4 Example: Single period capital rationing
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By choosing projects according to the PI, the resulting NPV (if only $60,000 is available) is increased by
$496.
3.4.1 Problems with the Profitability Index method
(a)
The approach can only be used if projects are divisible. If the projects are not divisible, a decision
has to be made by examining the absolute NPVs of all possible combinations of complete projects
that can be undertaken within the constraints of the capital available. The combination of projects
which remains at or under the limit of available capital without any of them being divided, and
which maximises the total NPV, should be chosen.
(b)
The selection criterion is fairly simplistic, taking no account of the possible strategic value of
individual investments in the context of the overall objectives of the organisation.
(c)
The method is of limited use when projects have differing cash flow patterns. These patterns may
be important to the company since they will affect the timing and availability of funds. With multiperiod capital rationing, it is possible that the project with the highest Profitability Index is the
slowest in generating returns.
(d)
The Profitability Index ignores the absolute size of individual projects. A project with a high index
might be very small and therefore only generate a small NPV.
Question
Capital rationing
A company is experiencing capital rationing in year 0, when only $60,000 of investment finance will be
available. No capital rationing is expected in future periods, but none of the three projects under
consideration by the company can be postponed. The expected cash flows of the three projects are as
follows.
Project
Year 0
$
(50,000)
(28,000)
(30,000)
A
B
C
Year 1
$
(20,000)
(50,000)
(30,000)
Year 2
$
20,000
40,000
30,000
Year 3
$
40,000
40,000
40,000
Year 4
$
40,000
20,000
10,000
The cost of capital is 10%. You are required to decide which projects should be undertaken in year 0, in
view of the capital rationing, given that projects are divisible.
Answer
The ratio of NPV at 10% to outlay in year 0 (the year of capital rationing) is as follows.
Outlay in
Year 0
$
50,000
28,000
30,000
Project
A
B
C
PV
$
55,700
31,290
34,380
NPV
$
5,700
3,290
4,380
Ratio
Ranking
1.114
1.118
1.146
3rd
2nd
1st
Discount factor 10%
Present value
$
(18,180)
16,520
30,040
27,320
55,700
Working
Present value A
Year
1
2
3
4
Cash flow
Cash flow
Cash flow
Cash flow
$
(20,000)
20,000
40,000
40,000
0.909
0.826
0.751
0.683
Part D Investment appraisal 11: Specific investment decisions
217
Present value B
Year
1
2
3
4
Discount factor 10%
$
(50,000)
40,000
40,000
20,000
Cash flow
Cash flow
Cash flow
Cash flow
0.909
0.826
0.751
0.683
Present value
$
(45,450)
33,040
30,040
13,660
31,290
Present value C
Year
1
2
3
4
Discount factor 10%
$
(30,000)
30,000
40,000
10,000
Cash flow
Cash flow
Cash flow
Cash flow
0.909
0.826
0.751
0.683
Present value
$
(27,270)
24,780
30,040
6,830
34,380
The optimal investment policy is as follows.
Ranking
1st
2nd
3rd
Project
C
B
A (balance)
Year 0 outlay
$
30,000
28,000
2,000 (*4% of 5,700)
NPV from total investment =
NPV
$
4,380
3,290
228
7,898
*4% = (2,000/50,000)
Exam focus
point
The June 2014 exam contained a calculation question on the profitability index. The question stated that
two of the projects were mutually exclusive. The ACCA examination team commented that some students
did not know what mutually exclusive meant, as they included both of the projects. If two projects are
mutually exclusive then only one of them can be undertaken.
3.5 Postponing projects
We have so far assumed that projects cannot be postponed until year 1. If this assumption is removed, the
choice of projects in year 0 would be made by reference to the loss of NPV from postponement.
3.6 Example: Postponing projects
The figures in the previous exercise will be used to illustrate the method. If any project, A, B or C, were
delayed by one year, the 'NPV' would now relate to year 1 values, so that in year 0 terms the NPVs would
be as follows.
NPV in Year 0
NPV in Year 1
Value
Loss in NPV
$
$
$
1
=
(a)
Project A
5,182
518
5,700
1.10
1
=
(b)
Project B
2,991
299
3,290
1.10
1
=
(c)
Project C
3,982
398
4,380
1.10
218
11: Specific investment decisions Part D Investment appraisal
An index of postponability would be calculated as follows.
Project
A
B
C
Loss in NPV from
one-year postponement
$
518
299
398
Postponability
index
(loss/outlay)
Outlay deferred
from year 0
$
50,000
28,000
30,000
0.0104
0.0107
0.0133
The loss in NPV by deferring investment would be greatest for Project C, and least for Project A. It is
therefore more profitable to postpone A, rather than B or C, as follows.
Investment in year 0:
Project
Outlay
$
30,000
28,000
2,000
60,000
C
B
A (balance)
NPV
$
4,380
3,290
228 (4% of 5,700)
7,898
Investment in year 1 (balance):
4,975 (96% of 5,182)
12,873
Project A
$48,000
Total NPV (as at year 0) of investments in years 0 and 1
3.7 Single period rationing with non-divisible projects
If the projects are not divisible then the method shown above may not result in the optimal solution.
Another complication which arises is that there is likely to be a small amount of unused capital with each
combination of projects. The best way to deal with this situation is to use trial and error and test the NPV
available from different combinations of projects. This can be a laborious process if there are a large
number of projects available.
3.8 Example: Single period rationing with non-divisible projects
Short O'Funds has capital of $95,000 available for investment in the forthcoming period. The directors
decide to consider projects P, Q and R only. They wish to invest only in whole projects, but surplus funds
can be invested. Which combination of projects will produce the highest NPV at a cost of capital of 20%?
Investment
required
$'000
40
50
30
Project
P
Q
R
Present value of
inflows at 20%
$'000
56.5
67.0
48.8
Solution
The investment combinations we need to consider are the various possible pairs of projects P, Q and R.
Projects
P and Q
P and R
Q and R
Required
investment
$'000
90
70
80
PV of
inflows
123.5
105.3
115.8
NPV from
projects
$'000
33.5
35.3
35.8
The highest NPV will be achieved by undertaking projects Q and R and investing the unused funds of
$15,000 externally.
Part D Investment appraisal 11: Specific investment decisions
219
Chapter Roundup
Leasing is a commonly used source of finance.
We distinguish three types of leasing:
–
–
–
Operating leases (lessor responsible for maintaining asset)
Finance leases (lessee responsible for maintenance)
Sale and leaseback arrangements
The decision whether to lease or buy an asset is a financing decision which interacts with the investment
decision to buy the asset. The assumption is that the preferred financing method should be the one with
the lower PV of cost. We identify the least-cost financing option by comparing the cash flows of
purchasing and leasing. We assume that if the asset is purchased, it will be financed with a bank loan;
therefore the cash flows are discounted at an after-tax cost of borrowing.
DCF techniques can assist asset replacement decisions, to decide how frequently an asset should be
replaced. When an asset is being replaced with an identical asset, the equivalent annual cost method can
be used to calculate an optimum replacement cycle.
Capital rationing may occur due to internal factors (soft capital rationing) or external factors (hard capital
rationing).
When capital rationing occurs in a single period, projects are ranked in terms of profitability index. This
is the ratio of the NPV of a project to its investment cost. The projects with the highest ratios should be
selected for investment.
Quick Quiz
1
Who is responsible for the servicing of a leased asset in the case of:
(a)
An operating lease?
(b)
A finance lease?
The lessee
2
$4,697
$3,575
$4,111
$3,109
Hard capital rationing occurs when a restriction on an organisation's ability to invest capital funds is
caused by an internal budget ceiling imposed by management.
True
False
4
Profitability Index (PI) =
(1)
(2)
What are (1) and (2)?
220
The lessor
The net present value of the costs of operating a machine for the next three years is $10,724 at a cost of
capital of 15%. What is the equivalent annual cost of operating the machine?
A
B
C
D
3
or
11: Specific investment decisions Part D Investment appraisal