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Unformatted text preview: 1 Applied interest rate analysis Reading • Luenberger, Chapter 5 Goals • Understand the basics of capital budgeting • Construct bond portfolios • Manage dynamic investments Kay Giesecke 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 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 01 programming problem maximize m X i =1 b i x i subject to m X i =1 c i x i ≤ C x i ∈ { , 1 } i = 1 , 2 ,...,m Kay Giesecke 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 ≤ – If project 3 is carried out, project 5 cannot be carried out: x 3 + x 5 ≤ 1 • Solution: branch and bound etc. Kay Giesecke MS&E 242: Applied interest rate analysis 5 Capital budgeting Independent projects • With several constraints, the problem is conveniently represented in matrix form • The 01 programming problem is then max x f T · x subject to A · x ≤ C, x i ∈ { , 1 } where – x is an mcolumn vector of binary decision variables – f is an mcolumn vector of coefficients – A is a n × m matrix describing n constraints – C is an ncolumn vector Kay Giesecke 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 PV i c i 3.00 2.50 2.33 2.20 2.00 1.67 1.33 Optimal x i 1 1 1 1 1 • The optimal solution has total cost 500 and total NPV 610 • The “bang for the buck” analysis based on the ratio PV i c i suggests projects 1–5 for a total cost of 370 (budget not exhausted) and NPV of 540 (suboptimal) Kay Giesecke 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 1 1 1 1 fval = 610 Kay Giesecke MS&E 242: Applied interest rate analysis...
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This note was uploaded on 04/20/2011 for the course MIE 375 taught by Professor R.kwon during the Spring '11 term at University of Toronto.
 Spring '11
 R.KWON

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