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Unformatted text preview: he market value at the end of study
period. If no market value
information available, use the
imputed market value technique . 37 Capital Rationing (Chapter 13.9 of SWK)
In practice, projects do not have to be mutually exclusive.
Some of them are independent, and some of them are
mutually exclusive.
Example: A company has different departments, sales,
research, manufacturing etc. Within each department the
projects may be mutually exclusive. But on the ﬁrm level, a
project of the sales department may be independent of the
project from the research.
There is often a capital constraint (limited amount of
money for investment).
Question: How do we allocate our capital to each project in
an optimal way? This is called capital rationing.
Objective: Maximizing the total PW.
Caveat: Maximizing the IRR is not the right criterion!
SEEM5740/ECLT5930 38 Example 6.8 4 independent projects (numbers are in millions of dollars).
Project CF0 CF1 CF2 PW(10%) A
B
C
D 10
5
5
0 30
5
5
40 5
20
15
60 21
16
12
13 Budget constraint: capital investment cannot exceed 10 million
at time 0. SEEM5740/ECLT5930 39 Example 6.8 xA : either 0 or 1.
xA = 0 means we do not invest in A.
xA = 1 means we invest in A.
xB , xC and xD are deﬁned similarly.
The present worth of all selected projects is
21xA + 16xB + 12xC + 13xD
The total capital investment is
10xA + 5xB + 5xC SEEM5740/ECLT5930 40 Example 6.8 To solve this problem, we can formulate it mathematically as
follows:
maximize 21xA + 16xB + 12xC + 13xD
subject to 10xA + 5xB + 5xC ≤ 10
xA , xB , xC , xD is either 0 or 1
This is a constrained optimization problem (called binary
integer programming). It can be easily solved by an
optimization solver (Excel has one).
∗
∗
∗
∗
Optimal solution: xA = 0, xB = xC = xD = 1, PW ∗ = 41. SEEM5740/ECLT5930 41 Example 6.8 Now suppose we have additional constraint: the capital
investment at the end of year 1 cannot exceed 10 million. So
the problem becomes
maximize 21xA + 16xB + 12xC + 13xD subject to 10xA + 5xB + 5xC ≤ 10
− 30xA − 5xB − 5xC + 40xD ≤ 10
xA , xB , xC , xD is either 0 or 1
∗...
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 Fall '12
 ZHOU,Xiang

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