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machine in 10 years, the replacement decision cash flows can be estimated as follows:
Net Initial Investment in New Machine = - \$150,000 + \$ 15,000 = \$ 135,000
Depreciation on the old system = \$ 5,000
Depreciation on the new system = \$ 15,000
Annual Tax Savings from Additional Depreciation on New Machine = (Depreciation on
old machine вЂ“ Depreciation on new machine) (Tax rate) = (\$15,000-\$5,000)*0.4 = \$
4000
Annual After-tax Savings in Operating Costs = \$40,000 (1-0.4) = \$ 24,000
The cost of capital for the company is 12%, resulting in a net present value from the
replacement decision of
Net Present Value of Replacement Decision = - \$135,000 + \$ 28,000 * PV(A,12%,10
years) = \$23,206
This result would suggest that replacing the old packaging machine with a new one will
increase the firmвЂ™s net present value by \$23,206 and would be a wise move to make.

Capital Rationing
16

In evaluating capital investments, we have implicitly assumed that investing
capital in a good project has no effect on subsequent projects that the firm may consider.
Implicitly, we are assuming that firms with good projects can raise capital from financial
markets, at a fair price, and without paying transactions costs. In reality, however, it is
possible that the capital required to finance a project can cause managers to reject other
good projects because the firm has access to limited capital. Capital rationing occurs
when a firm is unable to invest in projects that earn returns greater than the hurdle rates2.
Firms may face capital rationing constraints because they do not have either the capital
on hand or the capacity to raise the capital needed to finance these projects. This implies
that the firm does not have вЂ“вЂ“ and cannot raise вЂ“вЂ“ the capital to accept the positive net
present value projects that are available to it. A firm that has many projects and limited
resources on hand does not necessarily face capital rationing. It might still have the
capacity to raise the resources from financial markets to finance all these projects.

Reasons for Capital Rationing Constraints
In theory, there will be no capital rationing constraint as long as a firm can follow
this series of steps in locating and financing investments:
1. The firm identifies an attractive investment opportunity.
2. The firm goes to financial markets with a description of the project to seek
financing.
3. Financial markets believe the firmвЂ™s description of the project.
4. The firm issues securities вЂ“вЂ“ i.e., stocks and bonds вЂ“вЂ“ to raise the capital
needed to finance the project at fair market prices. Implicit here is the assumption
that markets are efficient and that expectations of future earnings and growth are
built into these prices.
5. The cost associated with issuing these securities is minimal.
If this were the case for every firm, then every worthwhile project would be financed and
no good project would ever be rejected for lack of funds; in other words, there would be
no capital rationing constraint.

2 For discussions of the effect of capital rationing on the investment decision, see Lorie and Savage (1955)
and Weingartner (1977).
17

The sequence described above depends on a several assumptions, some of which
are clearly unrealistic, at least for some firms. LetвЂ™s consider each step even more
closely.
1. Project Discovery: The implicit assumption that firms know when they have good
projects on hand underestimates the uncertainty and the errors associated with project
analysis. In very few cases can firms say with complete certainty that a prospective
project will be a good one.
2. Firm Announcements and Credibility: Financial markets tend to be skeptical about
announcements made by firms, especially when such announcements contain good news
about future projects. Since is easy for any firm to announce that its future projects are
good, regardless of whether this is true or not, financial markets often require more
substantial proof of the viability of projects.
3. Market Efficiency: If the securities issued by a firm are under priced by markets, firms
may be reluctant to issue stocks and bonds at these low prices to finance even good
projects. In particular, the gains from investing in a project for existing stockholders may
be overwhelmed by the loss from having to sell securities at or below their estimated true
value. To illustrate, assume that a firm is considering a project that requires an initial
investment of \$ 100 million and has a net present value of \$ 10 million. Also assume that
the stock of this company, which management believes should be trading for \$100 per
share, is actually trading at \$ 80 per share. If the company issues \$100 million of new
stock to take on the new project, its existing stockholders will gain their share of the net
present value of \$10 million but they will lose \$20 million (\$100 million - \$ 80 million)
to new investors in the company. There is an interesting converse to this problem. When
securities are overpriced, there may be a temptation to over invest, since existing
stockholders gain from the very process of issuing equities to new investors.
5. Flotation Costs: The costs associated with raising funds in financial markets, and can
be substantial. If these costs are larger than the net present value of the projects being
considered, it would not make sense to raise these funds and finance the projects.

Sources of Capital Rationing
18

What are the sources of capital rationing? Going through the process described in
the last section in Table 6.2, we can see the possible reasons for capital rationing at each
step:
Table 6.2: Capital Rationing: Theory vs. Practice

In theory In practice Source of Rationing

1. Project Discovery A business uncovers a A business believes, Uncertainty about true
good investment given the underlying value of projects may
opportunity. uncertainty, that it has cause capital rationing.
a good project.

2. Information The business conveys The business attempts Difficulty in
Revelation information about the to convey information conveying information
project to financial to financial markets. to markets may cause
markets. rationing.

3. Market Response Financial markets Financial markets may The greater the
believe the firm; i.e.,the not believe the вЂњcredibility gapвЂќ, the
information is announcement. greater the rationing
conveyed credibly. problem.

4. Market Efficiency The securities issued The securities issued With underpriced
by the business by the business may securities, firms will be
(stocks and bonds) are not be correctly priced. unwilling to raise
fairly priced. funds for projects.

5. Flotation Costs There are no costs There are significant The greater the
associated with raising costs associated with flotation costs, the
funds for projects. raising funds for larger will be the
projects. capital rationing
problem.

The three primary sources of capital rationing constraints, therefore, are lack of
credibility, under pricing of securities and flotation costs.
Researchers have collected data on firms to determine whether the firms face
capital rationing constraints, and if so, to identify the sources of such constraints. One
such survey was conducted by Scott and Martin and is summarized in Table 6.3.
Table 6.3: The Causes of Capital Rationing
Cause # firms %
Debt limit imposed by outside agreement 10 10.7
Debt limit placed by management external to firm 3 3.2
Limit placed on borrowing by internal management 65 69.1
Restrictive policy imposed on retained earnings 2 2.1
Maintenance of target EPS or PE ratio 14 14.9
Source: Martin and Scott (1976)
19

This survey suggests that although some firms face capital rationing constraints as a
result of external factors largely beyond their control, such as issuance costs and
credibility problems, most firms face self-imposed constraints, such as restrictive policies
to avoid over-extending themselves by investing too much in any period.

Project Selection with Capital Rationing
Whatever the reason, many firms have capital rationing constraints, limiting the
funds available for investment. Consequently, the investment analysis techniques
developed in Chapter 5, such as net present value, may prove inadequate because they are
based on the premise that all good projects will be accepted. In this section, we examine
some of the measures to incorporate the capital rationing constraint into project
evaluations.

Internal Rate of Return
As we noted in chapter 5, one reason many firms continue to use internal rate of
return rather than net present value in their investment decisions is because they perceive
themselves to be subject to capital rationing. Since the internal rate of return is a
percentage measure of return, it measures the return to a dollar of invested capital and
provides a way of directing capital to those investments where this return is highest. The
limitations of the IRR approach were also examined in chapter 5, especially with its
reinvestment rate assumptions and the potential for multiple and misleading internal rates
of return.

Profitability Index
The profitability index is the simplest method of including capital rationing in
investment analysis. It is particularly useful for firms that have a constraint for the current
period only, and relatively few projects. A scaled version of the net present value, the
profitability index is computed by dividing the net present value of the project by the
initial investment in the project.3

3 There is another version of the profitability index, whereby the present value of all cash inflows is divided
by the present value of cash outflows. The resulting ranking will be the same as with the profitability index,
as defined in this chapter.
20

Profitability Index = Net Present Value / Initial Investment
The profitability index provides a rough measure of the net present value the firm gets for
each dollar it invests. To use it in investment analysis, we first it for each investment the
firm is considering, and then pick projects based on the profitability index, starting with
the highest values and working down until we reach the capital constraint. When capital
is limited and a firm cannot accept every positive net present value, the profitability index
identifies the highest cumulative net present value from the funds available for capital
investment.
Although the profitability index is intuitively appealing, it has several limitations.
First, it assumes that the capital rationing constraint applies to the current period only and
does not include investment requirements in future periods. Thus, a firm may choose
projects with a total initial investment that is less than the current periodвЂ™s capital
constraint, but it may expose itself to capital rationing problems in future periods if these
projects have outlays in those periods. A related problem is the classification of cash
flows into an initial investment that occurs now and operating cash inflows that occur in
future periods. If projects have investments spread over multiple periods and operating
cash outflows, the profitability index may measure the projectвЂ™s contribution to value
incorrectly. Finally, the profitability index does not guarantee that the total investment
will add up to the capital rationing constraint. If it does not, we have to consider other
combinations of projects, which may yield a higher net present value. Although this is
feasible for firms with relatively few projects, it becomes increasing unwieldy as the
number of projects increases.

Illustration 6.7: Using the Profitability Index to select projects
Assume that Bookscape, as a private firm, has limited access to capital, has a
capital budget of \$100,000 in the current period. The projects available to the firm are
listed in Table 6.4.
Table 6.4: Available Projects
Project Initial Investment (in 000s) NPV (000s)
A \$ 25 \$10
B \$ 40 \$ 20
C \$5 \$5
D \$ 100 \$ 25
21

E \$ 50 \$ 15
F \$ 70 \$ 20
G \$ 35 \$ 20
Note that all the projects have positive net present values and would have been accepted
by a firm not subject to a capital rationing constraint.
In order to choose among these projects, we compute the profitability index of
each project in Table 6.5.
Table 6.5: Profitability Index for Projects
Project Initial Investment NPV Profitability Index Ranking
A \$25 \$10 0.40 4
B \$60 \$30 0.50 3
C \$5 \$5 1.00 1
D \$100 \$25 0.25 7
E \$50 \$15 0.30 5
F \$70 \$20 0.29 6
G \$35 \$20 0.57 2

The profitability index of 0.40 for project A means that the project earns a net present
value of 40 cents for every dollar of initial investment. Based on the profitability index,
we should accept projects B, C and G. This combination of projects would exhaust the
capital budget of \$100,000 while maximizing the net present value of the projects
accepted.
Note that this analysis is based on the assumption that the capital constraint is for
the current period only and that the initial investments on all these projects will occur in
the current period4. It also highlights the cost of the capital rationing constraint for this
firm; the net present value of the projects rejected as a consequence of the constraint is
\$70 million.

Building in Capital Rationing Constraints into Analysis
We recommend that firms separate the capital rationing constraint from traditional
investment analysis so they can observe how much these constraints cost. In the simplest
terms, the cost of a capital rationing constraint is the total net present value of the good
projects that could not be taken for lack of funds. There are two reasons why this

4 When capital rationing constraints occur over multiple periods, and there are dozens of projects,
mathematical programming has been suggested as a solution by Baumol and Quandt (1965).
22

knowledge is useful. First, if the firm is faced with the opportunity to relax these
constraints, knowing how much these constraints are costing the firm will be useful. For
instance, the firm may be able to enter into a strategic partnership with a larger firm with
excess funds and use the cash to take the good projects that would otherwise have been
rejected, sharing the net present value of these projects. Second, if the capital rationing is
self-imposed, managers in the firm are forced to confront the cost of the constraint. In
some cases, the sheer magnitude of this cost may be sufficient for them to drop or relax
the constraint.

6.3. в˜ћ: Mutually exclusive projects with different risk levels
Assume, in illustration 6.7, that the initial investment required for project B were
\$40,000. Which of the following would be your best combination of projects given your
capital rationing constraint of \$100,000?
a. B, C and G
b. A,B, C and G
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