Problem 1: The ABC Company has to determine its capital budget for the coming 3 years, for which data (in thousands of dollar) are given in the following table.
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Investment Project
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End of year
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Available Investment Capital
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1
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2
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3
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4
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5
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6
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0
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300
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-50
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-100
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-60
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-50
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-170
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-16
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1
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100
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-80
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-50
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-60
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-100
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-40
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-25
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2
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200
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20
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-20
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-60
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-150
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50
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-40
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Discounted Future revenues
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150
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210
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-220
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350
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200
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100
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At the start of year 1 the company has $300,000 available for investment; in year 2 another $100,000 becomes available, at the start of year 3 an additional $200,000 becomes available. Project 1 requires $50,000 at the start of year 1 and another $80,000 at the start of year 2; at the start of year 3, the project yields $20,000. The yield at the start of year 3 and the discounted yields for later years amount to $150,000. The company can borrow at most $50,000 plus 20% of the money invested so far in the various investment projects at an interest rate 12% per year. If the company deposits money at bank, the interest rate is 8%. The company has a bank debt of $10,000, on which it pays 11% interest and which may be repaid at the start of any year. Assume that the company may undertake 100% of each project or take a participation in each project of less than 100%.
a. Formulate the capital budgeting problem by using the horizon model.
b. Find the optimal capital allocations by using a linear programming package.
c. Find the optimal capital budget, assuming that no project can be undertaken partially.