Business Finance

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Chapter 2:
Consumption, Investment and
the Capital Market

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Learning Objectives
● Explain how a company’s managers can, in
principle, make financial decisions that will
be supported by all shareholders.
● Explain how the existence of a capital
market makes this result possible.
● Identify the company’s optimal
investment/dividend policy under conditions
of certainty.

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Fisher’s Separation Theorem:
A Simplified Example
● The foundation for many fundamental
results of finance theory.
● Assumptions:
▪ certainty
▪ frictionless capital markets
▪ interest rate for borrowers equals interest rate
for lenders

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Fisher’s Separation Theorem:
A Simplified Example (cont.)
● Implication of theorem:
▪ A company can make dividend/investment
decisions that are in the best interests of all
shareholders, regardless of differences in the
preferences of individual shareholders.

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Fisher’s Separation Theorem:
A Simplified Example (cont.)
● Simple example (without a capital market)
Assume:
▪ A company only has two shareholders (‘A’
and ‘B’) who hold equal shares.
▪ Only two projects are available (‘large’ and
‘small’), enabling dividends of $100 and
$300 respectively to be paid now.
▪ There is no capital market.
▪ Shareholder A wishes to consume $150 now and
shareholder B wishes to consume only $50 now.

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Fisher’s Separation Theorem:
A Simplified Example (cont.)
● Given their respective consumption
preferences, A and B will desire different
dividend policies from the company.
● Likewise, A will want the company to
invest in project small, while B will prefer
project large.
● Clearly, the company cannot make a
decision that will satisfy both
shareholders simultaneously. Therefore,
it is not possible to say which investment
is optimal.

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Fisher’s Separation Theorem:
A Simplified Example (cont.)
● Solution: introduce a capital market
▪ A solution can be found if there is a
capital market in which shareholders can
borrow and lend on their personal
accounts.
▪ Essentially, the shareholders can lend
excess income (dividends) in the capital
market or borrow to satisfy current
consumption if current dividends are
(temporarily) insufficient.

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Fisher’s Separation Theorem:
A Simplified Example (cont.)
● A resolution is possible because the
capital market enables one of the
shareholders to achieve a result that is
better than the result the company alone
could provide.
● The introduction of the capital market
also enables a company to use the net
present value (NPV) rule to identify the
optimal investment.

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Fisher’s Separation Theorem:
A Formal Approach
● The theorem attempts to provide a
consistent set of decision rules for making
investment, financing and dividend
decisions.
● While initially developed in a simplified
setting, the rules are applicable even when
more realistic assumptions are made.

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Fisher’s Separation Theorem:
A Formal Approach (cont.)
● Assumptions in Fisher’s analysis:
▪ There are only two points in time: the present
(time 1) and a later time (time 2).
▪ There is no uncertainty, and hence, the outcome
of all decisions is known now to everybody.
▪ There are no imperfections in the capital market.
▪ All decision makers are rational.
▪ The company’s managers wish to use the
company’s resources according to the wishes of
the shareholders.

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Fisher’s Separation Theorem:
A Formal Approach (cont.)
● The company
▪ Company is endowed with a fixed amount of
resources at time 1.
▪ Managers must decide how much to invest and
how much to pay out as dividends.
▪ The level of investment at time 1 determines the
resources available to pay dividends at time 2.
▪ These opportunities can be summarised in a
production possibilities curve (PPC).

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Fisher’s Separation Theorem: A
Formal Approach (cont.)
Production Possibilities
Curve
Time
2
Resources
(C2)
250
Q
160
0 150
200
Time 1
Resources
(C1)
Figure 2.1

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Fisher’s Separation Theorem:
A Formal Approach (cont.)
● PPC decisions (assuming 200 units of resources):
▪ Point (200, 0): whole 200 paid as dividend at
time 1, investment is zero, dividend at time 2
is zero.
▪ Point (0, 250): no dividend at time 1, whole of
resources invested at time 1, resources of 250
available for distribution at time 2.
▪ Point Q (150, 160): intermediate case. Time 1:
dividend of 150, 50 invested. Time 2:
resources of 160 available.

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Fisher’s Separation Theorem:
A Formal Approach (cont.)
● The shareholders
▪ Forgo current consumption by investing in a
company at time 1 in order to earn a return that
increases consumption opportunities at time 2.
▪ A person’s preference for consumption at time 1
or 2 can be represented by indifference curves.
▪ The convex shape of indifference curves shows
that a consumer’s desire to increase consumption
at a given time decreases as the level of
consumption at that time increases.

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Indifference
Curves
Time 2
resources (C2)
0
Time 1 resources
(C1)
Figure
2.2

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Fisher’s Separation Theorem:
A Formal Approach (cont.)
● The company’s decision
▪ Bringing the company and shareholders
together: what investment/dividend decision
should be made?
▪ Assuming two shareholders, A & B, with
indifference curves A1, A2, A3 and B1, B2, B3.
▪ As can be seen in the following diagram,
shareholder A’s utility is maximised at point A,
while shareholder B’s utility is maximised at
point B.

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Fisher’s Separation Theorem:
A Formal Approach (cont.)
A1
A
2 A3
250
228 A
B
144
B3
B2
B1
0 9
0
160
200
Figure 2.3

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Fisher’s Separation Theorem:
A Formal Approach (cont.)
● As Figure 2.3 illustrates, there is no
investment decision that can
simultaneously lead to maximum utility for
both shareholders.
● No simple decision rule can be used to
satisfy all shareholders.
● However, such a rule exists if there is a
capital market.

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Fisher’s Separation Theorem:
A Formal Approach (cont.)
● Solution: introduce a capital market
▪ Capital market can be thought of as a
place where current resources may be
transformed into future resources and
vice versa.
▪ Assume capital market is frictionless
(interest rate is the same for borrowers
and lenders).

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Fisher’s Separation Theorem:
A Formal Approach (cont.)
● The market opportunity line can be used to show
the combinations of current and future
consumption that an individual can achieve from a
given wealth level, using capital market
transactions:
W1 = C1 + C2 / [1 + i ]
where C1 = income at time 1
C2 = income at time 2
i = interest rate per period
W1 = person’s wealth at time 1

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Fisher’s Separation Theorem:
A Formal Approach (cont.)
Market Opportunity Line
C2
275
0 250 C1
Figure 2.4

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Fisher’s Separation Theorem:
A Formal Approach (cont.)
● Figure 2.5 (following slide) shows that shareholders
A and B can maximise utility by:
▪ Accepting their income streams of A and B.
▪ Then converting them to streams A ’ and B ’ by
means of a capital market transaction.
● However, stream A should be chosen because it
corresponds to a higher wealth level which, in turn,
ensures higher utility, given access to a capital
market.

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Fisher’s Separation Theorem:
A Formal Approach (cont.)
Market Opportunity
Line
Market Opportunity
Line
C2
27
5
A
16
0
A′
B′
B
0 17
0
25
0
C1
Figure 2.5

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Fisher’s Separation Theorem:
A Formal Approach (cont.)
● Proving there is an optimal policy
▪ Figure 2.6 (following slide) shows a
company, with E units of resources,
which is considering three investment
policies (P1, P2 and P ).
▪ Shareholders will unanimously prefer
policy P because the resulting wealth
level W is the maximum achievable.

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Fisher’s Separation Theorem:
A Formal Approach (cont.)
C
C 2
P2
P
P 3
E
W1 W2 W
C
1
Figure
2.6

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Fisher’s Separation Theorem:
A Formal Approach (cont.)
● Proving there is an optimal policy
▪ Figure 2.7 combines preferences of shareholder
A and B with companies optimal choice.
▪ Choices P1 and P2 provide shareholders with
inferior utility to the choice of P.
▪ Shareholders do not consume at point P.
▪ The capital market allows them to consume at
PA and PB respectively.
▪ This is the best they can do, given the interest
rate.

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Fisher’s Separation Theorem:
A Formal Approach (cont.)
“Insert Figure 2.7 here”

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Fisher’s Separation Theorem:
A Formal Approach (cont.)
● Identifying the optimal policy
▪ The following decision rule should be used:
▪ Accept the project if and only if
Return at time 2 / (1 + i ) – Δ > 0
Where Δ = outlay of units of resources required
i = interest rate per period

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Fisher’s Separation Theorem:
A Formal Approach (cont.)
● The previous decision rule is called the net
present value rule.
● The return next period is divided by the
factor (1 + i ) to convert the future return
to present value. The investment outlay is
then subtracted from the present value to
give the net present value (NPV ).
● If the NPV is positive, the project will
increase the wealth of the shareholders
and should, therefore, be accepted.

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Fisher’s Separation Theorem:
A Formal Approach (cont.)
● Implications for financial decision making
● Implications for investment, financing and
dividend decisions:
▪ Implications hold where there are perfect
markets for both capital and information.
▪ Implications unaffected by the introduction of
uncertainty, provided all participants have the
same expectations.
▪ Implications unaffected by extension to the
multiperiod case.

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Fisher’s Separation Theorem:
A Formal Approach (cont.)
● The investment decision
▪ The theorem means that a company
can make investment decisions in the
interests of every shareholder,
regardless of differences between
shareholders’ preferences.
▪ NPV analysis can be used to identify
the optimal decision.

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Fisher’s Separation Theorem:
A Formal Approach (cont.)
● The financing decision
▪ Fisher’s analysis uses a single market
interest rate.
▪ No distinction between debt and equity
securities, and cost to company of acquiring
funds is independent of the type of security
issued.
▪ Value of company and wealth of
shareholders is independent of the
company’s capital structure.
▪ Financing decision is irrelevant.

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Fisher’s Separation Theorem:
A Formal Approach (cont.)
● The dividend decision
▪ Dividend decision is irrelevant, provided the
company does not alter its investment
decision.
▪ This is possible because, unlike the situation
in Fisher’s analysis, companies can lend or
borrow in the capital market themselves.
▪ For example, a company can pay a higher
dividend and still maintain the optimal level
of investment by borrowing in the capital
market.

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Investors’ Reactions To
Managers’ Decisions
supplies funds
to
transact
in
transmits information
to
Figure
2.11
COMPANY
makes an investment,
funding or dividend
decision
CAPITAL MARKET
There is a
consequent effect on
the company's share
price
INVESTORS
adjust their
expectations

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Investors’ Reactions To
Managers’ Decisions (cont.)
● A company’s managers make an investment,
financing or dividend decision.
● Information about this decision is transmitted to
investors.
● Investors may adjust their expectations of
future returns from an investment and revise
their valuation of the company’s shares.
● Investors compare the market price with their
revised valuation and either buy or sell shares in
the company.

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Investors’ Reactions To
Managers’ Decisions (cont.)
● Certainty
▪ If managers knew with certainty an
investment’s cash flows, they would
know its NPV.
▪ All investors would also know the NPV
of the investment and there would be
an immediate increase in the price of
the company’s shares.

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Investors’ Reactions To
Managers’ Decisions (cont.)
● Uncertainty
▪ In practice, there is uncertainty.
▪ The effect on the share price of decisions made
by managers is no longer perfectly predictable.
▪ A simplification is to assume that the share price
will adjust immediately to reflect the new best
estimate of the ‘true’ value of the company.
▪ Empirical evidence suggests investors react
quickly to the receipt of new information with this
information being reflected in security prices.

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Summary
● How can diverse investors all be satisfied
with the decisions of management?
● Fisher’s Separation Theorem tells us that if
there is a capital market, managers are able
to make decisions that will satisfy all
shareholders.
● Companies should maximise shareholder
wealth and let shareholders use the capital
market to allocate this wealth over time.
● Company and shareholders decisions are
separate.