Show the application of the NPV rule in the choice between mutually exclusive projects, replacement decisions, projects with different lives etc. Understand the impact of inflation on mutually exclusive projects with unequal lives. Make choice between investments under capital rationing. Illustrate the use of linear programming under capital rationing situation.

1. Chapter - 11
Complex Investment
Decisions

2. 2Financial Management, Ninth
Chapter Objectives
Show the application of the NPV rule in the
choice between mutually exclusive projects,
replacement decisions, projects with different
lives etc.
 Understand the impact of inflation on mutually
exclusive projects with unequal lives.
 Make choice between investments under
capital rationing.
 Illustrate the use of linear programming under
capital rationing situation.

3. 3Financial Management, Ninth
Complex Investment Problems
 How shall choice be made between
investments with different lives?
 Should a firm make investment now, or
should it wait and invest later?
 When should an existing asset be replaced?
 How shall choice be made between
investments under capital rationing?

4. 4Financial Management, Ninth
Projects with Different Lives
 The choice between projects with different
lives should be made by evaluating them for
equal periods of time.
CashFlows(Rs000)
0 1 2 3 4 NPV,10%
Y1 60 40 40 0 0 129.42
Y2 0 0 60 40 40 106.96
Y= Y1 + Y2 60 40 100 40 40 236.38
X 120 30 30 30 30 215.10

5. 5Financial Management, Ninth
Annual Equivalent Value (AEV)
Method
 The method for handling the choice of the
mutually exclusive projects with different lives,
as discussed in last slide, can become quite
cumbersome if the projects’ lives are very long.
 We can calculate the annual equivalent value
(AEV) of cash flows of each project. We shall
select the project that has lower annual
equivalent cost.
NPV
AEV
Annuity factor
=

6. 6Financial Management, Ninth
AEV for Perpetuities
 When we assume that projects can be
replicated at constant scale indefinitely, we
imply that an annuity is paid at the end of every
n years starting from the first period.
 where NPV∞ is the present value of the
investment indefinitely, NPVn is the present
value of the investment for the original life, n
and k is the opportunity cost of capital.
(1 )
NPV (NPV )
(1 ) 1
n
n n
k
k
∞
 +
= +  + − 

7. 7Financial Management, Ninth
Inflation and Annual Equivalent
Value
Machines X Y X Y X Y
Real CashFlows(Rs 000) Nominal CashFlows (Rs 000)
Year Inflation5% Inflation15%
0 120.00 60.00 120.00 60.00 120.00 60.00
1 30.00 40.00 31.20 41.60 40.50 54.00
2 30.00 40.00 32.45 43.26 54.68 72.90
3 30.00 33.75 73.81
4 30.00 35.10 99.65
Discount rate .06 .06 .144 .144 .265 .265
NPV 215.10 129.42 215.10 129.42 215.10 129.42
PVAF 1.7355 3.1699 1.6382 2.8900 1.4154 2.2999
AEC 67.86 74.57 74.43 79.00 93.52 91.44

8. 8Financial Management, Ninth
Investment Timing and Duration
 The rule is
straightforward:
undertake the
project at that point
of time, which
maximizes the NPV.
Project Undertaken
at Period NPV
0 –100 + 150 × 0.909 =
36.35
1 –120 × 0.909 + 180 ×
0.826
=
39.60
2 –140 × 0.826 + 205 ×
0.751
=
38.32

9. 9Financial Management, Ninth
Tree Harvesting Problem
 The maximisation of the investment’s NPV would
depend on when we harvest trees. The net future value
of trees increases when harvesting is postponed; but
the opportunity cost of capital is incurred by not realising
the value by harvesting the trees. The NPV will be
maximised when the trees are harvested at the point
where the percentage increase in value equals the
opportunity cost of capital.
 Suppose the net future value obtained over the years
from harvesting the trees is At and if the opportunity cost
of capital is k, then the net present value (NPV) of the
net realisable value of trees is given by:
–
NPV = kt
t eA – C

10. 10Financial Management, Ninth
Tree Harvesting Problem
 To determine the optimum harvesting time, which
maximizes the NPV, we set the derivative of the
NPV with respect to t in Equation equal to zero.
 Land may have value since the trees can be
replanted. Therefore, the correct formulation of
the problem will be to assume that once the trees
are harvested, the land will be replanted. Thus, if
we consider a constant replication of the tree-
harvesting investment indefinitely, then the NPV
will:
( )
NPV
1
t
kt
A C
C
e
−
= − +
−

11. 11Financial Management, Ninth
Replacement of an Existing Asset
 Compare the annual
equivalent value (AEV) of
the old and new equipment
as given below.
 It is indicated that a chain of
new machines is equivalent
to an annuity of Rs 9,630
÷ 3.605 = Rs 2,671 a year
for the life of the chain. The
existing machine is still
capable of providing an
annuity of: Rs 7,390 ÷ 2.402
= Rs 3,076. So long as the
existing machine generates
a cash inflow of more than
Rs 2,671 there does not
seem to be an economic
justification for replacing it.
Equipment C0 C1 C2 C3 C4 C5 NPVat
12%
New –12 6 6 6 6 6 9.63
Old – 4 3 2 – – 7.39
AEV,New – 2.67 2.67 2.67 2.67 2.67 9.63
AEV,Old – 3.08 3.08 3.08 – – 7.39

12. 12Financial Management, Ninth
Investment Decisions Under Capital
Rationing
 Capital rationing refers to a situation where
the firm is constrained for external, or self-
imposed, reasons to obtain necessary funds
to invest in all investment projects with
positive NPV. Under capital rationing, the
management has not simply to determine the
profitable investment opportunities, but it has
also to decide to obtain that combination of
the profitable projects which yields highest
NPV within the available funds.

13. 13Financial Management, Ninth
Why Capital Rationing
 There are two types of capital rationing:
 External capital rationing.
 Internal capital rationing.

14. 14Financial Management, Ninth
Profitability Index
 The NPV rule should be modified while
choosing among projects under capital
constraint. The objective should be to maximise
NPV per rupee of capital rather than to
maximise NPV. Projects should be ranked by
their profitability index, and top-ranked projects
should be undertaken until funds are
exhausted.
 The Profitability Index does not always work.
It fails in two situations:
 Multi-period capital constraints.
 Project indivisibility.

15. 15Financial Management, Ninth
Programming Approach to Capital
Rationing
 Linear Programming (LP)
 Integer Programming (IP)
 Dual variable