Page 3 of 5 Question 2 The University's endowment fund has 1 million available that can be invested in utility stocks, tech stocks, and gold stocks. The annual average rates of return for the three types of stocks are 9% for utility stocks, 10% for tech stocks, and 12% for gold stocks. Management of the endowment fund has decided that at least 45% of the available fund must be invested in utility stocks. Besides, management has specified that the ratio of the amount invested in tech stocks to that of gold stocks should not exceed 2. Each 1 invested in utility stocks, tech stocks, and gold stocks has a risk index of 0.006, 0.004, and 0.004 respectively. Management of the endowment fund can only accept a total risk index of 4500 from the three stocks. An analyst has formulated a linear programming model that can be used to determine how much money the endowment fund should allocate to each type of stock to maximise the total annual return accrued for the 1 million investments. Below is the sensitivity report of the endowment fund LP problem solved using Excel's solver. Answer the questions that follow using the information in the reports. Variable Cells Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease $B$9 Utility stocks 450000 0 0.09 0.09 1E+30 $C$9 Tech stocks 0 -0.02 0.1 0.02 1E+30 $D$9 Gold stocks 450000 0 0.12 1E+30 0.02 Constraints Final Shadow Constraint Allowable Allowable Cell Name Value Price R.H. Side Increase Decrease $B$14 Funds avail. const. 900000 0 1000000 1E+30 100000 $B$15 Utility stock const. 450000 -0.09 450000 300000 200000 $B$16 Tech to Gold const. -900000 0 0 1E+30 900000 $B$17 Risk tolerance const. 4500 30 4500 400 1800 a. Advise management on the optimal investment plan and the expected total return. [15 marks]

Page 4 of 5 b. The current proposal does not allow for investment in Tech stocks; however, management is interested in investing in tech stocks. At what minimum return will it be profitable to invest in Tech stocks? [15 marks] c. If the endowment fund is willing to increase its total risk index by 100 index points, would there be a gain or loss in annual total return and by how much? [25 marks] d. Management is considering either increasing the total amount of funds available for investment by 10,000 or reducing the proportion of investment in utility stocks to 35% of the available funds, but not both. Which option will you advise? Explain. [25 marks] e. In your opinion why do you think, only 900,000 of the available 1 million was invested although it appears it is profitable to invest in any of the three funds. [20 marks