Rebecca Quintal MBA 555, Fall 2011 CAL# 1 04 October 2011...Rebecca Quintal MBA 555, Fall 2011 CAL# 1 04 October 2011 2 of 35 The figure below shows the Adj. NPV Profile for these

Rebecca Quintal MBA 555, Fall 2011 CAL# 1 04 October 2011

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PART I 1. Differentiate between the use of duration and modified duration to the decision maker.

Duration, as defined by Federick R. Macaulay, is the weighted average of time until cash flows are received (in present values) from the instrument / capital project that equal the investment. Shorter durations are preferable since that means that the individual cash flows are larger (shorter time required to earn back the investment). Duration is generally used for instruments that have a fixed cash flow. Modified Duration is generally used for instruments / capital projects that are sensitive to interest rates and have cash flows that are not fixed. The modified duration provides a measure of how the instrument / capital project duration changes based on interest rate changes. Therefore capital projects that have fixed rates of return may find Macaulay’s Duration a good indicator of the value to be received from the project (expressed in units of time), while capital projects that are susceptible to varying rates of return, will find modified duration (expressed in the percent change in the value of a project) a better aid in decision making.

2. Examine the NPV Profile diagnostic graph. What does the crossover of NPV profiles mean to the decision-maker?

A crossover of the Net Present Value Profile indicates that a project that has a better return at say a low discount rate, and is preferred over other projects, will have another project crossover it and the other project will then become the preferred project at a higher discount rate. The crossover point indicates at what discount rate there is a switch to a different preferred project. Decision makers can use this information to decide which capital project to select based on the discount rate they expect to achieve.

Graphs of the Adjusted Net Present Value (Adj. NPV) Profile of the top 5 ranking projects were made and analyzed. As the table below shows, the top five projects ranked on Adj. NPV were 7, 17, 19, 9 and 20.

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The figure below shows the Adj. NPV Profile for these five projects and there is no crossover observed. Project 7 is the preferred project (highest Adj. NPV) at all interest rates used in the graph.

However, if the top projects, as identified if the Conditional Variance at Risk (CVaR), are graphed (4, 6, 14, 16 and 2) we do see a crossover point. Project 2 has the highest Adj. NPV at low discount rates, but then at approximately 7%, project 6 becomes the preferred project. Project 6 remains the preferred project for all interest rates graphed greater than 7%. Project 2 continues to “crossover” the other projects, and becomes the least preferred project once the discount rate reaches approximately 12% or greater.

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3. Are rankings produced by the traditional ranking methods consistent across all twenty projects? Focus on NPV (Adj NPV), IRR, and CVaR at a minimum.

The project rankings produced by the traditional ranking methods do not produce the same order of project rankings. A subset of Table 1 is provided below, which displays the Adj NPV, IRR, and CVaR values. Adjusted Net Present Value and Internal Rate of Return provide the same results for the top five projects, while Conditional Value at Risk ranks the projects very differently. CVaR provides a measure of the potential losses and provides a weighted average of VaR and the losses that exceed VaR. Thus, a project that may rank high in CVaR (minimal risk) may not provide the best returns if the project is successful, which can be determined by such indicator as Adj. NPV and IRR.

Project Rankings Adj. NPV IRR CVaR

Rank 1 Project 7 Project 7 Project 4 Rank 2 Project 17 Project 17 Project 6 Rank 3 Project 19 Project 19 Project 14 Rank 4 Project 9 Project 9 Project 16 Rank 5 Project 20 Project 20 Project 2 Rank 6 Project 5 Project 10 Project 13


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Rank 7 Project 1 Project 11 Project 11 Rank 8 Project 3 Project 5 Project 10 Rank 9 Project 10 Project 15 Project 15

Rank 10 Project 15 Project 13 Project 12 Rank 11 Project 11 Project 3 Project 3 Rank 12 Project 13 Project 1 Project 20 Rank 13 Project 6 Project 18 Project 9 Rank 14 Project 4 Project 8 Project 8 Rank 15 Project 16 Project 12 Project 19 Rank 16 Project 2 Project 2 Project 18 Rank 17 Project 14 Project 16 Project 5 Rank 18 Project 8 Project 6 Project 1 Rank 19 Project 18 Project 14 Project 17 Rank 20 Project 12 Project 4 Project 7

4. Are project ranks produced by Duration consistent with those produced by Time Spread? If not, then, how different are the rankings (that is, is the difference material to the decision maker?).

The project rankings as produced by Duration (Dur@R) and Time Spread (TS@R) are very similar with the only differences occurring at the ranking of the 10th and 11th project (see first table). The Duration technique places project 20 in 10th place and project 10 in 11th place, while the Time Spread technique ranks project 10 and 20 in the opposite order. All other rankings are identical. Therefore, the project ranking from one of these methods compared to the other is not really material to the decision maker. The techniques appear to provide redundant information.

5. As a decision-maker, how can you use the VaR and CVaR measures to resolve conflicts between NPV (or Adjusted NPV) and IRR)? Since VaR and CVaR provides an estimate of the level of loss on a project, the company decision makers can use these measures to choose projects that are likely to provide good cash flows but also limit the amount of risk to the company if the project(s) should fail.

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PART II

1. Identify which projects (optima portfolio) the firm should accept/reject under the constrained optimization plan. Under the constrained optimization plan the best projects to accept are Projects 2, 5, 7, 9, 10, 11, 15, 17, 19, and 20 as shown in the table reproduced below. The optimal budget is $410,787.00.

OPTIMAL Iterations 82

Obj. Value 410787

VARIABLE VALUE Project 1 0 Project 2 1 Project 3 0 Project 4 0 Project 5 1 Project 6 0 Project 7 1 Project 8 0 Project 9 1 Project 10 1 Project 11 1 Project 12 0 Project 13 0 Project 14 0 Project 15 1 Project 16 0 Project 17 1 Project 18 0 Project 19 1 Project 20 1 Project 21 0

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2. Compare the solution in (a) above with that achieved by the traditional ranking method

(portfolio). If we compare the project rankings in the constrained optimization plan to the traditional portfolio method we will see that many of the same projects were selected. For example, in the table below several of the selected projects in the constrained optimization plan (left two columns) are highlighted in yellow. Projects, 7, 17, 19, 9, 20 and 5 were ranked 1 through 6, respectively in Adj. NPV and ranked 1 through 5, and then ranking 8, respectively in IRR. Note that many of these same projects are ranked low in CVaR, which indicates, should these projects fail, that the losses could be significant.


VARIABLE VALUE

Rank 1 Project 7 Project 7 Project 4

Project 1 0 Rank 2 Project 17 Project 17 Project 6

Project 2 1



Project 4 0



Project 6 0



Project 8 0



Project 10 1



Project 12 0



Project 14 0



Project 16 0



Project 18 0



Project 20 1

Project 21 0

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3. As a manager, how would you reconcile the portfolio of accepted projects obtained by the

simple ranking method compared to that produced by the efficient optimization? As a manager, I would select the projects that rank highest in NPV that also were selected by the constrained optimization plan. With this approach, we would be positioned to provide the best cash flows (in present value). The optimal budget, as determined by constrained optimization plan, is $410,787.00. Based on Adj. NPV that means that we should accept the top six ranked projects as is shown in the below table. The cumulative Adj. NPV of the top six projects is $399,152. Taking on the seventh project would increase the budget to $416,609 and therefore would exceed the optimal budget.

PART III

1. Analyze the results. When making capital budget decisions such as choosing which projects to launch, many variables must be considered. First the selected projects must have positive Adj. NPV. As can be seen in the table below, and the Decision tables at the end of this document, Projects, 2, 4, 6, 8, 12, 14, 16 and 18 all have both negative Adj. NPV and also negative NVP with timed outflows. The doesn’t mean that the projects are expected to lose money, but rather the initial investment many be large and the annual returns may be small in comparison and therefore require many years to break even. Project 18 is an example of this type of project; it has an initial investment of $93,443 and the sum of cash flows after 10 periods is only $134,023.54. Therefore, the NPV of that project ends up being negative.


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Other variables that a manager would evaluate when selecting capital projects are the Duration and Time Spread at the Discount Rate. For both duration and time spread, it is better to have the numbers below. That is the amount of time that it takes to earn back money invested for the project (time spread) and can also take into consideration the size of the of the cash flows (duration). The preferred projects have returns on the investment that are high and come quickly after the initial investment. As can be seen below, two of the top six projects, as defined in the rankings, have comparatively low time spread and duration (projects 7 and 17). Projects with very high duration and time spread are not good candidates (e.g. project 2, 4, 6, 12, 14, and 16).


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Other considerations when selecting capital projects is to compare the rewards of the project (Adj. NPV) to the potential risk of losing money on the investment if the project does not perform as proposed. The below table plots both Adj. NPV and two risk indicators Variance at Risk (VaR) and Conditional Variance at Risk (CVaR). First only projects with positive Adj. NPV would be selected. Next a decision maker would look at projects that have relatively high Adj. NPV compared to the VaR and CVaR values. This means that the likely rewards are great compared to the risks. Certainly, projects with too high VaR and CVaR should be avoided as too risky. As the graphic shows below, projects, 7, 17, 19, 9, 20 and 5 are the best candidates (in that order) based on this analysis. This is also the exact order the projects were ranked in the traditional ranking method using the Adj. NPV indicator alone.

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TABLES / GRAPHICS

Cash Flows Project 1 Project 1 Project 2 Project 2 Project 3

E R E R E

Discount Rate (eg: 0.15)

11.00% 11.00% 11.00% 11.00% 11.00%

Purchase ($) \ Salvage ($)

$80,262 $840 $16,460 $91 $44,530

Period_1 $16,134 $1,652

Period_2 $16,083 $1,648

Period_3 $16,017 $1,643

Period_4 $16,100 $1,649

Period_5 $16,069 $1,647

Period_6 $815 $16,027 $1,644

Period_7 $807 $15,924 $1,636

Period_8 $797 $16,163 $1,654

Period_9 $809 $16,037 $1,644

Period_10 $805 $16,132 $1,651

Period_11 $1,644

Period_12 $1,644

Period_13 $1,653

Period_14 $1,648

Period_15 $1,640

Period_16

Period_17

Period_18

Period_19

Period_20

Sum of Flows -->

$84,297.30 $160,690.53 $16,460.93 $24,705.93 $44,530.58


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Cash Flows

Project 3 Project 4 Project 4 Project 5 Project 5 Project 6

R E R E R E


11.00% 11.00% 11.00% 11.00% 11.00% 11.00%


$740 $6,039 $99 $80,307 $7,637 $5,094

Period_1 $8,826 $337 $15,353

Period_2 $8,934 $334 $15,218

Period_3 $8,943 $328 $15,935

Period_4 $8,852 $332 $16,574

Period_5 $8,867 $335 $15,839

Period_6 $8,903 $333 $15,570

Period_7 $8,852 $347 $16,781

Period_8 $8,890 $330 $16,473

Period_9 $8,890 $339 $16,343

Period_10 $8,939 $329 $17,099

Period_11 $342

Period_12 $333

Period_13 $325

Period_14 $328

Period_15 $328

Period_16 $334

Period_17 $320

Period_18 $328

Period_19 $329

Period_20 $333

Sum of Flows -->

$88,902.01 $6,039.14 $6,653.96 $80,307.91 $161,191.29 $5,094.76


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Cash Flows

Project 6 Project 7 Project 7 Project 8 Project 8

R E R E R


11.00% 11.00% 11.00% 11.00% 11.00%


$75 $49,945 $4,360 $76,647 $1,195

Period_1 $387 $35,750 $11,151

Period_2 $386 $34,926 $11,083

Period_3 $391 $36,025 $11,173

Period_4 $395 $33,581 $10,973

Period_5 $390 $11,004

Period_6 $388 $11,056

Period_7 $396 $10,938

Period_8 $394 $10,905

Period_9 $393 $10,771

Period_10 $398 $10,919

Period_11 $392

Period_12 $384

Period_13 $392

Period_14 $384

Period_15 $387

Period_16

Period_17

Period_18

Period_19

Period_20

Sum of Flows -->

$5,863.49 $49,945.22 $140,284.21 $76,647.03 $109,978.08


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Cash Flows


E R E R E


11.00% 11.00% 11.00% 11.00% 11.00%


$33,394 $2,764 $11,676 $893 $11,676

Period_1 $10,990 $2,873

Period_2 $11,087 $2,904

Period_3 $11,456 $3,023

Period_4 $11,213 $2,945

Period_5 $11,323 $2,981

Period_6 $10,940 $2,857

Period_7 $11,144 $2,923

Period_8 $11,057 $2,895

Period_9 $11,291 $2,970

Period_10 $11,268 $2,963

Period_11

Period_12

Period_13

Period_14

Period_15

Period_16

Period_17

Period_18

Period_19

Period_20

Sum of Flows -->

$33,394.57 $111,773.88 $11,676.21 $29,338.76 $11,676.21


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Cash Flows


R E R E R


11.00% 11.00% 11.00% 11.00% 11.00%


$893 $87,532 $8,019 $10,889 $698

Period_1 $2,419 $7,999 $2,112

Period_2 $2,297 $8,825 $2,184

Period_3 $2,310 $8,557 $2,160

Period_4 $2,395 $8,678 $2,171

Period_5 $2,090 $8,712 $2,174

Period_6 $2,360 $9,757 $2,265

Period_7 $2,323 $7,881 $2,101

Period_8 $2,480 $8,698 $2,173

Period_9 $2,266 $7,679 $2,084

Period_10 $2,435 $8,650 $2,168

Period_11 $9,542

Period_12 $9,032

Period_13 $8,662

Period_14 $10,334

Period_15 $9,294

Period_16

Period_17

Period_18

Period_19

Period_20

Sum of Flows -->

$23,380.87 $87,532.16 $132,305.51 $10,889.31 $21,596.24


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Cash Flows


E R E R E


11.00% 11.00% 11.00% 11.00% 11.00%


$9,788 $679 $20,430 $1,918 $7,369

Period_1 $470 $3,670

Period_2 $576 $4,269

Period_3 $572 $4,246

Period_4 $526 $3,986

Period_5 $527 $3,995

Period_6 $553 $4,139

Period_7 $590 $4,349

Period_8 $514 $3,918

Period_9 $507 $3,878

Period_10 $538 $4,059

Period_11 $566

Period_12 $528

Period_13 $572

Period_14 $553

Period_15 $574

Period_16 $541

Period_17 $468

Period_18 $565

Period_19 $580

Period_20 $560

Sum of Flows -->

$9,788.03 $10,887.74 $20,430.98 $40,513.56 $7,369.72


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Cash Flows


R E R E R


11.00% 11.00% 11.00% 11.00% 11.00%


$586 $34,431 $1,938 $93,443 $3,273

Period_1 $536 $22,451 $13,985

Period_2 $552 $22,712 $13,635

Period_3 $577 $23,134 $13,170

Period_4 $519 $22,163 $13,476

Period_5 $588 $13,242

Period_6 $565 $13,287

Period_7 $596 $13,481

Period_8 $575 $13,316

Period_9 $542 $13,417

Period_10 $568 $13,010

Period_11 $538

Period_12 $558

Period_13 $603

Period_14 $572

Period_15 $536

Period_16

Period_17

Period_18

Period_19

Period_20

Sum of Flows -->

$8,431.97 $34,431.95 $90,461.81 $93,443.22 $134,023.54


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Cash Flows

Project 19 Project 19 Project 20 Project 20

E R E R


11.00% 11.00% 11.00% 11.00%


$37,912 $3,185 $37,912 $3,185

Period_1 $13,256 $9,777

Period_2 $12,916 $9,378

Period_3 $12,463 $9,722

Period_4 $12,761 $8,866

Period_5 $12,533 $9,435

Period_6 $12,577 $9,628

Period_7 $12,766 $9,450

Period_8 $12,606 $10,019

Period_9 $12,704 $9,411

Period_10 $12,308 $9,432

Period_11

Period_12

Period_13

Period_14

Period_15

Period_16

Period_17

Period_18

Period_19

Period_20

Sum of Flows --> $37,912.71 $126,894.61 $37,912.71 $95,122.74


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Decision

Project 1 Project 2 Project 3 Project 4 Ranking Criterion

Payback(Simple) 4.991 9.993 5.012 18.147

Naive ROR 20.04% 10.01% 19.95% 5.51%

Payback(Discounted) 7.905 #NUM! 7.692 #NUM!

Unrecovered Investment (E)

$0 $21,991 $0 $27,157

Unrecovered Investment (R)

$0 $21,991 $0 $27,157

IRR w/ Timed Outflows (UIRR)

13.76% 5.45% 14.11% 1.07%

MIRR w/ Timed Outflows (UMIRR)

12.86% 5.19% 13.28% 1.04%

NPV w/ Timed Outflows (UNPV)

$12,910 $(4,596) $8,073 $(3,368)

Profitability Index (PI) 1.161 0.721 1.181 0.442

Adj. NPV $17,456 $(5,090) $10,916 $(3,368)

Adjusted PI 1.217 0.691 1.245 0.442

Duration @R Rate 4.669 6.140 4.683 7.294

Duration @IRR 4.478 7.038 4.468 10.239

Modified Duration 4.104 5.822 4.104 7.216

Time Spread (TS) @R Rate

5.092 7.064 5.108 8.889

Time Spread (TS) @IRR

4.993 7.529 4.996 10.420

StdDev of Net DCF $3,124 $361 $1,633 $79

VaR (NPV) $14,443 $1,386 $7,929 $264

CVaR (NPV) $15,724 $1,534 $8,599 $297


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Decision


Payback(Simple) 5.089 13.009 1.406 6.933

Naive ROR 19.65% 7.69% 71.10% 14.42%



$0 $10,854 $0 $32,046


$0 $10,854 $0 $32,046


14.40% 1.94% 47.64% 7.12%


14.13% 1.85% 43.00% 6.64%


$16,503 $(2,268) $61,944 $(11,286)


Adj. NPV $22,315 $(2,512) $158,998 $(15,261)

Adjusted PI 1.278 0.507 4.183 0.801

Duration @R Rate 4.881 6.184 2.394 4.665

Duration @IRR 4.631 7.721 2.050 4.952



5.329 7.116 2.460 5.090


5.200 7.903 2.284 5.236

StdDev of Net DCF $2,670 $85 $4,199 $2,092

VaR (NPV) $13,817 $327 $34,183 $9,946

CVaR (NPV) $14,912 $362 $35,905 $10,804


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Decision


Payback(Simple) 2.988 3.976 5.069 10.219

Naive ROR 33.47% 25.15% 19.73% 9.79%

Payback(Discounted) 3.828 5.530 7.689 #NUM!


$0 $0 $0 $111,608


$0 $0 $0 $111,608


27.30% 19.75% 14.48% 5.95%


26.59% 19.19% 14.07% 5.98%


$33,360 $5,902 $2,392 $(23,326)


Adj. NPV $45,109 $7,981 $3,235 $(25,832)

Adjusted PI 2.351 1.684 1.277 0.705

Duration @R Rate 4.739 4.759 4.777 6.475

Duration @IRR 3.731 4.168 4.522 7.372



5.173 5.196 5.227 7.492


4.630 4.885 5.095 7.956

StdDev of Net DCF $2,040 $534 $437 $1,805

VaR (NPV) $9,944 $2,608 $2,096 $7,147

CVaR (NPV) $10,781 $2,827 $2,275 $7,887


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Decision


Payback(Simple) 5.038 18.071 5.064 13.082

Naive ROR 19.85% 5.53% 19.75% 7.64%



$0 $43,530 $0 $15,404


$0 $43,530 $0 $15,404


14.23% 1.54% 14.33% 2.45%


13.74% 1.56% 14.05% 2.47%


$2,078 $(5,399) $4,072 $(3,219)


Adj. NPV $2,809 $(5,399) $5,507 $(3,565)

Adjusted PI 1.258 0.448 1.270 0.516

Duration @R Rate 4.757 7.573 4.822 6.431

Duration @IRR 4.528 10.566 4.583 7.988



5.193 9.287 5.261 7.437


5.074 10.843 5.138 8.233

StdDev of Net DCF $396 $125 $733 $119

VaR (NPV) $1,926 $423 $3,593 $466

CVaR (NPV) $2,089 $474 $3,893 $515


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Decision Project 17 Project 18 Project 19 Project 20

Ranking Criterion

Payback(Simple) 1.527 6.938 2.942 4.018

Naive ROR 65.47% 14.41% 33.99% 24.89%

Payback(Discounted)

1.771 #NUM! 3.758 5.572


$0 $37,068 $0 $0


$0 $37,068 $0 $0


43.67% 7.32% 27.67% 19.79%


38.76% 6.92% 26.94% 19.29%


$37,020 $(13,054) $38,238 $19,227

Profitability Index (PI)

2.075 0.860 2.009 1.507

Adj. NPV $95,024 $(17,652) $51,705 $25,998

Adjusted PI 3.760 0.811 2.364 1.686

Duration @R Rate 2.398 4.693 4.694 4.757

Duration @IRR 2.087 4.972 3.664 4.155



2.464 5.129 5.131 5.199


2.304 5.271 4.574 4.883

StdDev of Net DCF $2,384 $2,608 $2,473 $1,777

VaR (NPV) $21,477 $12,227 $11,583 $8,534

CVaR (NPV) $22,455 $13,296 $12,597 $9,262


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Rankings

Project Rankings

Payback IRR MIRR NPV Adj. NPV

Rank 1 Project 7 Project 7 Project 7 Project 7 Project 7





















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Rankings

Project Rankings Dur@R TS@R CVaR






















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Cumulative Benefits

Cum. Benefits Payback IRR MIRR NPV Adj. NPV

Rank 1 1.406 47.60% 43.00% $61,944 $158,998

Rank 2 1.527 43.70% 38.80% $100,182 $254,023

Rank 3 2.942 27.70% 26.90% $137,203 $305,728

Rank 4 2.988 27.30% 26.60% $170,564 $350,838

Rank 5 3.976 19.80% 19.30% $189,791 $376,836

Rank 6 4.018 19.70% 19.20% $206,294 $399,152

Rank 7 4.991 14.50% 14.10% $219,205 $416,609

Rank 8 5.012 14.40% 14.10% $227,278 $427,526

Rank 9 5.038 14.30% 14.10% $233,180 $435,507

Rank 10 5.064 14.20% 13.70% $237,253 $441,014

Rank 11 5.069 14.10% 13.30% $239,646 $444,249

Rank 12 5.089 13.80% 12.90% $241,724 $447,059

Rank 13 6.933 7.30% 6.90% $239,455 $444,547

Rank 14 6.938 7.10% 6.60% $236,236 $441,179

Rank 15 9.993 5.90% 6.00% $232,867 $437,613

Rank 16 10.219 5.50% 5.20% $228,271 $432,523

Rank 17 13.009 2.50% 2.50% $222,872 $427,124

Rank 18 13.082 1.90% 1.90% $211,585 $411,863

Rank 19 18.071 1.50% 1.60% $198,530 $394,210

Rank 20 18.147 1.10% 1.00% $175,204 $368,377


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Cumulative Benefits

Cum. Benefits Dur@R TS@R CVaR Optimal

Rank 1 2.394 2.460 297.399 $410,787

Rank 2 2.398 2.464 362.699

Rank 3 4.665 5.090 474.701

Rank 4 4.669 5.092 515.183

Rank 5 4.683 5.108 1534.753

Rank 6 4.693 5.129 2089.101

Rank 7 4.694 5.131 2275.847

Rank 8 4.739 5.173 2827.577

Rank 9 4.757 5.193 3893.840

Rank 10 4.757 5.196 7887.820

Rank 11 4.759 5.199 8599.811

Rank 12 4.777 5.227 9262.778

Rank 13 4.822 5.261 10781.312

Rank 14 4.881 5.329 10804.041

Rank 15 6.140 7.064 12597.744

Rank 16 6.184 7.116 13296.484

Rank 17 6.431 7.437 14912.686

Rank 18 6.475 7.492 15724.653

Rank 19 7.294 8.889 22455.221

Rank 20 7.573 9.287 35905.608


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Zero/One Model Project 1 Project 2 Project 3 Project 4 Project 5 I I I I I

MAX NPV (Adjusted) 17,456 -5,090 10,916 -3,368 22,315

Expense 80,262 16,460 44,530 6,039 80,307

C2:Mutually Exclusive 1

C3:Time Delay P(7)

C4:Mutually Exclusive

C5:At least 4 from 8 1

P(2) if P(9) is accepted

1


1

Zero/One Model

Project 6 Project 7 Project 8 Project 9 Project 10 I I I I I

MAX NPV (Adjusted) -2,512 158,998 -15,261 45,109 7,981

Expense 5,094 49,945 76,647 33,394 11,676


C3:Time Delay P(7) 1


C5:At least 4 from 8 1 1 1 1


-1



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Zero/One Model Project 11 Project 12 Project 13 Project 14 Project 15 I I I I I

MAX NPV (Adjusted)

3,235 -25,832 2,809 -5,399 5,507

Expense 11,676 87,532 10,889 9,788 20,430


C3:Time Delay P(7)


1

C5:At least 4 from 8 1 1



Zero/One Model

Project 16 Project 17 Project 18 Project 19 Project 20 I I I I I

MAX NPV (Adjusted)

-3,565 95,024 -17,652 51,705 25,998

Expense 7,369 34,431 93,443 37,912 37,912


C3:Time Delay P(7)


C5:At least 4 from 8 1



-1


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Zero/One Model

Project 21 Sense RHS I

MAX NPV (Adjusted) 143098

Expense ≤ 680,171

C2:Mutually Exclusive ≤ 1

C3:Time Delay P(7) 1 ≤ 1

C4:Mutually Exclusive ≤ 1

C5:At least 4 from 8 ≥ 4

P(2) if P(9) is accepted = 0

P(3) if P(18) is accepted = 0


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Capital Budgeting Optimal Solution

OPTIMAL

Iterations 82.000

Obj. Value 410787.000

VARIABLE VALUE

Project 1 0.000

Project 2 1.000

Project 3 0.000

Project 4 0.000

Project 5 1.000

Project 6 0.000

Project 7 1.000

Project 8 0.000

Project 9 1.000

Project 10 1.000

Project 11 1.000

Project 12 0.000

Project 13 0.000

Project 14 0.000

Project 15 1.000

Project 16 0.000

Project 17 1.000

Project 18 0.000

Project 19 1.000

Project 20 1.000

Project 21 0.000


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Documents

Rebecca Quintal MBA 555, Fall 2011 CAL# 1 04 October 2011...Rebecca Quintal MBA 555, Fall 2011 CAL# 1 04 October 2011 2 of 35 The figure below shows the Adj. NPV Profile for these