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2 Example: Replacement of an identical asset

2 Example: Replacement of an identical asset

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(b)

Replacement every two years:
Equivalent annual cost =

(c)

Replacement every three years:
Equivalent annual cost =

(d)

$(32,644)
 $(18,804)
1.736

$(44,659)
 $(17,957)
2.487

Replacement every four years:
Equivalent annual cost =

$(58,829)
 $(18,558)
3.170

The optimum replacement policy is the one with the lowest equivalent annual cost. This is every three
years.

2.3 Equivalent annual benefit
Key term

The equivalent annual benefit is the annual annuity with the same value as the net present value of an
investment project.
The equivalent annual annuity =

NPV of project
Annuity factor

For example, a project A with an NPV of $3.75m and a duration of 6 years, given a discount rate of 12%,
3.75
will have an equivalent annual annuity of
 0.91
4.11
An alternative project B with an NPV of $4.45m and a duration of 7 years will have an equivalent annual
4.45
annuity of
 0.98
4.564
Project B will therefore be ranked higher than project A. This method is a useful way of comparing
projects with unequal lives.

Exam focus
point

You may find it useful to read the article called Equivalent Annual Costs and Benefits on the ACCA website.

3 Capital rationing
FAST FORWARD

Key terms

12/09, 12/11, 6/14

Capital rationing may occur due to internal factors (soft capital rationing) or external factors (hard capital
rationing).

Capital rationing is a situation in which a company has a limited amount of capital to invest in potential
projects, such that the different possible investments need to be compared with one another in order to
allocate the capital available most effectively.
Soft capital rationing is brought about by internal factors and decisions by management.
Hard capital rationing is brought about by external factors, such as limited availability of new external
finance.

If an organisation is in a capital rationing situation it will not be able to enter into all projects with positive
NPVs because there is not enough capital for all the investments.

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11: Specific investment decisions  Part D Investment appraisal

3.1 Soft and hard capital rationing
Soft capital rationing may arise for one of the following reasons.

(a)

Management may be reluctant to issue additional share capital because of concern that this may
lead to outsiders gaining control of the business.

(b)

Management may be unwilling to issue additional share capital if it will lead to a dilution of
earnings per share.

(c)

Management may not want to raise additional debt capital because they do not wish to be
committed to large fixed interest payments.

(d)

Management may wish to limit investment to a level that can be financed solely from retained
earnings.

Hard capital rationing may arise for one of the following reasons.

(a)

Raising new finance through the stock market may not be possible if share prices are depressed.

(b)

There may be restrictions on bank lending due to government control.

(c)

Lending institutions may consider an organisation to be too risky to be granted further loan
facilities.

(d)

The costs associated with making small issues of capital may be too great.

3.2 Relaxation of capital constraints
If an organisation adopts a policy that restricts funds available for investment (soft capital rationing), the
policy may be less than optimal. The organisation may reject projects with a positive net present value and
forgo opportunities that would have enhanced the market value of the organisation.
A company may be able to limit the effects of hard capital rationing and exploit new opportunities.
(a)

It might seek joint venture partners with which to share projects.

(b)

As an alternative to direct investment in a project, the company may be able to consider a licensing
or franchising agreement with another enterprise, under which the licensor/franchisor company
would receive royalties.

(c)

It may be possible to contract out parts of a project to reduce the initial capital outlay required.

(d)

The company may seek new alternative sources of capital (subject to any restrictions which apply
to it), for example:
(i)
Venture capital
(ii)
Debt finance secured on the assets of the project
(iii)
Sale and leaseback of property or equipment (see the next chapter)
(iv)
Grant aid
(v)
More effective capital management

3.3 Single period capital rationing
FAST FORWARD

6/14

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.
We shall begin our analysis by assuming that capital rationing occurs in a single period, and that capital is
freely available at all other times.

Part D Investment appraisal  11: Specific investment decisions

215

The following further assumptions will be made.
(a)

If a company does not accept and undertake a project during the period of capital rationing, the
opportunity to undertake it is lost. The project cannot be postponed until a subsequent period
when no capital rationing exists.

(b)

There is complete certainty about the outcome of each project, so that the choice between projects
is not affected by considerations of risk.

(c)

Projects are divisible, so that it is possible to undertake, say, half of Project X in order to earn half
of the net present value (NPV) of the whole project.

The basic approach is to rank all investment opportunities so that the NPVs can be maximised from the
use of the available funds.
Ranking in terms of absolute NPVs will normally give incorrect results. This method leads to the selection
of large projects, each of which has a high individual NPV but which have, in total, a lower NPV than a
large number of smaller projects with lower individual NPVs. Ranking is therefore in terms of what is
called the profitability index.
This profitability index is a ratio that measures the PV of future cash flows per $1 of investment, and so
indicates which investments make the best use of the limited resources available.

Key term

Profitability index is the ratio of the present value of the project's future cash flows (not including the
capital investment) divided by the present value of the total capital investment.

3.4 Example: Single period capital rationing
Suppose that Hard Times Co is considering four projects, W, X, Y and Z. Relevant details are as follows.

Project

W
X
Y
Z

Investment
required
$
(10,000)
(20,000)
(30,000)
(40,000)

Present value
of cash inflows
$
11,240
20,991
32,230
43,801

NPV
$
1,240
991
2,230
3,801

Profitability
index
(PI)

Ranking
as per
NPV

Ranking
as per PI

1.12
1.05
1.07
1.10

3
4
2
1

1
4
3
2

Without capital rationing all four projects would be viable investments. Suppose, however, that only
$60,000 was available for capital investment. Let us look at the resulting NPV if we select projects in the
order of ranking per NPV.
Project

Z
Y (balance)*

Priority

1st
2nd

Outlay
$
40,000
20,000
60,000

NPV
$
3,801
1,487
5,288

(2/3 of $2,230)

* Projects are divisible. By spending the balancing $20,000 on project Y, two-thirds of the full investment

would be made to earn two-thirds of the NPV.
Suppose, on the other hand, that we adopt the profitability index approach. The selection of projects will
be as follows.
Project

W
Z
Y (balance)

216

Priority

1st
2nd
3rd

11: Specific investment decisions  Part D Investment appraisal

Outlay
$
10,000
40,000
10,000
60,000

NPV
$
1,240
3,801
743
5,784

(1/3 of $2,230)

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