Chapter 04

# Chapter 04 - 1 Applied interest rate analysis Topics This...

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1 Applied interest rate analysis Topics This class: Capital budgeting Cash matching Kay Giesecke

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Finance 2 Capital budgeting Capital budgeting is the allocation of a fixed capital budget among a number of investments or projects Often arise in a firm where several proposed projects compete for funding The projects di ff er in scale, costs, payo ff s etc. and are sometimes not mutually exclusive The budget limits the realization of projects; the goal is to select the optimal set of projects Kay Giesecke
Finance 3 Capital budgeting Independent projects Suppose we need to select from a list of m independent projects given a budget (total capital) of C b i is the benefit (e.g. NPV of payo ff s) of project i c i is the cost (e.g. PV of cash outflows) of project i We formulate the 0-1 programming problem maximize m i =1 b i x i subject to m i =1 c i x i C x i { 0 , 1 } i = 1 , 2 , . . . , m Kay Giesecke

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Finance 4 Capital budgeting Independent projects The variable x i is an indicator variable x i = 0 : project i is not carried out x i = 1 : project i is carried out Additional constraints can easily be added At most 3 projects can be carried out: m i =1 x i 3 If project 1 is carried out, project 4 must also be carried out: x 1 x 4 0 If project 3 is carried out, project 5 cannot be carried out: x 3 + x 5 1 Solution: branch and bound etc. Kay Giesecke
Finance 5 Capital budgeting Independent projects With several constraints, the problem is conveniently represented in matrix form The 0-1 programming problem is then max x f T · x subject to A · x C, x i { 0 , 1 } where x is an m

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