Scenario Your corporation has just approved an 8-year expansion plan to grow its market share. The plan requires an influx of cash in each of the 8 years. Management wants to develop a financial plan to ensure the cash needed for the expansion will be available at the beginning of each of the 8 years. The corporation has the following investment options: Security Price per unit Return Rate (%) Years to Maturity 1 $1,200 10.255 5 2 $1,000 6.7550 6 3 $1,175 12.110 7 Savings Account 5.500 Each unit of security 1, 2, and 3 guarantees to pay $1,000 at maturity. Investments in these securities must take place only at the beginning of year 1 and will be held until maturity. Any funds not invested in securities will be invested in a savings account that pays the annual interest rates noted above. The following table summarizes the cash needs for the expansion plan for each of the 8 years: Year 1 = $250,000 Year 5 = $295,000 Year 2 = $300,000 Year 6 = $310,000 Year 3 = $225,000 Year 7 = $280,000 Year 4 = $235,000 Year 8 = $305,000 1. Develop a linear programming model to minimize the total dollars needed to be invested now to meet the expansion cash needs in the next 8 years. Hint: this is the objective function. Use Excel Solver, solving method: Simplex LP. 2. How many units of each security 1, 2, and 3 should the corporation purchase? What is the investment amount in each security 1, 2, and 3 in year 1? 3. How much should the corporation place in the savings account in each of the 8 years? Assuming the corporation currently has $1.8 Million available cash to invest and given the cash needs for the expansion, is the investment plan that you developed feasible? Explain your answer and provide reasoning
Scenario
Your corporation has just approved an 8-year expansion plan to grow its market share. The plan requires an influx of cash in each of the 8 years. Management wants to develop a financial plan to ensure the cash needed for the expansion will be available at the beginning of each of the 8 years.
The corporation has the following investment options:
|
Security |
Price per unit |
Return Rate (%) |
Years to Maturity |
|
1 |
$1,200 |
10.255 |
5 |
|
2 |
$1,000 |
6.7550 |
6 |
|
3 |
$1,175 |
12.110 |
7 |
|
Savings Account |
|
5.500 |
|
Each unit of security 1, 2, and 3 guarantees to pay $1,000 at maturity. Investments in these securities must take place only at the beginning of year 1 and will be held until maturity. Any funds not invested in securities will be invested in a savings account that pays the annual interest rates noted above.
The following table summarizes the cash needs for the expansion plan for each of the 8 years:
|
Year 1 = $250,000 |
Year 5 = $295,000 |
|
Year 2 = $300,000 |
Year 6 = $310,000 |
|
Year 3 = $225,000 |
Year 7 = $280,000 |
|
Year 4 = $235,000 |
Year 8 = $305,000 |
1. Develop a linear programming model to minimize the total dollars needed to be invested now to meet the expansion cash needs in the next 8 years. Hint: this is the objective function. Use Excel Solver, solving method: Simplex LP.
2. How many units of each security 1, 2, and 3 should the corporation purchase? What is the investment amount in each security 1, 2, and 3 in year 1?
3. How much should the corporation place in the savings account in each of the 8 years? Assuming the corporation currently has $1.8 Million available cash to invest and given the cash needs for the expansion, is the investment plan that you developed feasible? Explain your answer and provide reasoning.
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