Innis Investment manages funds for a number of companies and wealthy clients. The investment strategy is tailored to each client's needs. For a new client, Innis has been authorized to invest up to $1.2 million in two investment funds: a stock fund and a money market fund. Each unit of the stock fund costs $50 and provide an annual rate of return of 10%; each unit of the money market fund costs $100 and provides an annual rate of return of 4%. The client wants to minimize risk (note that risk is not measured in dollars, but rather in risk index points) subject to the requirement that the annual income from the investment be at least $60,000. According to Innis's risk measurement system, each unit invested in the stock fund has a risk index of 8, and each unit invested in the money market fund has a risk index of 3; the higher risk index associated with the stock fund simply indicates that it is the riskier investment. Innis's client also specifies that at least $300,000 (which is equivalent to at least 3,000 units = $300,000/$100) be invested in the money market fund. Let S = number of units purchased in the stock fund by Innis Investment for a new client Let M = number of units purchased in the money market fund by Innis Investment for a new client Use the sensitivity report to answer questions: Variable Cells Final Cell Name Value $B$13 DV's values: StockFunds 4000 $C$13 DVs values: Money Market 10000 Reduced Cost 0 0 Objective Allowable Allowable Coefficient Increase Decrease 8 1E+30 4.25 3 3.4 1E+30 Constraints Cell Name $B$18 Funds Available $B$19 Annual income $B$20 Units in money market Final Shadow Constraint Allowable Allowable Value Price R.H. Side Increase Decrease 1200000 -0.056666667 1200000 300000 420000 60000 2.166666667 60000 42000 12000 10000 0 3000 7000 1E+30 3. State the ranges of optimality for each of the objective function coefficients. Interpret RO for one of them 4. How much annual income will be earned by the portfolio? (hint: LHS with plugged values of DVs) 5. What is the rate of return for the portfolio? 6. What is the shadow price for the funds available constraint? Provide interpretation. 7. Suppose the risk index for the stock fund increases from its current value of 8 to 12. How does the optimal solution point change, if at all? Can you determine the value of objective function without Excel resolving? Show calculations (if possible) 8. Suppose the risk index for the money market fund increases from its current value of 3 to 6.5. How does the optimal solution point changes, if at all? Can you determine the value of objective function without Excel? Show calculations (if possible) 9. Which constraints are binding? Explain how it can be shown from the model and from the provided report 10. To minimize risk more, what option is better for the client (a) to invest extra 10K or (b) to decrease annual income requirement by 2 or (c) increase the minimum requirements for units in money market up to 5,000? Show calculations for each part. (hint: use shadow prices and ranges of fesibility)
