The Cost of Capital, Corporation Finance and The Theory of Investment

THE COST OF CAPITAL,
CORPORATION FINANCE AND
THE THEORY OF INVESTMENT
Raju Basnet Chhetri
25 May 2020

DESCRIPTION OF
THE ARTICLE Authors: Franco Modigliani,
Professor of Economics, and Merton
H. Miller, Associate Professor of
Economics, Graduate School of
Industrial Administration, Carnegie
Institute of Technology.
Title: The Cost of
Capital, Corporation
Finance and The Theory
of Investment
Journal: The American Economic
Review, Vol XLVIII, No. 3, June 1958,
pp. 261-297.

BACKGROUND
Under the assumption of certainty either of the two rational decision-
making criteria persists:
1) maximization of profits
2) maximization of market value.
Some attempts have been usually made to allow for existence of
uncertainty by subtracting risk discount from expected yield or by
adding risk premium to the market rate of interest and called “risk
adjusted” or “certainty equivalent” yield with the market rate of
interest.
With the recognition of uncertainty, the profit maximization criteria
has evolved into utility maximization. Nevertheless, the utility
maximization also has serious drawbacks for normative and analytical
purposes.

RESEARCH GAP/MOTIVATION
The lack of adequate theory of the effect of financial structure on
market valuations was the motivation for the research. Hence, the
research was concerned with development of a theory and discuss its
implications.

PURPOSE
1) To develop a basic theory of capital structure.
2) To show how the theory can be used to answer the cost-of-capital
question and how it permits to develop a theory of investment of
the firm under conditions of uncertainty.

METHODOLOGY
The authors have propounded propositions and proved their
propositions by way of empirical proof/evidences, illustrations and
diagrammatic explanations. The study uses descriptive and analytical
research design.
Data was used from two researches for preliminary evidence on basic
propositions propounded in the research.
1) the average value of actual net returns of 43 large electric utilities
based on years 1947 and 1948 drawn from Allen (1954), and
2) the actual net returns of 42 oil companies based on year 1953
drawn from Smith (1955).

METHODOLOGY
Regression analysis was performed to analyze the relationship
between variables and correlation coefficient was used to test the
degree of relationship.
Scatter diagrams were used to identify linear/non-linear
relationships between variables.
Numerical illustrations were presented for elaboration of models and
empirical verification.
Preliminary numerical illustrations were explained to support the
results of analyses.

DISCUSSION AND RESULTS
Discussed in two major sections:
I. The valuation of Securities, Leverage, and the Cost of Capital
A. The Capitalization rate for Uncertain Streams
B. Debt Financing and Its Effects on Security Prices
C. Some Qualifications and Extensions of the Basic Propositions
D. The relation of Propositions I and II to Current Doctrines
E. Some Preliminary Evidence on the Basic Propositions
II. Implications of the Analysis for the Theory of Investment.
A. Capital Structure and Investment Policy
B. Proposition III and Financial Planning by Firms
C. The Effect of the Corporate Income Tax on Investment Decisions

PROPOSITION I
The market value of any firm is independent of its capital
structure and is given by capitalizing its expected return at
the rate 𝑝 𝑘 appropriate to its class.
For any firms j in class k,
𝑉𝑗 ≡ 𝑆𝑗 + 𝐷𝑗 = 𝑋𝑗/𝑝 𝑘
where,
𝑋𝑗 = expected return on the assets owned by company, 𝐷𝑗 = market
value of debts of the company, 𝑆𝑗 = market value of its common
shares, 𝑉𝑗 ≡ 𝑆𝑗 + 𝐷𝑗 = market value of all its securities (or market
value of firm).

Proposition I was stated in terms of firm’s average cost of capital as:
The average cost of capital to any firm is completely
independent of its capital structure and is equal to the
capitalization rate of a pure equity stream of its class.
For any firms j in class k,
𝑋𝑗/ 𝑆𝑗 + 𝐷𝑗 = 𝑋𝑗/𝑉𝑗
where,
𝑋𝑗/𝑉𝑗= ratio of expected return to the market value of firm

Assumptions in deriving Proposition I
All bonds (including any debts issued by households for the purpose
of carrying shares) yield a constant income per unit of time.
Bonds are traded in perfect market.
In any given class, the price of share must be proportional to its
expected return. For any firms j in class k (From Marshallian Price
Theory),
𝑝𝑗 =
1
𝑝 𝑘
∗ 𝑥𝑗
where,
𝑝𝑗 = price, 𝑥𝑗= expected return per share,
𝑥 𝑗
𝑝 𝑗
= 𝑝 𝑘 a constant.

Proving Proposition I
To prove Proposition I, the author had illustrated by way of
numerical expression that as long as the equations of proposition I
does not hold between any pair of firms in a class, arbitrage will take
place and restore the stated equalities.

PROPOSITION II
The expected yield of a share of stock is equal to the
appropriate capitalization rate 𝑝 𝑘 for a pure equity stream in the
class, plus a premium related to financial risk equal to the
debt-to-equity ratio times the spread between 𝑝 𝑘 and r.
𝑟𝑗 = 𝑝 𝑘 + (𝑝 𝑘 − 𝑟) 𝐷𝑗/𝑆𝑗
Capitalization rate
Premium related to financial risk (i.e. D/E times spread)

EFFECTS OF TAXING
CORPORATIONS
𝑋𝑗
𝑟
≡ 𝑋𝑗 − 𝑟𝐷𝑗 1 − 𝑟 + 𝑟𝐷𝑗 ≡ 𝑝𝑖 𝑗
𝑟
+𝑟𝐷𝑗
where,
𝑋𝑗
𝑟
= total income net of taxes, 𝑝𝑖 𝑗
𝑟
= expected net income, r = average rate of
corporate income tax
Incorporating the effects of taxing corporations proposition I and II were
expressed as,
Proposition I:
𝑋𝑗
𝑟
𝑉 𝑗
= 𝑝 𝑘
𝑟
Proposition II:
𝑖𝑗 ≡
𝑝𝑖 𝑗
𝑟
𝑆 𝑗
= 𝑝 𝑘
𝑟
− 𝑟 𝐷𝑗/𝑆𝑗

EFFECTS OF PLURALITY OF
BONDS AND INTEREST RATES
Proposition I: Unaffected by the fact that, the
increased cost of borrowed funds with increase
in leverage will tend to be offset by a
corresponding reduction in the yield of common
stock.
Proposition II: The relation between common
stock yields and leverage was no longer strictly
liner as original proposition. It was found that, if
the yield curve r=r(D/S) increases with leverage,
the yield i will still tend to rise as D/S increases,
but at a decreasing rather than a constant rate.
Beyond some high level of leverage, depending
on the exact form of the interest function, the
yield may even start to fall.

EFFECT OF LEVERAGE ON THE
COST OF CAPITAL: PRELIMINARY
EVIDENCE
The average cost of capital
𝑋𝑗
𝑟
𝑉 𝑗
(denoted by x) and leverage
𝐷
𝑉
(denoted
by d) was regressed to find the following results:
Electric Utilities x = 5.3 + 0.006d r = 0.12
(± 0.008)
Oil Companies x = 8.5 + 0.006d r = 0.04
(± 0.024)
The results provided no evidence of any tendency for the cost of
capital to fall as the debt ratio increases suggesting that the cost of
capital is not affected by capital structure.
Correlation coefficients:
Close to zero. Not statistically significan

EFFECT OF LEVERAGE ON
COMMON STOCK YIELDS:
PRELIMINARY EVIDENCE
The expected yield on common stock
𝑝𝑖 𝑗
𝑟
𝑆 𝑗
(denoted by z) and debt-to-
equity
𝐷
𝑆
(denoted by h) was regressed to find the following results:
Electric Utilities x = 6.6 + 0.017h r = 0.53
(± 0.04)
Oil Companies x = 8.9 + 0.051h r = 0.53
(± 0.012)
The results and transformation with square term supported the
tendency of yield on common stock to increase with leverage.
Correlation coefficients:
Positive and statistically significant.

PROPOSITION III
The cut-off point for investment in the firm will in all cases be
𝑝 𝑘 and will be completely unaffected by the type of security
used to finance the investment.
i.e. A firm will exploit an investment opportunity if and only if the
rate of return on the investment is equal to or larger than 𝑝 𝑘.
This was illustrated using three major financing alternatives: bonds,
retained earnings, and common stock issues.

PROPOSITION III AND FINANCIAL
PLANNING BY FIRMS
It was analyzed that the alternatives in financial plans may not be a
matter of indifference and for investment decisions, the marginal cost
of capital is 𝑝 𝑘.

THE EFFECT OF THE CORPORATE
INCOME TAX ON INVESTMENT
DECISIONS
In this case, it was found that the cost of capital depends on the debt
ratio.
Thus, with interest deductible corporate tax, gains can accrue to
shareholders from having debt in capital structure, even when capital
markets are perfect.
However, it was also inferred that the magnitude of gain is small and
lower rate of interest tend to lower the gain from debt.

LIMITATIONS OF THE RESEARCH
The focus of study was on firm and industry level (partial equilibrium)
and not on entire economy level (general equilibrium).
No attempt was made to test the possible influence of dividend pay-
out ratio in the model.
Only the state of atomistic competition in capital markets was
assumed.

CONCLUSION
Development of Propositions I and II leading to Proposition III evolved
a new concept that can be used as basis for rational investment
decision making within firm.
It was concluded that
the market value of any firm is independent of its capital structure;
the return or cost on equity increases with increase in leverage;
the cut-off point for investment in the firm will in all cases be the
expected rate of return from shares and will be completely unaffected
by capital structure of the investment.

REFLECTION FROM THE ARTICLE
The research consisted of development of theory, empirical
evaluation and numerical illustration to support the model and the
findings, which provided us ample examples for validity of findings
which could be used in further researches.
The research was revised version of previous research which provided
a reflection that research is ongoing process and helps to unfold what
was previously unseen.

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