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Posted on Aug 29, 2024

Kathleen Allen has up to $70,000 to divide among several investments. The alternative investments are municipal bonds (MB) with an 8.5% annual return, certificates of

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Kathleen Allen has up to $70,000 to divide among several investments. The alternative investments are municipal bonds (MB) with an 8.5% annual return, certificates of deposits (CD) with a 5% return, treasury bills (TB) with a 6.5% return and a growth stock (GS) fund with a 13% annual return. The investments are all evaluated after one year. However, each investment has a different perceived risk to the investor; thus, it is advisable to diversify and maybe leave some amount un-invested. Kathleen wants to know how much to invest in each alternative in order to maximize return. The following guidelines for diversification have been established so that the risk is minimized. No more than 20% of total amount available should be in municipal bonds. The amount invested in certificates of deposit should not exceed the amount invested in the other 3 alternatives. At least 30% of the available amount for investment should be in treasury bills and certificates of deposit. To be safe, more should be invested in CDs and treasury bills than in municipal bonds and growth stock fund by a ratio of at least 1.2 to 1. The following table is the sensitivity report for this problem. Adjustable Cells Cell Name $B$ 11 $ amount in $C$ 11 $ amount in $D$ 11 $ amount in $E$11 $ amount in MB CD TB GS Final Reduced Objective Allowable Allowable Value Cost Coefficient Increase Decrease ? -0. 045 0. 085 ? 0 ? 0.05 0.015 1E+30 38181. 82 ? 0. 065 0. 065 0.015 31818. 18 0 0. 13 1E+30 0. 045 Constraints Cell Name $B$18 Fund LHS $B$ 19 MB LHS $B$20 CD & others LHS $B$21 CD & TB LHS $B$22 Ratio LHS Final Shadow Value Price ? 0.094545 ? 0 -70000 ? 38181. 82 ? ? -0. 02955 Constraint Allowable Allowable R. H. Side Increase Decrease 70000 1E+30 31500 14000 ? 14000 ? ? 21000 ? ? O 70000 37800 Find the following question marks for objective function and justify your answer: a) Final Value of MB. (1 marks) b) Allowable Increase of MB. (1 marks) c) Allowable Decrease of MB. (1 marks) d) Reduced Cost of CD. (1 marks) e) Reduced Cost of TB. (1 marks) For the constraints, find the following question marks with justification. f) Final value of FUND (constraint). (1 marks) g) Final value of MB (constraint). (1 marks) h) Allowable Increase of MB (constraint) (1 marks) k) Shadow Price of CD& others (constraint) (1 marks) i) Allowable Increase of CD& others (constraint). (1 marks) j) Allowable Decrease of CD& others (constraint) (1 marks) k) Shadow price of CD& TB (constraint) (1 marks) 1) Allowable Increase of CD& TB (constraint) (1 marks) m) Allowable Decrease of CD& TB (constraint). (1 marks) n) Final value of Ratio (constraint). (1 marks) Kathleen Allen has up to $70,000 to divide among several investments. The alternative investments are municipal bonds (MB) with an 8.5% annual return, certificates of deposits (CD) with a 5% return, treasury bills (TB) with a 6.5% return and a growth stock (GS) fund with a 13% annual return. The investments are all evaluated after one year. However, each investment has a different perceived risk to the investor; thus, it is advisable to diversify and maybe leave some amount un-invested. Kathleen wants to know how much to invest in each alternative in order to maximize return. The following guidelines for diversification have been established so that the risk is minimized. No more than 20% of total amount available should be in municipal bonds. The amount invested in certificates of deposit should not exceed the amount invested in the other 3 alternatives. At least 30% of the available amount for investment should be in treasury bills and certificates of deposit. To be safe, more should be invested in CDs and treasury bills than in municipal bonds and growth stock fund by a ratio of at least 1.2 to 1. The following table is the sensitivity report for this problem. Adjustable Cells Cell Name $B$ 11 $ amount in $C$ 11 $ amount in $D$ 11 $ amount in $E$11 $ amount in MB CD TB GS Final Reduced Objective Allowable Allowable Value Cost Coefficient Increase Decrease ? -0. 045 0. 085 ? 0 ? 0.05 0.015 1E+30 38181. 82 ? 0. 065 0. 065 0.015 31818. 18 0 0. 13 1E+30 0. 045 Constraints Cell Name $B$18 Fund LHS $B$ 19 MB LHS $B$20 CD & others LHS $B$21 CD & TB LHS $B$22 Ratio LHS Final Shadow Value Price ? 0.094545 ? 0 -70000 ? 38181. 82 ? ? -0. 02955 Constraint Allowable Allowable R. H. Side Increase Decrease 70000 1E+30 31500 14000 ? 14000 ? ? 21000 ? ? O 70000 37800 Find the following question marks for objective function and justify your answer: a) Final Value of MB. (1 marks) b) Allowable Increase of MB. (1 marks) c) Allowable Decrease of MB. (1 marks) d) Reduced Cost of CD. (1 marks) e) Reduced Cost of TB. (1 marks) For the constraints, find the following question marks with justification. f) Final value of FUND (constraint). (1 marks) g) Final value of MB (constraint). (1 marks) h) Allowable Increase of MB (constraint) (1 marks) k) Shadow Price of CD& others (constraint) (1 marks) i) Allowable Increase of CD& others (constraint). (1 marks) j) Allowable Decrease of CD& others (constraint) (1 marks) k) Shadow price of CD& TB (constraint) (1 marks) 1) Allowable Increase of CD& TB (constraint) (1 marks) m) Allowable Decrease of CD& TB (constraint). (1 marks) n) Final value of Ratio (constraint). (1 marks)