mie375_applied_interest_rate_analysis

mie375_applied_interest_rate_analysis - 1 Applied interest...

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1 Applied interest rate analysis Reading Luenberger, Chapter 5 Goals Understand the basics of capital budgeting Construct bond portfolios Manage dynamic investments Kay Giesecke
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MS&E 242: Applied interest rate analysis 2 Capital allocation Capital allocation is the allocation of a fixed capital budget among a number of investments or projects Capital budgeting Portfolio problems (established markets) We start by considering capital budgeting problems Often arise in a firm where several proposed projects compete for funding The projects differ in scale, costs, payoffs etc. and are sometimes not mutually exclusive The budget limits the realization of projects Kay Giesecke
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MS&E 242: Applied interest rate analysis 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 payoffs) 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 X i =1 b i x i subject to m X i =1 c i x i C x i ∈ { 0 , 1 } i = 1 , 2 , . . . , m Kay Giesecke
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MS&E 242: Applied interest rate analysis 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
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MS&E 242: Applied interest rate analysis 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 -column vector of binary decision variables f is an m -column vector of coefficients A is a n × m matrix describing n constraints C is an n -column vector Kay Giesecke
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MS&E 242: Applied interest rate analysis 6 Capital budgeting Independent projects: example Given a budget C = 500 , select from the following m = 7 projects: 1 2 3 4 5 6 7 Benefit PV i 300 50 350 110 100 250 200 Cost PV c i 100 20 150 50 50 150 150 NPV b i = PV i - c i 200 30 200 60 50 100 50 P V i c i 3.00 2.50 2.33 2.20 2.00 1.67 1.33 Optimal x i 1 0 1 1 1 1 0 The optimal solution has total cost 500 and total NPV 610 The “bang for the buck” analysis based on the ratio P V i c i suggests projects 1–5 for a total cost of 370 (budget not exhausted) and NPV of 540 (suboptimal) Kay Giesecke
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MS&E 242: Applied interest rate analysis 7 Capital budgeting Using Matlab’s Binary Integer Programming function bintprog f = [-200; -30; -200; -60; -50; -100; -50]; A = [100 20 150 50 50 150 150]; c = [500]; [x,fval] = bintprog(f,A,c) x = 1 0 1 1 1 1 0 fval = -610 Kay Giesecke
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MS&E 242: Applied interest rate analysis 8 Capital budgeting Interdependent projects Suppose there are m independent goals and associated with goal i there are
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