A Unified Analytical Theory of Production
and Capital Structure of Firms
Irrelevance of capital structure in a
perfect market
• Modigliani and Miller (1958)
• If an imperfection is identified, this type of
imperfection would be gradually reduced
over time from competition or regulation.
So we might expect capital structures of
firms will be less and less relevant and
financial decision making becomes simpler
and simpler over time.
• Reality is not the case.
Question on the assumption of
imperfection
• Miller (1998) on agency cost
• Tax as an imperfection
• But the impacts of taxes can be precisely
measured
Empirical investigation on capital
structure
• puzzles in corporate finance often result
not from “imperfect market” but rather from
“imperfect theory” (Molina, 2005).
Relation between production and
capital structure of firms
• In early literature production of a firm is
independent from financing decisions
• Empirical evidences: firm’s financial
decisions are closely related to the
operational side of the firm and market
environment (Istaitieh and RodriguesFernandez, 2005; Khanna and Tice,
2005).
• A unified theory is desirable.
analytical theory of production and
capital structure of firms
• natural extension from an analytical theory
of production
• the main result is an analytical formula of
variable cost of production as a function of
fixed cost and uncertainty
fixed cost and variable cost
• Fixed costs are pre-committed costs
• Variable cost changes with the many
environmental factors, including the value
of the product.
Extension to capital structure
theory
• Problems on capital structure can be naturally
incorporated into the theory on production from
a simple observation.
• Debt is fixed income for investors and hence
fixed cost for issuing firms. The increase of debt
increases the fixed cost of firms.
• The decision on capital structure is part of the
decision process that determines the level of the
fixed cost and variable cost of firms to achieve a
high rate of return based on the understanding
of current and future market conditions.
Empirical findings
• The new theory, by integrating financial
decisions into the general firm decision
processes, offers a simple and
parsimonious understanding to a broad
range of empirical patterns documented in
the literature.
Capital structure and the level of
uncertainty
• Two projects are producing two different products. Both projects
have 1.5 million dollar fixed cost in production, which are financed
by equity. Suppose the annual revenue of both products is 1 million.
Both production facilities will last for 10 years. The diffusion rate for
the first product is 40% per annum and the diffusion rate for the
second product is 60% per annum. The discount rate is 5% per
annum. What is the variable cost for each product? What are the
NPV for each project? The equity owners of the two projects are
concerned that their capital structures may not be optimal. They try
to determine the optimal fixed cost level for the projects by
maximizing NPV value with respect to fixed costs for each project,
assuming all other parameters, i.e., diffusion rate, duration of project
and discount rate, are the same. What are the optimal fixed costs
for both projects? Suppose the extra fixed costs are generated
through debts. What are the amounts of debts for both projects?
What are the resulting debt equity ratios for both projects?
Solution
S
1
S
1
K
1.5
K
2.5417
R
0.05
R
0.05
T
10
T
10
sigma
0.4
sigma
0.4
c
0.4978
c
profit
3.5222
profit
0.36
3.858
ratio of profit
1.0954
asset
6.3997
equity
5.358
debt/equity ratio
0.1944
Notes on calculation
• Debt level = Optimal fixed cost – operating
fixed cost
• 2.5417-1.5
• Asset = (S-C)T
• Equity = asset - debt
S
1
S
1
K
1.5
K
1.7319
R
0.05
R
0.05
T
10
T
10
sigma
0.6
sigma
0.6
c
0.6732
c
0.6487
profit
1.7675
profit
1.7807
ratio of profit
1.0075
asset
3.5126
equity
3.2807
debt/equity ratio
0.0707
Discussion
• Intuition suggests the debt equity ration
increases when uncertainty declines.
• The calculation from this example confirms
it.
• New industries, high uncertainty, mostly
equity financed.
• Mature industry, less uncertainty, more
debt financed.
Capital structure and duration of
projects
• Two projects are producing two different products. Both projects
have 2 million dollar fixed cost in production, which are financed by
equity. Suppose the annual output of both products is 1 million. One
project will last for 10 years and the other project will last for 15
years. The diffusion rate for both projects is 35% per annum. The
discount rate is 5% per annum. What is the variable cost for each
product? What are the NPV for two projects? The equity owners of
the two projects are concerned that their capital structures may not
be optimal. They try to determine the optimal fixed cost level for the
projects by maximizing NPV value with respect to fixed costs for
each project, assuming all other parameters, i.e., diffusion rate,
duration of project, market size and discount rate, are the same.
What are the optimal fixed costs for both projects? Suppose the
extra fixed costs are generated through debts. What are the debt
level of the two projects? What are the debt equity ratios of both
projects?
Solution
K
2
K
2.627984
R
0.05
R
0.05
T
10
T
10
sigma
c
market size
profit
0.35
0.364565
10
4.354347
sigma
c
market size
0.35
0.289776
10
profit
4.474257
ratio of profit
1.027538
debt/equity ratio
0.140355
S
1
S
1
K
2
K
3.628384
R
0.05
R
0.05
T
15
T
15
sigma
c
market size
profit
0.35
0.51621
15
5.256845
sigma
c
market size
0.35
0.368485
15
profit
5.844339
ratio of profit
1.111758
debt/equity ratio
0.278626
Discussion
• In general, longer term projects are more
leveraged.
• Companies with more tangible assets
usually are more leveraged, as tangible
assets are long term assets.
• In accounting, long term debts are treated
as capital.
• Short term debts are liabilities.
Capital structure and operating
leverages
• Two projects are producing two different products. One project has 1
million dollar fixed cost in production and another project has 2
million dollar fixed cost in production, which are financed by equity.
Suppose the annual output of both products is 1 million. Both
projects will last for 15 years. The diffusion rate for both projects is
40% per annum. The discount rate is 4% per annum. What is the
variable cost for each product? What are the NPV for two projects?
The equity owners of the two projects are concerned that their
capital structures may not be optimal. They try to determine the
optimal fixed cost level for the projects by maximizing NPV value
with respect to fixed costs for each project, assuming all other
parameters, i.e., diffusion rate, duration of project, market size and
discount rate, are the same. What are the optimal fixed costs for
both projects? Suppose the extra fixed costs are generated through
debts. What are the debt equity ratios are both projects?
S
1
1
1
K
3.349835
2
1
R
0.04
0.04
0.04
T
15
15
15
sigma
0.4
0.4
0.4
c
0.425279
0.540881
0.685679
profit
5.270984
4.886782
3.714818
profit ratio
1.078621
1.418908
debt/equity ratio
0.276222
0.632557
Discussion
• Projects with low operating leverages
often have high financial leverages.
Dividend payout policy
• Two projects are producing two different products. Both projects
have 2 .5 million dollar fixed cost in production. Suppose the annual
output of both products is 1 million. Both projects will last for 10
years. The discount rate is 8% per annum. The diffusion rate for one
projects is 50% per annum and for another project is 60% per
annum. What is the variable cost for each product? What are the
NPV for two projects? The equity owners of the two projects are
concerned that their capital structures may not be optimal. They try
to determine the optimal fixed cost level for the projects by
maximizing NPV value with respect to fixed costs for each project,
assuming all other parameters are the same. What are the optimal
fixed costs for both projects? Suppose the excess fixed costs can be
reduced through additional dividend payout. What are the amounts
of additional dividend payout you recommend for two projects?
Solution
S
1
S
1
K
2.5
K
2.1326
R
0.08
R
0.08
T
10
T
10
sigma
0.5
sigma
0.5
c
0.5457
c
0.5799
profit
2.0434
profit
2.0681
ratio of profit
1.0121
additional dividend payout
0.3674
Notes on solution
• Fixed cost on right half of the slide is the
level of fixed cost that maximize profit.
• Additional dividend payout is the
difference between two fixed costs.
S
1
S
1
K
2.5
K
1.5665
R
0.08
R
0.08
T
10
T
10
sigma
0.6
sigma
0.6
c
profit
0.637
1.1296
c
0.7149
profit
1.2845
ratio of profit
1.1371
additional dividend payout
0.9335
Discussion
• When the diffusion rate is high, the
dividend payout is high.
• For declining businesses with high
diffusion rate, dividend payout should be
speeded so capital can be utilized in
higher return projects.
Life cycle of financing
• Initially, uncertainty is high, mainly equity
financing.
• Later, with lower uncertainty, debt finance
kicks in.
• As firms grow and develop more tangible
assets, debt/equity ratio can increase
further.
• In a declining stage, cash flows should be
distributed to more promising areas.
Example
• Berkshire Hathaway
• When Warren Buffett controlled Berkshire
Hathaway, it had large amount of cash
flows due to past success. But its share
price was very low due to its dim future
prospect.
• Warren Buffett diverted its cash flows to
higher return investments.
Life cycle of firms and human
beings
• There are three basic principles in
corporate finance: the investment
principle, the financing principle and the
dividend principle. We will discuss human
life from these three principles.
• A young firm often tries different kinds of businesses
before settle on one. Similarly, a small child often tries
different things. One year, she may learn skating, next
year, skiing, then, soccer, swimming and many other
things. You may find your favorite sport eventually and
stick to one or several you do best. When a firm is
young, it may try out many different things before settling
down on one or several main businesses. When a firm is
young, a lot of investments are needed. When a firm
matures, little investment is needed. It turns into a cash
cow. Similarly, when a person is young, she needs to
attend school and receive a lot of different trainings.
When she is at a mature age, she takes very little
training but earns a high income.
• The ability to learn new things changes with age,
both with humans and with firms. A child can
pick up a new language easily. An adult almost
impossible. A child can learn new skills, such as
skating, with great ease. For an adult, it often
takes great courage to step on ice for the first
time. The same is with firms. Young firms can
change direction very easily. But established
firms can rarely invest in new types of business
with ease. This is because small fixed cost
systems are more flexible than high fixed cost
systems.
• A firm can be financed by either equity or debt. A small child is
mainly financed by her parents, that is, financed by equities. When
she grows up and earns an income, she has more abilities to get
debt financing. For example, she can apply a mortgage or obtain a
credit card easily if she has steady income. When she gets older,
she may have paid off her mortgages and other debts. At this stage,
she mainly finances her activities with her own internally generated
funds, that is, her own incomes.
• You will find similar financing patterns for firms. It is almost
impossible to get debt financing for start up firms. They generally are
funded by owners’ own money, or equities. When a firm generates
more steady income and accumulate tangible and intangible assets,
they can get debt financing easier to expand. At mature stage, firms
rarely need external financing. Internally generated funds are often
more than enough to cover investment needs.
• A firm’s value is total sum of dividends discounted over
time. A small child apparently doesn’t pay out dividend,
just like a young firm rarely pays out much
dividend. When a person grows up, her ability to help
others grows. The most substantial dividend for a person
must be her children. If we look at patterns of child
bearing over the years, the ages that people start to
have children become older and older. This pattern is
similarly reflected in corporate dividend payouts. The
time that a firm starts to pay out dividend has increased
over time and the payout ratio has declined over time
because the cost of investment has increased over time.
• Similarly, people start to have children later because of
the longer years of school education and longer period of
training in works. Is it a good trend? Canadian birthrate
has dropped to 1.5 per woman, which is unsustainable.
The high tech firms, which pay out scanty dividends,
have dropped sharply in their value since 2000. In
general, higher dividend growth is equal to high earning
growth (Arnott and Asness, 2003). In any business,
common sense is our most important asset. By offering a
unified understanding of human life and corporate life,
we can extend our everyday experiences directly to
financial matters.
Conclusion
• Firm’s capital structure is an integrated
part of corporate strategy.
• “market imperfection” is not needed in
understanding empirical patterns.