A private equity firm is considering five competing projects in which to invest in the upcoming quarter. The firm needs to decide how to allocate its available capital based upon the combination of projects (denoted as A to E) selected to maximize returns (based upon net present value (NPV)). Table 1 below presents the capital requirements and the NPV for each project, along with the associated risk (given as a percentage of the initial investment). The company has $43 million in capital to allocate, with the goal of having an average associated risk of no more than 5%. There are some additional constraints to be met: (i) if project B is selected, then project E is also selected; (ii) one of the two projects A and C must be selected but not both; (iii) at least one of projects A, B, and D is selected. Table 1: Project Data Project NPV (M$) Risk (%) Capital (M$) A 19 4 14 B 22 5 10 C 24 6 12 D 27 7 15 E 21 5 13 Find the defining decision variables Find the objective function equation Selecting it as the correct type i.e. max or min Find constraint 1 Find constraint 2 Find constraint 3 Find constraint 4 Find constraint 5 Identifying the binary integer constraints Use excel and write it out.
A private equity firm is considering five competing projects in which to invest in the upcoming quarter. The firm needs to decide how to allocate its available capital based upon the combination of projects (denoted as A to E) selected to maximize returns (based upon
Table 1: Project Data
Project |
NPV (M$) |
Risk (%) |
Capital (M$) |
A |
19 |
4 |
14 |
B |
22 |
5 |
10 |
C |
24 |
6 |
12 |
D |
27 |
7 |
15 |
E |
21 |
5 |
13 |
Find the defining decision variables
Find the objective function equation
Selecting it as the correct type i.e. max or min
Find constraint 1
Find constraint 2
Find constraint 3
Find constraint 4
Find constraint 5
Identifying the binary integer constraints
Use excel and write it out.
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