Financial Management

Chapter 3 CP - 12 Case Problem 2: Investment Strategy 1. The first step is to develop a linear programming model for maximizing return subject to constraints for funds available, diversity, and risk tolerance. Let G = Amount invested in growth fund I = Amount invested in income fund M = Amount invested in money market fund The LP formulation and optimal solution found using The Management Scientist are shown. MAX .18G +.125I +.075M S.T. 1) G + I + M < 800000 Funds Available 2) .8G -.2I -.2M > 0 Min growth fund 3) .6G -.4I -.4M < 0 Max growth fund 4) -.2G +.8I -.2M > 0 Min income fund 5) -.5G +.5I -.5M < 0 Max income fund 6) -.3G -.3I +.7M > 0 Min money market fund 7) .05G + .02I -.04M < 0 Max risk OPTIMAL SOLUTION Objective Function Value = 94133.336 Variable Value Reduced Costs -------------- --------------- ------------------ G 248888.906 0.000 I 160000.000 0.000 M 391111.094 0.000 Constraint Slack/Surplus Dual Prices -------------- --------------- ------------------ 1 0.000 0.118 2 88888.898 0.000 3 71111.109 0.000 4 0.000 -0.020 5 240000.000 0.000 6 151111.109 0.000 7 0.000 1.167 OBJECTIVE COEFFICIENT RANGES Variable Lower Limit Current Value Upper Limit ------------ --------------- --------------- --------------- G 0.150 0.180 No Upper Limit I -0.463 0.125 0.145 M 0.015 0.075 0.180 Solutions to Case Problems CP - 13 RIGHT HAND SIDE RANGES Constraint Lower Limit Current Value Upper Limit ------------ --------------- --------------- --------------- 1 0.188 800000.000 No Upper Limit 2 No Lower Limit 0.000 88888.898 3 -71111.109 0.000 No Upper Limit 4 -106666.641 0.000 133333.313 5 -240000.000 0.000 No Upper Limit 6 No Lower Limit 0.000 151111.109 7 -8000.000 0.000 6399.999 Rounding to the nearest dollar, the portfolio recommendation for Langford is as follows. Amount Fund: Invested Growth $248,889 Income 160,000 Money Market 391,111 Total $800,000 Yield = 94,133 / 800,000 = .118 The portfolio yield is .118 or 11.8%. Note that the portfolio yield equals the dual price for the funds available constraint. 2. If Langford’s risk index is increased by .005 that is the same as increasing the right-hand side of constraint 7 by .005 (800,000) = 4000. Since this amount of increase is within the right-hand-side range, we would expect an increase in return of 1.167 (4000) = 4668. The revised formulation and new optimal solution are shown below. Except for rounding, the value has increased as predicted; the new optimal allocation is Amount Fund: Invested Growth $293,333 Income 160,000 Money Market 346,667 Total $800,000 The portfolio yield becomes 98,800/800,000 = .124 or 12.4% MAX .18G +.125I +.075M S.T. 1) G + I + M < 800000 2) .8G -.2I -.2M > 0 3) .6G -.4I -.4M < 0 4) -.2G +.8I -.2M > 0 5) -.5G +.5I -.5M < 0 6) -.3G -.3I +.7M > 0 7) .045G + .015I-.045M < 0

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