Assignment Questions on Investment Decisions Project
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Assignment I
1. Let’s say XYZ cpny is considering investing in several projects that have varying capital requirements over the next four years. Faced with limited capital each year, management would like to select the most profitable projects. The estimated net present value for each project, the capital requirements, and the available capital over the four-year period are shown in Table below.
| Project | Plant Expansion | Warehouse Expansion | New Machinery | New Product Research | Total Capital Available | ||
| Present Value | $90,000 | $40,000 | $10,000 | $37,000 | |||
| Year 1 Cap Rqmt | $15,000 | $10,000 | $10,000 | $15,000 | $40,000 | ||
| Year 2 Cap Rqmt | $20,000 | $15,000 | – | $10,000 | $50,000 | ||
| Year 3 Cap Rqmt | $20,000 | $20,000 | – | $10,000 | $40,000 | ||
| Year 4 Cap Rqmt | $15,000 | $5,000 | $4,000 | $10,000 | $35,000 |
- Formulate the problem as LP.
- If these projects are mutually exclusive and the organization has no sufficient fund to finance all projects simultaneously, which project(s) should be selected to maximize the present value?
2. The manager of a department store in Adama has decided to prepare a promotion campaign on project basis to decide on the types and amounts of advertising the store should use. He has invited representatives from the local radio station, television station, and newspaper to make presentations in which they describe their audiences.
(a) The television station representative indicates that a TV commercial, which costs Birr 15,000, would reach 25,000 potential customers. The breakdown of the audience is as follows.
Male Female
Old 5,000 5,000
Young 5,000 10,000
(b) The news paper representative claims to be able to provide an audience of 10,000 potential customers at a cost of Birr 4000 per ad. The breakdown of the audience is as follows.
Male Female
Old 4,000 3,000
Young 2,000 1,000
(c) The radio station representative says that the audience for one of the station’s commercials, which costs Birr 6000, is 15,000 customers. The breakdown of the audience is as follows.
Male Female
Old 1,500 1,500
Young 4,500 7,500
The store has the following advertising policy:
- Use at least twice as many radio commercials as news paper ads.
- Reach at least 100,000 customers
- Reach at least twice as many young people as old people
- Make sure that at least 30% of the audience is women.
Available space limits the number newspaper ads to 7. The store wants to know the optimal number of each type of advertising to purchase to minimize total cost.
Required:
- Formulate appropriate linear programming model.
- Standardize the model
- Develop initial simplex table
- Solve the problem using Excel solver
3. In Southern Region there are a group of three Zones (communal farming communities). Overall planning for this group is done in its Coordinating Technical Office. This office currently is planning agricultural production for the coming year. The agricultural output of each zone is limited by both the amount of available irrigable land and the quantity of water allocated for irrigation by the Water Commissioner (a national government official). These data are given in the following table.
TABLE 1 Resource data for the Southern Confederation of the Three Zones
| Zone | Usable Land (Acres) | Water Allocation (Acre Feet) |
| 1 | 400 | 600 |
| 2 | 600 | 800 |
| 3 | 300 | 375 |
The crops suited for this region include sugar beets, cotton, and sorghum, and these are the three being considered for the upcoming season. These crops differ primarily in their expected net return per acre and their consumption of water. In addition, the Ministry of Agriculture has set a maximum quota for the total acreage that can be devoted to each of these crops by the Southern Region of Three Zones, as shown in Table 2 below.
TABLE 2. Crop data for the Southern region of Three Zones
| Crop | Maximum Quota (Acres) | Water Consumption
(Acre Feet/Acre) |
Net Return
($/Acre) |
| Sugar beets | 600 | 3 | 1,000 |
| Cotton | 500 | 2 | 750 |
| Sorghum | 325 | 1 | 250 |
Because of the limited water available for irrigation, the Southern region of three zones will not be able to use all its irrigable land for planting crops in the upcoming season. To ensure equity between the three zones, it has been agreed that every zone will plant the same proportion of its available irrigable land. For example, if zone 1 plants 200 of its available 400 acres, then zone 2 must plant 300 of its 600 acres, while zone 3 plants 150 acres of its 300 acres. However, any combination of the crops may be grown at any of the zones. The job facing the Coordinating Technical Office is to plan how many acres to devote to each crop at the respective zone while satisfying the given restrictions. The objective is to maximize the total net return to the Southern region of three zones as a whole.
- Develop the problem as LP
- Standardize the model
- Solve the problem using excel solver
4. Using graphic approach(Extreme Corner point),
- Find the optimal solution for (a) below
- If there exist multiple solution for (b) below taking the same constraints, determine at least 4 integer multiple solutions.
ZMin a) 1500x+2400y
- b) 1600x+2400y
Subjected to:
4x+Y>24
2x+3y>42
X+4y>36
X<14
y<14
x, y>0
5. Innis consulting group Investments 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 provides an annual rate of return of $5 per dollar invested ; each unit of the money market fund costs $100 and provides an annual rate of return of $4 for each dollar invested . The client wants to minimize risk 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 specified that at least $3000 be invested in the money market fund.
(a) Determine how many units of each fund Innis should purchase for the client to minimize the total risk index for the portfolio.
(b) How much annual income will this investment strategy generate?
(c) Suppose the client desires to maximize annual return. How should the funds be invested?
(d) What is the optimal solution, and what is the minimum total risk?
(e) Specify the objective coefficient ranges.
(f) How much annual income will be earned by the portfolio?
(g) What is the rate of return for the portfolio?
(h) What is the dual value for the funds available constraint?
(i) What is the marginal rate of return on extra funds added to the portfolio?
(j) Suppose the risk index for the stock fund (the value of CS) increases from its current value of 8 to 12. How does the optimal solution change, if at all?. Suppose the risk index for the money market fund (the value of CM) increases from its current value of 3 to 3.5. How does the optimal solution change, if at all?
1. Suppose CS increases to 12 and CM increases to 3.5. How does the optimal solution change, if at all?
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