San Tomas Development Management (STDM) in the country of UABS is in the process of completing its investment plans for the next three years. Their currency is the double, symbol D$. They currently have 2 million D$ available for investment. Every six months over the next three years, they expect the following income stream from previous investments: D$500,000 in six months, D$400,000, D$380,000, D$360,000, D$340,000, and D$ 300,000 at the end of the 3d year. There are three development projects in which STDM is considering participating. If STDM participated fully, The First City Development would have the following (projected) cash flow stream at six month intervals over the next three years (negative numbers represent investments, positive numbers represent income): -D$3,000,000,-D$1,000,000,-D$1,800,000, D$400,000, D$1,800,000, D$1,800,000, and D$5,500,000 The last number is its estimated value at the end of three years. A second project involves taking over the operations of an old middle-lower income housing on the condition that certain initial repairs be made and that it be demolished at the end of the three years. If STDM participated fully, the cash flow stream for that project would be -D$2,000,000,-D$500,000, D$1,500,000, D$1,500,000, D$1,500,000, D$200,000, and - D$1,000,000 The third project, the Delta-Orleans Hotel, would have the following cash flow stream at six month intervals: -D$2,000,000,-D$2,000,000,-D$1,800,000, D$1,000,000, D$1,000,000, D$1,000,000, and D$6,000,000 STDM can borrow money for half-year intervals at 3.5% interest per half year. At most, 2 million dollars can be borrowed at one time, i.e., the total outstanding principal can never exceed 2 million. STDM can invest surplus funds at 3% per half year. Assume first that we ignore taxes. Formulate the problem of maximizing STDM's net worth at the end of three years as a linear programming problem. If STDM participates in a project at less than 100%, all the cash flows of that project are reduced appropriately. Explain the choice of variables and constraints. Solve the model. Analyze the results, in particular pay attention to dual prices and the binding constraints. Now take taxes into account. Consider the following simplified situation. There is a tax rate of 50% on profit for any period. If there is a loss in a period, 80 percent can be carried forward to the next period. Revenues minus expenses for the three projects for each period are listed below. Expenses include depreciation. PERIOD FIRST CITY -100,000 -300,000 -600,000 -100,000 500,000 1,000,000 4,000,000 PROJECT MID HOUSING -200.000l -400,000 -200,000 500,000 1,000,000 100,000 -1,000,000 DELTA HOTEL -150,000 -200,000 -300,000 -200,000 500,000 800,000 5,000,000 17 Twenty percent of the future cash flows (the D$500,000, D$400,000, etc.) will be taxable. Formulate the problem. Analyze the results. In particular explain the impact of taxes on the optimal solution. 3 The 80% carry forward rule is only an approximation to reality. The actual rule is as follows. A loss in year i can be used to reduce the taxable profits in any of the years 1-1, 1-2, 1-3, and thereby generate an immediate refund, or it may be carried forward fully to reduce to reduce taxable profits in years i+1,i+2, 143, i+4, +5,. That is, a loss can be carried back three years and forward 5 years. The law requires that a loss be applied to the earliest year to which it is applicable. This restriction is important if the tax rate is not the same in every year. An example where the tax rate can change is if the form of company ownership changed, in which case different tax rules might apply. Assume for simplicity that each period is a year. What changes will have to be made? Do not solve. San Tomas Development Management (STDM) in the country of UABS is in the process of completing its investment plans for the next three years. Their currency is the double, symbol D$. They currently have 2 million D$ available for investment. Every six months over the next three years, they expect the following income stream from previous investments: D$500,000 in six months, D$400,000, D$380,000, D$360,000, D$340,000, and D$ 300,000 at the end of the 3d year. There are three development projects in which STDM is considering participating. If STDM participated fully, The First City Development would have the following (projected) cash flow stream at six month intervals over the next three years (negative numbers represent investments, positive numbers represent income): -D$3,000,000,-D$1,000,000,-D$1,800,000, D$400,000, D$1,800,000, D$1,800,000, and D$5,500,000 The last number is its estimated value at the end of three years. A second project involves taking over the operations of an old middle-lower income housing on the condition that certain initial repairs be made and that it be demolished at the end of the three years. If STDM participated fully, the cash flow stream for that project would be -D$2,000,000,-D$500,000, D$1,500,000, D$1,500,000, D$1,500,000, D$200,000, and - D$1,000,000 The third project, the Delta-Orleans Hotel, would have the following cash flow stream at six month intervals: -D$2,000,000,-D$2,000,000,-D$1,800,000, D$1,000,000, D$1,000,000, D$1,000,000, and D$6,000,000 STDM can borrow money for half-year intervals at 3.5% interest per half year. At most, 2 million dollars can be borrowed at one time, i.e., the total outstanding principal can never exceed 2 million. STDM can invest surplus funds at 3% per half year. Assume first that we ignore taxes. Formulate the problem of maximizing STDM's net worth at the end of three years as a linear programming problem. If STDM participates in a project at less than 100%, all the cash flows of that project are reduced appropriately. Explain the choice of variables and constraints. Solve the model. Analyze the results, in particular pay attention to dual prices and the binding constraints. Now take taxes into account. Consider the following simplified situation. There is a tax rate of 50% on profit for any period. If there is a loss in a period, 80 percent can be carried forward to the next period. Revenues minus expenses for the three projects for each period are listed below. Expenses include depreciation. PERIOD FIRST CITY -100,000 -300,000 -600,000 -100,000 500,000 1,000,000 4,000,000 PROJECT MID HOUSING -200.000l -400,000 -200,000 500,000 1,000,000 100,000 -1,000,000 DELTA HOTEL -150,000 -200,000 -300,000 -200,000 500,000 800,000 5,000,000 17 Twenty percent of the future cash flows (the D$500,000, D$400,000, etc.) will be taxable. Formulate the problem. Analyze the results. In particular explain the impact of taxes on the optimal solution. 3 The 80% carry forward rule is only an approximation to reality. The actual rule is as follows. A loss in year i can be used to reduce the taxable profits in any of the years 1-1, 1-2, 1-3, and thereby generate an immediate refund, or it may be carried forward fully to reduce to reduce taxable profits in years i+1,i+2, 143, i+4, +5,. That is, a loss can be carried back three years and forward 5 years. The law requires that a loss be applied to the earliest year to which it is applicable. This restriction is important if the tax rate is not the same in every year. An example where the tax rate can change is if the form of company ownership changed, in which case different tax rules might apply. Assume for simplicity that each period is a year. What changes will have to be made? Do not solve