A private equity firm is considering five competing projects in which to invest
ID: 1175054 • Letter: A
Question
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 $43 million in capital to allocate, with the goal of having an average associated risk of no more than 5%.There are some additional constraints to be met: i) if project B is selected, then project e is also selected;ii) if either project a is selected or project c selected, but not both; iii) at least one of projects a,b,d, is selected.
Table 1. project data
project
Npv(M$)
Risk(%)
Capital(M$)
a
19
4
14
b
22
5
10
c
24
6
12
d
27
7
15
e
21
5
13
make linear programing
project
Npv(M$)
Risk(%)
Capital(M$)
a
19
4
14
b
22
5
10
c
24
6
12
d
27
7
15
e
21
5
13
Explanation / Answer
Capital Constraint : 14 a + 10 b + 12 c + 15 d + 13 e <= 43
Risk Constraint : 4% a + 5% b + 6% c + 7% d + 5% e <= 5%
Maximise: 19 a + 22 b + 24 c + 27 d + 21 e
Subject to additional constraints:
b + e => 1 (since the project values can be integers only); when b is selected e should also be selected but not vice versa
a cannot equal c
a + b + d => 1
all a , b , c , d and e are non zero variables hence they can be either 0 (not selected) or 1 (selected for investments).
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