00 250 233 220 200 167 133 optimal xi 1 0 1 1 1 1 0

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Unformatted text preview: st PV ci 100 20 150 50 50 150 150 NPV bi = P Vi − ci 200 30 200 60 50 100 50 P Vi ci 3.00 2.50 2.33 2.20 2.00 1.67 1.33 Optimal xi 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 PcVi suggests i projects 1–5 for a total cost of 370 (budget not exhausted) and NPV of 540 (suboptimal) Kay Giesecke Finance Capital budgeting Matlab formulation using 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 7 Finance Capital budgeting Increasing the budget by 20 increases the NPV by 30 f = [200; 30; 200; 60; 50; 100; 50]; A = [100 20 150 50 50 150 150]; c = [520]; [x,fval] = bintprog(-f,A,c) x= 1 1 1 1 1 1 0 fval = -640 Kay Giesecke 8 Finance 9 Capital budgeting Interdependent projects • Suppose there are m independent goals and associated with goal i there are ni possible projects; only one project can be selected for any goal and the budget is C . Then the problem is maximize m ni ￿￿ bij xij i=1 j =1 subject to m ni ￿￿ i=1 j =1 ni ￿ j =1 cij xij ≤ C xij ≤ 1 xij ∈ {0, 1} Kay Giesecke i = 1, 2, . . . , m ∀i, j Finance Capital budgeting Interdependent projects Kay Giesecke 10 Finance 11 Applied interest rate analysis Topics • Capital budgeting • This class: Cash matching Kay Giesecke Finance 12 Cash matching • Suppose we face a fixed sequence of future payment obligations y = (y1 , y2 , . . . , yn ) starting the next period (e.g. pension annuities) • We acquire a bond portfolio today and use the coupons and proceeds from the sale to meet these obligations • What is the optimal, i.e. minimum-cost portfolio? • See team project Kay Giesecke Finance 13 Cash matching • Consider a universe of m bonds and let pi be today’s price of bond i with cash stream ci = (ci1 , ci2 , . . . , cin ) starting next period; the coupon times j = 1, 2, . . . , n are assumed to be identical across the bonds and to match the pay...
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This document was uploaded on 02/10/2014.

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