Ewing Natural Gas: Investment Portfolio

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Question :

37345 Quantitative Management Practice  


You are to undertake a study to balance the risk and return of the investment portfolio of a large energy company for the next three years. 

Paper and seminar

Project selection at Ewing Natural Gas

Ewing Natural Gas is a large energy company with headquarters in Dallas, Texas. The company offers a wide variety of energy products and has annual revenues of approximately $50 billion. Because of the diverse nature of the company, its Manager for Project Development, Cliff Erland, is under continual pressure to manage project proposals from the functional areas of the company. At any point in time, there might be dozens of projects at various stages requiring a wide variety of capital expenditures, promising widely varying future revenue streams, and containing varying degrees of risk. Cliff has a difficult balancing act. The company’s CEO, J.R. Bayer, is very concerned about keeping capital expenditures within a fixed budget and managing risk. The heads of the company’s functional areas are less worried about budgets and risks; they are most concerned that their pet projects are approved. 

Cliff is currently about to meet with all parties involved to discuss project proposals for the next three years. He has proposals from the various functional areas for projects they would like to undertake. Each of these is accompanied by a schedule of capital expenditures over the next three years and a financial analysis of the expected revenue streams. These lead to an NPV for each proposal. (See the attached data file) J.R. Bayer has stated that the total of capital expenditures for the approved projects can be no more than $10 billion and that no more than $4 billion should be spent in any single year. Unfortunately, the capital expenditures for the potential list of projects is well over $10 billion, so Cliff knows that some of these very promising projects will not be approved. Each functional area wants as many of its projects to be approved as possible, but it certainly does not want to be shut out altogether. 


  1. Deterministic case: assuming there is no uncertainty to consider, find the best set of projects to invest for Cliff. 
  2. Risk evaluation: Now all of the capital expenditures in the data file shall be replaced with beta-PERT distributions. The values in the data file should be the most likely values, and each minimum and maximum for the distribution should be, respectively, 15% below and 30% above the most likely value. The NPVs should also be modelled with beta-PERT distributions, using the values in the data file as most likely values. However, their minimum and maximum values should be, respectively, 20% below and 15% above the most likely value. Given the set of projects selected in question 1, simulate the probability distribution of total NPV, and the probability that each budget is satisfied. For example, the results should include the fraction of iterations where total capital expenditures for the three-year period are no greater than $10 billion. 
  3. Recommend a set of projects to invest for Cliff under the uncertainties considered in question 2. The objective is to maximize the mean total NPV. There shall be a probability constraint on each budget: the probability that capital expenditures are within the budget should be at least 0.95. There will also be the usual (non-probabilistic) constraints that each functional area should have at least one project approved. Try to find the best set of projects and explain the solution approach you take in the report. 
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Answer :


The aim of this report is to provide the projects that suit the company’s following assumptions. They are the CAPEX of the approved project cannot be higher than $10 billion and every year, a total less than $4 billion should be spent on the projects. With the following as an aim, the first part of the study is carried out. The second part of the study, on the other hand, is quite different as some restrictions are imposed to determine the best projects for consideration based on the probability. The third part of this report will focus on identifying the suitable projects, therefore, the explanation regarding the approach taken in the report. 


The first step is about measuring the suitability of the projects when there is no uncertainty to consider. The best projects are selected based on the excel calculations such as NPV. 

Best Sets of Cases to consider

The best cases to consider will be decided based on the NPV values measured. In order to determine that, the NPV as % of total CAPEX ratio is considered to select the projects with higher NPV. If all 12 projects are considered, the best possible options can be these. The Projects selected are 4, 5, 7, 10 and 11. 4 and 5 belong to the Functional Area 1 and the projects 7 belong to the Functional Area 2. The projects 11 and 10 belong to the Functional Area 3. The following will be the CAPEX of the company and Functional Areas of the project.  

CAPEX of the company and Functional Areas of the project

Figure 1 Part-A Analysis

The Projects has the following values as NPV. The highest NPV is for the project 7 with 22.8% of total CAPEX. 

Table 1 Part-A CAPEX NPV

Project CodeNPV as % of total CAPEXNPV


This part started with the 15% below and 30% above the most likely Capex limit for the project is considered. The minimum and maximum value allocated for the NPV, on the other hand, is 15% and 20%. The beta-PERT model is identified as a suitable model and it is used for the analysis. The probability distribution of the NPV is simulated with the help of simulation tools. The following will act as the histogram for the analysis. The projects selected from the question 1 are 4, 5, 7, 10 and 11. And the following are the NPV identified. 

Table 2 Part-B NPV

Project CodeNPV

The minimum value of the NPV here is for the project 10 where the NPV is 100. The Maximum NPV is for the case is 410 million. The total worth of the projects undertaken is closer to 1.15 billion. 

 Pert Distribution

Figure 4 Histogram

The Pert Distribution indicates that the data here for the NPV is skewed positively. The simulation considered is based on a total of 2000 results. Based on it, the CAPEX and the NPV are selected to carry out the further research. 


Based on the analysis, these are the projects can be considered for the selection. 

Table 3 Projects selected

Projects Selected 
FA1 2,4 & 5 
FA3 10 & 11 

The Projects selected are 2, 4, 5, 7, 10 and 11. The projects 2, 4 and 5 belong to the Functional Area 1 and the projects 7 belong to the Functional Area 2. The projects 11 and 10 belong to the Functional Area 3. The following will be the CAPEX of the company and Functional Areas of the project.  

Table 4 NPV as % of CAPEX

Project CodeNPV as % of CAPEX 

The projects 2, 4 and 5 belong to the Functional Area 1 and the projects 7 belong to the Functional Area 2. The projects 11 and 10 belong to the Functional Area 3. Therefore, one project from each and every Functional Area is considered for the study.

Table 5 Total NPV and CAPEX

Project Code NPV as % of total CAPEX NPV CAPEX 
2 16.30% 53.5 326.7 
4 20.00% 310.00 1395.00 
5 15.70% 165.00 945.00 
7 22.80% 410.00 1620 
10 14.30% 100.00 630.00 
11 17.30% 130.00 675.00 
1115.00 5591.7 

The NPV is highest for the Project is highest for the project 7 and project 4 is the second highest on the list. The rest of the projects are selected because they meet the requirements issued by the board. The table below will exhibit the total spending of the company and a breakdown of how much they spent on each project. The total worth of the CAPEX after the end of all projects would be 5.59 billion and the NPV would be 1.15 billion. 

Table 6 Breakdown

Year 1Year 2Year 3

The Part-C chart will exhibit the table above in a chart format. 

breakdown of how much company spent on each project

Figure 5 Part-C