Invest A company is planning to invest in three available projects. Investing in each project has the
Question:
Invest A company is planning to invest in three available projects. Investing in each project has the realized cash flows (in millions of dollars) as listed in the table below
Terms(6 months) | Cash Flow Project 1 | Cash Flow Project 2 | Cash Flow Project 3 |
---|---|---|---|
Initial (Term 0) | -3 | -2 | -2.0 |
1 | -1 | -0.5 | -2.0 |
2 | -1.8 | 1.5 | -1.8 |
3 | 0.4 | 1.5 | 1 |
4 | 1.8 | 1.5 | 1 |
5 | 1.8 | 0.2 | 1 |
6 | 5.5 | -1 | 6 |
For example, Project 1 requires an initial cash outflow of $3 million, relatively smaller outflows continue in the first and the second terms, it begins paying a small return in the third term, and a final payback of $5.5 million in the sixth term. Today Invest A has $2 million in cash. At the beginning of each term (0,1,2,3,4,5,6) the company can, if desired, borrow up to $2 million at 3.5% (per term) interest rate providing that it will be paid back next term. Leftover cash earns 3% (per term) interest. For example, if after borrowing and investing at time 0, Invest A has $1 million, it would receive $30,000 in the first term as interest. The company’s goal is to maximize cash on hand after cash flows 3 years from now are accounted for. What investment and borrowing strategy should it use? Assume that the company can invest in a fraction of a project. For example, if it invests in 0.5 of Project 3, it has, for example, cash outflows of -$1 million at the time 0 and at the first term. However it is not possible to invest in a project more than 100%. Hint: Cash flow should be balanced for every term (i.e flow in = flow out).
a) (20 Pts.) Formulate a linear programming model to optimize the investment plan.
b) (20 Pts.) Solve the model using GAMS.
c) (10 Pts.) Submit an executive summary report