The ZapCon Company is considering investing in three projects. If it fully invests in a project, the realized cash flows (in millions of dollars) will be as listed in the file P04_99.xlsx. For example, project 1 requires a cash outflow of $3 million today and returns

$5.5 million 3 years from now. Today ZapCon has $2 million in cash. At each time point (0, 0.5, 1, 1.5, 2, and 2.5 years from today), the company can, if desired, borrow up to $2 million at 3.5% (per 6 months) interest. Leftover cash earns 3% (per 6 months) interest. For example, if after borrowing and investing at time 0, ZapCon has $1 million, it would receive $30,000 in interest at time 0.5 year. 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 times 0 and 0.5.