Problem 1.4. You have to invest exactly $40 for one year. You can invest among projects A, B, C, D, and E. Investment E represents investing in a bank at the interest rate of 6%. The following table shows the incremental cash flow you will get back next year for each dollar invested in these projects. For example, if you invest just $l in project A, you will get back $l.7 after one year. If however, you invest $3 in project A, you will get back

$l.7+$l.6+$l.5=$4.8 after one year. Assume you can invest in multiples of $l in any project.

Dollar invested Marginal Cash Flow Next Year

	Project A	Project B	Project C	Project D	Project E
l	l.7	2.5	l.6	2.3	l.06
2	l.6	2.3	l.55	2.l5	l.06
3	l.5	2.l	l.5	2	l.06
4	l.4	l.9	l.45	l.85	l.06
5	l.3	l.7	l.4	l.7	l.06
6	l.2	l.5	l.35	l.55	l.06
7	l.l	l.3	l.3	l.4	l.06
8	l	l.l	l.25	l.25	l.06
9	0.9	0.9	l.2	l.l	l.06
l0	0.8	0.7	l.l5	0.95	l.06
ll	0.7	0.5	l.l	0.8	l.06
l2	0.6	0.5	l.05	0.65	l.06
l3	0.6	0.5	l	0.5	l.06
l4	0.6	0.5	0.95	0.5	l.06
l5	0.6	0.5	0.9	0.5	l.06

How should you allocate your investment across the projects to maximize the total amount you get back after one year? You cannot invest negative amount in a project. You may invest in all projects or only some projects.

Now suppose you have no cash but own all shares of firms A, B, C, D, and E. Each firm has $8 in cash. Firm A has project A, firm B has project B, and so on. Each firm chooses how much to invest in its project. If it invests more than the $8 cash it has, it raises the additional investment needed from you. If it invests less than the $8 cash it has, it pays out the rest cash to you as dividend. The cash flow next year from all investments will be returned to you. Since you lack any cash, you invest in a firm only from cash dividends you get from another firm. Assume you dont keep any cash idle with you. Firms want to maximize the total cash you get after one year. For each firm, determine the capital it will raise or the dividend it will pay. Ignore taxes.

This part is not graded but if you like additional challenge, determine the value of each firm.