Use for Examples
PW -$4.98
Fed Taxes
0.00% Total Cash Flow
Depr % Fed Income Fed Tax Taxes After Tax
-40,000.00
0.00% 20,000.00 0.00 0.00 20,000.00
0.00% 24,000.00 0.00 0.00 24,000.00
0.00% 0.00 0.00 0.00 0.00
0.00% 0.00 0.00 0.00 0.00
0.00% 0.00 0.00 0.00 0.00
0.00% 0.00 0.00 0.00 0.00
0.00% 0.00 0.00 0.00 0.00
0.00% 0.00 0.00 0.00 0.00
0.00% 0.00 0.00 0.00 0.00
0.00% 0.00 0.00 0.00 0.00
ROR 6.394%
se for Examples
MARR 14% PW -$3,988.92
Downpayment Rate Term State Taxes Fed Taxes
2 State Tax 12.00% 5 7.50% 31.00%
Period Revenues Expenses Depr % Interest Principal State Income State Tax Depr %
0 10
1 2 1 20.00% 0.960 1.259 -1.96 -0.147 20.00%
2 2 1 20.00% 0.809 1.410 -1.81 -0.13567 32.00%
3 2 1 20.00% 0.640 1.580 -1.64 -0.12297 19.20%
4 2 1 20.00% 0.450 1.769 -1.45 -0.10876 11.52%
5 2 1 20.00% 0.238 1.981 -1.24 -0.09283 11.52%
6 2 1 0.00% 0.000 0.000 1.00 0.075 5.76%
7 2 1 0.00% 0.000 0.000 1.00 0.075 0.00%
8 2 1 0.00% 0.000 0.000 1.00 0.075 0.00%
9 2 1 0.00% 0.000 0.000 1.00 0.075 0.00%
10 2 1 0.00% 0.000 0.000 1.00 0.075 0.00%
DO NOT TOUCH!
R E D T t NIBT NIAT ATCF
0 0 0 0 0.00% 0 0 0 Input
R E D T t NIBT NIAT ATCF
0 0 0 Unknown
Cash Flow After Tax
Fed Income Fed Tax Total Taxes Paid CFAT Period Revenues
-2 0
-1.813 -0.562 -0.709 -0.510 1 70,000
-2.873 -0.891 -1.026 -0.193 2 70,000
-1.437 -0.445 -0.568 -0.651 3 70,000
-0.493 -0.153 -0.262 -0.958 4 70,000
-0.297 -0.092 -0.185 -1.034 5 90,000
0.349 0.108 0.183 0.817 6 0
0.925 0.287 0.362 0.638 7 0
0.925 0.287 0.362 0.638 8 0
0.925 0.287 0.362 0.638 9 0
0.925 0.287 0.362 0.638 10 0
ROR -7.920%
Input
Unknown
Downpayment Rate Term State Taxes Fed Taxes
20,000 State Tax 8.00% 4 35.00% 0.00%
Expenses Depr % Interest Principal State Income State Tax Depr % Fed Income
100,000
36,000 33.33% 6,400.000 17,753.664 -5730.00 -2005.5 20.00% 9,605.50
41,000 44.45% 4,979.707 19,173.958 -20429.71 -7150.4 32.00% -829.31
46,000 14.81% 3,445.790 20,707.874 5744.21 2010.473 19.20% -656.26
51,000 7.41% 1,789.160 22,364.504 9800.84 3430.294 11.52% 2,260.55
56,000 0.00% 0.000 0.000 34000.00 11900 11.52% 10,580.00
0 0.00% 0.000 0.000 0.00 0 0.00% 0.00
0 0.00% 0.000 0.000 0.00 0 0.00% 0.00
0 0.00% 0.000 0.000 0.00 0 0.00% 0.00
0 0.00% 0.000 0.000 0.00 0 0.00% 0.00
0 0.00% 0.000 0.000 0.00 0 0.00% 0.00
Use for Examples
Cash Flow After Tax
Fed Tax Total Taxes Paid CFAT
-20,000.00
0.00 -2,005.50 11,851.84
0.00 -7,150.40 11,996.73
0.00 2,010.47 -2,164.14
0.00 3,430.29 -8,583.96
0.00 11,900.00 22,100.00
0.00 0.00 0.00
0.00 0.00 0.00
0.00 0.00 0.00
0.00 0.00 0.00
0.00 0.00 0.00
ROR 24.369%
Benefit Cost Spreadsheet
Interest Rate 6.00%
First Cost 60,000 First Cost
Period Costs Benefits Disbenefits
1 10,000 32,340 0
2 10,000 32,340 0
3 10,000 32,340 0
4 0 0 0
5 0 0 0
6 0 0 0
7 0 0 0
8 0 0 0
9 0 0 0
10 0 0 0
PW 26,730.12 86,445.21 0.00
Traditional B/C 0.9967
Modified B/C 0.9953
Damage 150,000 Probability 1.00000 Annual Damage 150,000.00
I 6.00% Capital Damage Annual
N 30 Costs AW Capital Operating Reduction Benefit
Option A 800,000 58,119.13 87,000 53.33% 80,000.00
B 0 0.00 -100,000 80.00% 120,000.00
C 1,450,000 105,340.92 5,000 86.67% 130,000.00
Accept Lowest Capital Cost First and then Change based on Incremental
Incremental B/C Annual Costs
Delta B vs. A -800,000 -58,119 -187,000 -245,119 40,000
C vs. B 1,450,000 105,341 105,000 210,341 10,000
Acceptance Criteria
1 Costs + Benefits Ratio >=1
2 Costs - Benefits + Ratio
3 Costs - Benefits - Ratio <=1
Incremental B/C
Interest Rate 6.00% Delta First
1,000,000 940,000 Delta Delta
Period Costs Benefits Disbenefits Period Costs Benefits
1 20,000 70,000 0 1 10,000 37,660
2 0 0 0 2 -10,000 -32,340
3 0 0 0 3 -10,000 -32,340
4 0 0 0 4 0 0
5 0 0 0 5 0 0
6 0 0 0 6 0 0
7 0 0 0 7 0 0
8 0 0 0 8 0 0
9 0 0 0 9 0 0
10 0 0 0 10 0 0
PW 18,867.92 66,037.74 0.00 PW -7,862.19 -20,407.47
Traditional B/C 0.0648 Traditional B/C
Modified B/C 0.0472 Modified B/C
Annual Traditional Modified Permanent First Cost Costs
Disbenefit B/C B/C 0 105,000
25,000.00 0.37900 -0.55059
0.00 -1.20000 #DIV/0!
0.00 1.17817 1.18662
ed on Incremental
-25,000 -0.26518 -4.33592
0 0.04754 -0.90183
Delta
Disbenefits
0
0
0
0
0
0
0
0
0
0
0.00
-0.0219
-0.0133
Benefits Interest B/C Ratio
290,000 6.00% #DIV/0!
Volume 12,000 cars/day
Opportunity Cost $0.60 per min
Location Type
Main Benefit # of Cars Time Saved Conversion Total
2000 20 0.016666667 400
Exit Benefit # of Cars Time Saved Conversion Total
2000 24 0.016666667 480
Main Cost # of Cars Time Saved Conversion Total
5000 29.6052632 0.016666667 -1,480
Main Cost # of Cars Time Saved Conversion Total
5000 8.42105263 0.016666667 -421
Project Total -1,021
Find the Real Rate of Return
Market Inflation Real i
5.50% 2.75% 2.68%
Find the Real Rate of Return
Market Real i Inflation
5.25% 1.94% 3.25%
Find the Market or Nomincal Rate
Real i Inflation Market
8.00% 6.00% 14.48%
Use P/F Templates as necessary
Inflation 6.00% Tax Rate 34.00%
Period Fixed OC Inflation OC Tax Income Taxes ATCF ATCF w/o Inflation
0 1,500 2,000 -3,500 -1,190 -2,310 -2,310
1 1,500 2,120 -3,620 -1,231 -2,389 -2,310
2 1,500 2,247 -3,747 -1,274 -2,473 -2,310
3 1,500 2,382 -3,882 -1,320 -2,562 -2,310
4 1,500 2,525 -4,025 -1,368 -2,656 -2,310
5 1,500 2,676 -4,176 -1,420 -2,756 -2,310
-2,250
-2,300 0 2 4 6 8
-2,350
-2,400
-2,450
-2,500 ATCF w/o Inflation
-2,550 ATCF
-2,600
-2,650
-2,700
-2,750
-2,800
Downpayment Rate Term State Taxes
5,000 State Tax 18.00% 3 31.00%
Period Revenues Expenses Depr % Interest Principal State Income State Tax
0 50,000
1 100,000 63,000 33.33% 8,100.000 12,596.574 12235.00 3792.85
2 102,500 67,095 44.45% 5,832.617 14,863.957 7347.38 2277.688814
3 105,063 71,472 14.81% 3,157.104 17,539.469 23028.47 7138.825865
4 107,689 76,151 7.41% 0.000 0.000 27832.68 8628.130374
5 0 0 0.00% 0.000 0.000 0.00 0
6 0 0 0.00% 0.000 0.000 0.00 0
7 0 0 0.00% 0.000 0.000 0.00 0
8 0 0 0.00% 0.000 0.000 0.00 0
9 0 0 0.00% 0.000 0.000 0.00 0
10 0 0 0.00% 0.000 0.000 0.00 0
Use for Examples
Revenues Consumables Labor Total Cost
2.50% 9.00% 5.50%
1 100,000 18,000 45,000 63,000
2 102,500 19,620 47,475 67,095
3 105,063 21,386 50,086 71,472
4 107,689 23,311 52,841 76,151
5 0 0 0 0
6 0 0 0 0
7 0 0 0 0
8 0 0 0 0
9 0 0 0 0
10 0 0 0 0
Fed Taxes
0.00% Cash Flow After Tax
Depr % Fed IncomeFed Tax Total Taxes Paid CFAT
-5,000.00
0.00% 25,107.15 0.00 3,792.85 12,510.58
0.00% 27,294.69 0.00 2,277.69 12,430.74
0.00% 23,294.64 0.00 7,138.83 5,755.18
0.00% 22,909.55 0.00 8,628.13 22,909.55
0.00% 0.00 0.00 0.00 0.00
0.00% 0.00 0.00 0.00 0.00
0.00% 0.00 0.00 0.00 0.00
0.00% 0.00 0.00 0.00 0.00
0.00% 0.00 0.00 0.00 0.00
0.00% 0.00 0.00 0.00 0.00
ROR 243.609%
P S A I n PW ROR S % Delta From Base S ROR
40,000 2,000 20,000 10.00% 2 -3,636.36 3.26% 2,000 0.00% 2,000 3.26%
40,000 3,000 20,000 10.00% 2 -2,809.92 4.84% 3,000 50.00% 3,000 4.84%
40,000 4,000 20,000 10.00% 2 -1,983.47 6.39% 4,000 100.00% 4,000 6.39%
40,000 5,000 20,000 10.00% 2 -1,157.02 7.92% 5,000 150.00% 5,000 7.92%
40,000 6,000 20,000 10.00% 2 -330.58 9.41% 6,000 200.00% 6,000 9.41%
40,000 7,000 20,000 10.00% 2 495.87 10.88% 7,000 250.00% 7,000 10.88%
40,000 8,000 20,000 10.00% 2 1,322.31 12.32% 8,000 300.00% 8,000 12.32%
40,000 9,000 20,000 10.00% 2 2,148.76 13.74% 9,000 350.00% 9,000 13.74%
40,000 10,000 20,000 10.00% 2 2,975.21 15.14% 10,000 400.00% 10,000 15.14%
40,000 11,000 20,000 10.00% 2 3,801.65 16.52% 11,000 450.00% 11,000 16.52%
40,000 12,000 20,000 10.00% 2 4,628.10 17.87% 12,000 500.00% 12,000 17.87%
20.00%
18.00%
16.00%
14.00%
12.00%
10.00%
ROR
8.00%
6.00%
4.00%
2.00%
0.00%
0 2,000 4,000 6,000 8,000 10,000 12,000 14,000
Alt 1 Alt 2 I PW1 PW2
0 -100,000 -100,000 10% 113,636 97,249 0
1 10,000 55,000 14% 77,417 76,521 1
2 20,000 49,000 18% 49,068 59,291 2
3 30,000 43,000 22% 26,610 44,809 3
4 40,000 37,000 26% 8,616 32,514 4
5 50,000 31,000 30% -5,953 21,979 5
6 60,000 25,000 34% -17,869 12,874 6
7 70,000 19,000 38% -27,704 4,944 7
8 80,000 13,000 42% -35,893 -2,012 8
9 9
10 10
140,000 35.00%
120,000
30.00%
100,000
25.00%
80,000
60,000 20.00%
PW1
40,000
PW2 15.00%
20,000
10.00%
0
0% 10% 20% 30% 40% 50%
-20,000 5.00%
-40,000
0.00%
-60,000 0.00%
Rev Cost Profit ROR 0.00% 2.00% 4.00% 6.00%
-10,000 Inflation -10,000 28.65% -10,000 -10,000 -10,000 -10,000
6,000 2,000 4,000 4,000 3,960 3,920 3,880
6,000 2,000 4,000 4,000 3,919 3,837 3,753
6,000 2,000 4,000 4,000 3,878 3,750 3,618
6,000 2,000 4,000 4,000 3,835 3,660 3,475
6,000 2,000 4,000 4,000 3,792 3,567 3,324
F 0.00% 2.00% 4.00% 6.00%
ROR 28.65% 27.32% 25.89% 24.35%
0.00% 2.00% 4.00% 6.00% 8.00% 10.00% 12.00%
8.00% 10.00% 12.00%
-10,000 -10,000 -10,000
3,840 3,800 3,760
3,667 3,580 3,491
3,481 3,338 3,190
3,279 3,072 2,853
3,061 2,779 2,475
8.00% 10.00% 12.00%
22.69% 20.87% 18.89%
ROR
12.00% 14.00%
Face Face Interest Payment Periods Term Purchase Raw ROR Inflation Real ROR
11,000 5.00% 1 9 8,500 8.75% 3.30% 5.28%
11,000 5.00% 1 9 8,500 8.75% 3.30% 5.28%
Face Face Interest Payment Periods Term Raw ROR Inflation Real ROR Purchase
11,000 5.00% 1 6 9.50% 3.30% 13.33% $7,370.46
Face Face Interest Payment Periods Term Purchase Raw ROR Inflation Real ROR
5,000 6.00% 1 6 2,500 21.66% 0.00% 21.66%
5,000 6.00% 1 6 2,800 18.86% 0.00% 18.86% 25.00%
5,000 6.00% 1 6 3,100 16.43% 0.00% 16.43%
5,000 6.00% 1 6 3,400 14.30% 0.00% 14.30% 20.00%
5,000 6.00% 1 6 3,700 12.39% 0.00% 12.39%
5,000 6.00% 1 6 4,000 10.68% 0.00% 10.68% 15.00%
5,000 6.00% 1 6 4,300 9.13% 0.00% 9.13% 10.00%
5,000 6.00% 1 6 4,600 7.72% 0.00% 7.72%
5,000 6.00% 1 6 4,900 6.41% 0.00% 6.41% 5.00%
5,000 6.00% 1 6 5,200 5.21% 0.00% 5.21%
5,000 6.00% 1 6 5,500 4.09% 0.00% 4.09% 0.00%
0
5,000 6.00% 1 6 5,800 3.04% 0.00% 3.04%
Value 2,500 4,000 1,000 -2,000 0 0 550
Prob 10.00% 20.00% 30.00% 40.00% 0.00% 0.00%
Dominance. Look at each state of nature and identify the best alternative for each state. If one alternative comes up as the b
Expectation. Using the probability that a state of nature will occur, calculate the expected outcome for each alternative and
Most Probable Future. Pick the alternative that has the best outcome for the most probable state of nature.
Aspiration - Level. Set a goal in terms of outcome and pick the alternative that has the maximum probability of equaling or e
Minimax (Maximin). Pessimistic approach which points to choosing the alternative which has the best worst outcome of all a
Maximax (Minimin). Optimistic approach which points to choosing the alternative which has the best of the best outcomes o
Hurwicz Principle. Apply a probability that the best outcome will occur for each alternative and the complement for the wors
Laplace. All outcomes equally likely, find expected value and choose best alternative of expected outcome.
Minimax Regret. Calculate the regret for each alternative for each state of nature as the difference between the outcome an
Real ROR
0 1,000 2,000 3,000 4,000 5,000 6,000 7,000
rnative comes up as the best often, we might choose it because it dominates all other alternatives.
for each alternative and select the alternative with the most favorable expected outcome.
f nature.
obability of equaling or exceeding the goal.
est worst outcome of all alternatives.
st of the best outcomes of all alternatives.
complement for the worst and calculate the expected value and pick the best expected value.
utcome.
between the outcome and the best outcome for that state. Choose the alternative that has the minimum maximum regret.
m maximum regret.
Newsboy Problem
Purchase $10.00 Newsboy Payoff Table
Price $25.00 Sell
Salvage $2.00 0 10 20 30 40 50 60
10 -$80 $150 $150 $150 $150 $150 $150
20 -$160 $70 $300 $300 $300 $300 $300
30 -$240 -$10 $220 $450 $450 $450 $450
Buy 40 -$320 -$90 $140 $370 $600 $600 $600
50 -$400 -$170 $60 $290 $520 $750 $750
60 -$480 -$250 -$20 $210 $440 $670 $900
70 -$560 -$330 -$100 $130 $360 $590 $820
Prob 0.05 0.1 0.15 0.25 0.2 0.1 0.1
Regret Matrix 0 10 20 30 40 50 60
10 $0 $0 $150 $300 $450 $600 $750
20 $80 $80 $0 $150 $300 $450 $600
30 $160 $160 $80 $0 $150 $300 $450
40 $240 $240 $160 $80 $0 $150 $300
50 $320 $320 $240 $160 $80 $0 $150
60 $400 $400 $320 $240 $160 $80 $0
70 $480 $480 $400 $320 $240 $160 $80
70 Exp Sales
$150 $138.5 34
$300 $254.0
$450 $335.0
$600 $358.5
$750 $336.0
$900 $290.5
$1,050 $222.0
0.05 1
70 Max
$900 $900
$750 $750
$600 $600
$450 $450
$300 $320
$150 $400
$0 $480
Marr 9.00% Investment 110,000 Investment 60,000
Fixed AOC 1 5,000 Fixed AOC 2 2,500
Life 7 Life 5
Capacity/Time 12 Capacity/Time 8
STAFF 1 STAFF 2
STAFF HRLY Cost 30 STAFF HRLY Cost 21
ANN Fixed Cost $26,855.96 ANN Fixed Cost $17,925.55
Per Volume Cost 2.5 Per Volume Cost 5.25
Red = Trouble
Annual Crossover 3,247.42 Time (hrs) 270.61847 # of Hours in a year = 8760
Total Cost for 2000 $31,855.96 2000 $28,425.55
4000 $36,855.96 4000 $38,925.55
6000 $41,855.96 6000 $49,425.55
Life 5 MARR 10.00%
Machine A B C
Investment 40,000 60,000 110,000
Variable Cost 21 18.5 13.5
Salvage 0 0 0
AWC $10,551.90 $15,827.85 $29,017.72
AW Delta Cost Delta Crossover
A to B $5,275.95 (2.50) 2,110.38
A to C $18,465.82 (7.50) 2,462.11
B to C $13,189.87 (5.00) 2,637.97
Needs to be RED
# of Hours in a year = 8760
MARR 8.00% Capital 150,000
Project Investment Project Equivalent Life Present Capital Feasibility
Amount Annual Cash Flow Years Worth Used 1 = Yes PW Feasible
A 60,000 12,000 4 ($20,254.48) 60,000 1 ($20,254.48)
B 80,000 13,000 5 ($28,094.77) 80,000 1 ($28,094.77)
C 40,000 9,000 7 $6,857.33 40,000 1 $6,857.33
D $0.00 0 1 $0.00
E $0.00 0 1 $0.00
AB 140,000 25,000 -$48,349.25 140,000 1 ($48,349.25)
AC 100,000 21,000 -$13,397.15 100,000 1 ($13,397.15)
AD 60,000 12,000 -$20,254.48 60,000 1 ($20,254.48)
AE 60,000 12,000 -$20,254.48 60,000 1 ($20,254.48)
BC 120,000 22,000 -$21,237.44 120,000 1 ($21,237.44)
BD 80,000 13,000 -$28,094.77 80,000 1 ($28,094.77)
BE 80,000 13,000 -$28,094.77 80,000 1 ($28,094.77)
CD 40,000 9,000 $6,857.33 40,000 1 $6,857.33
CE 40,000 9,000 $6,857.33 40,000 1 $6,857.33
DE 0 0 $0.00 0 1 $0.00
ABC 180,000 34,000 -$41,491.92 180,000 0 $0.00
ABD 140,000 25,000 -$48,349.25 140,000 1 ($48,349.25)
ABE 140,000 25,000 -$48,349.25 140,000 1 ($48,349.25)
ACD 100,000 21,000 -$13,397.15 100,000 1 ($13,397.15)
ACE 100,000 21,000 -$13,397.15 100,000 1 ($13,397.15)
ADE 60,000 12,000 -$20,254.48 60,000 1 ($20,254.48)
BCD 120,000 22,000 -$21,237.44 120,000 1 ($21,237.44)
BCE 120,000 22,000 -$21,237.44 120,000 1 ($21,237.44)
BDE 80,000 13,000 -$28,094.77 80,000 1 ($28,094.77)
CDE 40,000 9,000 $6,857.33 40,000 1 $6,857.33
ABCD 180,000 34,000 -$41,491.92 180,000 0 $0.00
ABCE 180,000 34,000 -$41,491.92 180,000 0 $0.00
ABDE 140,000 25,000 -$48,349.25 140,000 1 ($48,349.25)
ACDE 100,000 21,000 -$13,397.15 100,000 1 ($13,397.15)
BCDE 120,000 22,000 -$21,237.44 120,000 1 ($21,237.44)
ABCDE 180,000 34,000 -$41,491.92 180,000 0 $0.00
$6,857.33
Max
Length Width Depth Cost Volume Surface
45 20 8 $15,000 7,200 1940
40 24 6 $14,500 5,760 1728
36 18 7 $12,900 4,536 1404
20 10 5 $8,900 1,000 500
32 24 9 $18,500 6,912 1776
30 15 5 2,250 900
Estimate $10,191 $10,360 $10,956
Option Capacity Cost Relationship
1 800,000 $10,000,000 0.5
2 1,600,000 $14,142,136