1. The Volta River Authority (VRA) has scheduled the construction of new thermal plants five, ten,...

  
 
 

 

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1. The Volta River Authority (VRA) has scheduled the construction of new thermal plants five, ten, and twenty years from now to meet the needs of the country's growing population. To finance the construction of these plants, VRA needs to invest some of the company's money now to meet these future cash-flow needs. VRA may invest in only three kinds of financial assets, each of which costs $1 million per unit. Fractional units may be purchased. The assets will yield income five, ten, and twenty years from now, and that income is needed to cover at least the minimum cash- flow requirements in those years. (Any excess income above the minimum requirement for each time period will be used to increase dividend payments to shareholders rather than saving it to help meet the minimum cash-flow requirement in the next time period.) The following table shows both the amount of income generated by each unit of each asset and the minimum amount of income needed for each of the future time periods when a new thermal plant will be constructed. Year five ten twenty Income per Unit of Asset Asset 2 $1 million $0.5 million $1.5 million Asset 1 $2 million $0.5 million 0 Asset 3 $0.5 million $1 million $2 million Minimum Cash Flow Required 400 million $100 million $300 million VRA wishes to determine the mix of investments in these assets that will cover the cash-flow requirements while minimizing the total amount invested. (a) Formulate a linear programming model for this problem (7 marks). (b) Suppose VRA plans to purchase a mix of 100 units of Asset 1, 100 units of Asset 2, and 80 units of Asset 3. i. How much cash flow would this mix of investments generate five, ten, and twenty years from now and what would be the total amount invested? (4 marks) Year 5 Cash flow Year 20 Cash flow Year 10 Cash flow- Total cost- il. Is this purchasing plan feasible? Explain. (3 marks) Below is a portion of the sensitivity report for VRA's investment problem. Variable Cells (values are in Smillions) Asset 1 = Asset 3 == Name Asset 1 Asset 2 Asset 3 aminer: D Final Reduced Objective Allowable Allowable Value Cost Coefficient Increase Decrease 100 $0 0.2 200 SO 0.5 0 0.083333 0.0833333 1 1 1 Constraints (values are in Smillion) Name Year 5 Year 10 150 Year 20 300 Final Shadow Constraint Value Price R.H. Side 400 0.5 0 0.333333 400 100 300 1 0.0625 1E+30 e. What are the optimal units of Asset 1, Asset 2 and Asset 3 to purchase in order to realize the stated objective of VRA (3 marks) Allowable Increase IE+30 50 300 Allowable Decrease 200 1E+30 300 Asset 2= d. Given the reported optimal units of Asset 1, Asset 2 and Asset 3 to purchase in order to realize the stated objective of VRA, what would be the respective cash flows realized in year five, ten and twenty? (3 marks) Year 5 Cash flow- Year 20 Cash flow === Year 10 Cash flow- e. Suppose the cost per unit of Asset 1 changes to $950,000. Will the optimal purchased units change, and what will be the effect on total cost of the three assets? (3 marks) f. How would you explain the reduced cost of Asset 3 in relation to the final value of zero for Asset 3? (2 marks) 1. The Volta River Authority (VRA) has scheduled the construction of new thermal plants five, ten, and twenty years from now to meet the needs of the country's growing population. To finance the construction of these plants, VRA needs to invest some of the company's money now to meet these future cash-flow needs. VRA may invest in only three kinds of financial assets, each of which costs $1 million per unit. Fractional units may be purchased. The assets will yield income five, ten, and twenty years from now, and that income is needed to cover at least the minimum cash- flow requirements in those years. (Any excess income above the minimum requirement for each time period will be used to increase dividend payments to shareholders rather than saving it to help meet the minimum cash-flow requirement in the next time period.) The following table shows both the amount of income generated by each unit of each asset and the minimum amount of income needed for each of the future time periods when a new thermal plant will be constructed. Year five ten twenty Income per Unit of Asset Asset 2 $1 million $0.5 million $1.5 million Asset 1 $2 million $0.5 million 0 Asset 3 $0.5 million $1 million $2 million Minimum Cash Flow Required 400 million $100 million $300 million VRA wishes to determine the mix of investments in these assets that will cover the cash-flow requirements while minimizing the total amount invested. (a) Formulate a linear programming model for this problem (7 marks). (b) Suppose VRA plans to purchase a mix of 100 units of Asset 1, 100 units of Asset 2, and 80 units of Asset 3. i. How much cash flow would this mix of investments generate five, ten, and twenty years from now and what would be the total amount invested? (4 marks) Year 5 Cash flow Year 20 Cash flow Year 10 Cash flow- Total cost- il. Is this purchasing plan feasible? Explain. (3 marks) Below is a portion of the sensitivity report for VRA's investment problem. Variable Cells (values are in Smillions) Asset 1 = Asset 3 == Name Asset 1 Asset 2 Asset 3 aminer: D Final Reduced Objective Allowable Allowable Value Cost Coefficient Increase Decrease 100 $0 0.2 200 SO 0.5 0 0.083333 0.0833333 1 1 1 Constraints (values are in Smillion) Name Year 5 Year 10 150 Year 20 300 Final Shadow Constraint Value Price R.H. Side 400 0.5 0 0.333333 400 100 300 1 0.0625 1E+30 e. What are the optimal units of Asset 1, Asset 2 and Asset 3 to purchase in order to realize the stated objective of VRA (3 marks) Allowable Increase IE+30 50 300 Allowable Decrease 200 1E+30 300 Asset 2= d. Given the reported optimal units of Asset 1, Asset 2 and Asset 3 to purchase in order to realize the stated objective of VRA, what would be the respective cash flows realized in year five, ten and twenty? (3 marks) Year 5 Cash flow- Year 20 Cash flow === Year 10 Cash flow- e. Suppose the cost per unit of Asset 1 changes to $950,000. Will the optimal purchased units change, and what will be the effect on total cost of the three assets? (3 marks) f. How would you explain the reduced cost of Asset 3 in relation to the final value of zero for Asset 3? (2 marks)

Answer rating: 100% (QA)

a Formulate a linear programming model for this problem Let x number of units of Asset 1 to be purchased x number of units of Asset 2 to be purchased ... View the full answer