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# (L07)Applied_ns - Topic 7 Applied Interest Rate Analysis...

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Primbs/Investment Science 1 Topic 7: Applied Interest Rate Analysis Reading: Luenberger Chapter 5, Sections 1, 6

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Primbs/Investment Science 2 Applied Interest Rate Analysis Capital Budgeting Valuation of a firm
Primbs/Investment Science 3 Capital Budgeting Deciding on which projects to invest in. C 1 C 2 C m

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Primbs/Investment Science 4 Capital Budgeting We need to choose a “portfolio” of these projects which maximizes our net present value. In this portfolio, we either select the entire project or we don’t do it at all. We cannot do a half of a project.
Primbs/Investment Science 5 A simple heuristic: Benefit-Cost ratio Rank projects according to their benefit-cost ratio where here benefit refers to the present value of the cash flows received after the initial cost. C 1 PV=B 1 Select the projects with the maximum benefit-cost ratio until the budget constraint is reached. (This procedure is not optimal)

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Primbs/Investment Science 6 Example Project Cost Benefit Benefit/Cost 1 100 300 3 2 20 50 2.50 3 150 350 2.33 4 50 110 2.20 Budget: \$150 Select Projects 1 and 2.
Primbs/Investment Science 7 Optimal Capital Budgeting Select a portfolio of these projects. c 1 b 1 =PV (of entire cash flow stream) x 1 Project 1: c 2 b 2 =PV x 2 Project 2: c m b m =PV x m Project m:

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Primbs/Investment Science 8 Optimal Capital Budgeting Let x i represent the amount of project i. x i =0 or 1 . The present value of our portfolio of chosen projects is: = = + + + m i i i m m b x b x b x b x 1 2 2 1 1 ... The cost of this portfolio is: = = + + + m i i i m m c x c x c x c x 0 2 2 1 1 ...
Primbs/Investment Science 9 Optimal Capital Budgeting (Can be solved in Excel) = m i i i x x b 1 max (Present Value) C x c m i i i = 1 s.t. (Budget Constraint) 1 or 0 = i x for i=1,...,m (All or nothing)

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Primbs/Investment Science 10 Interdependent Projects Different projects may represent different implementations of the same thing. Hence, we can choose one at most. c 1 b 1 =PV Project 1: c 2 b 2 =PV Project 2: Underpass Traffic Light c m b 4 =PV Project 4: c 1 b 3 =PV Project 3: One Lane Two Lane
Primbs/Investment Science 11 Optimization (More complicated dependencies can be handled likewise) (See Spreadsheet Example) = m i i i x x b 1 max (Present Value) C x c m i i i = 1 s.t. (Budget Constraint) 1 or 0 = i x for i=1,...,m (All or nothing) 1 2 1 + x x (Project 1 or 2) 1 4 3 + x x (Project 3 or 4)

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Primbs/Investment Science 12 Project Cost NPV Optimal Total 1 Concrete, 2 lanes 2000 4000 0 2 Concrete, 4 lanes 3000 5000 1 3 Asphalt, 2 lanes 1500 3000 0 4 Asphalt, 4 lanes 2200 4300 0 1
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(L07)Applied_ns - Topic 7 Applied Interest Rate Analysis...

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