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CENTRAL UNIVERSITY COLLEGE

CORPORATE FINANCE

GROUP ASSIGNMENT

MEMBERS INDEX NUMBERS

JOSHUA LAMPTEY ECS/08/01/0052

SUSUANA ODOI ECS/08/01/0038

ASIAMA REXFORD K. ECS/08/01/0047

HAROLD OPOKU ECS/08/01/0063

JAMILA ZAKARI ECS/08/01/0034

JOYCE DENTEH ECS/08/01/0042

Q: DISCUSS THE MM THEORY OF CAPITAL STRUCTURE WITH NO

TAXES.

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The M&M theorem-no taxes, also called the Capital Structure Irrelevance Principle or the

Net Operating Income Approach, forms the basis of modern thinking for capital structure. It is

the fundamental framework or model for the analysis of capital structure, with considerations

made for taxes thereof, which was developed in 1958. The traditional theory of capital structure

existed before and was questioned by two Nobel Prize laureates, Franco Modigliani and Merton

Miller, hence the nameM&M.

Miller and Modigliani wrote the article that gave birth to this theory when they were both

professors at the Graduate School of Industrial Administration (GSIA) of Carnegie Mellon

University. It is through the article that the theorem was derived. Miller and Modigliani were set

to teach corporate finance for business students and despite the fact that they had no prior

experience in corporate finance. When they read the material that existed, they found it

inconsistent so they sat down together and tried to figure it out. The result of this was the article

in theAmerican Economic Review and what has now come to be known as the M&M theorem.

The M&M theorem is in two parts. But our consideration is on the propositions made by

Miller and Modigliani that involve no tax, otherwise referred to as the M&M theorem-no taxes.

The theorem makes a number of assumptions that help in drawing the conclusions that are made

by the propositions. These include:

y All investors are price takers, i.e. no individual can influence market prices bythe scale of his/her transactions.

y All market participants, firms and investors, can lend or borrow at the same risk-free rate.

y There are neither personal nor corporate income taxes.y There are no brokerage or other transactions charges.y Investors are all rational wealth seekers.y Firms can be grouped into homogenous risk classes such that the market seeks

the same return from all member firms in each group.

y Investors formulate similar expectations about future company earnings. Theseare described by a normal probability distribution.

y The assets of an insolvent firm can be sold at full market values.

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Following the assumptions that are presented above, the book Corporate Finance and

Investment Decisions and Strategies shows that Miller and Modigliani made three propositions

that describe this theorem. Our first consideration is below:

Proposition I:

The central proposition is that a firms Weighted Average Cost of Capital (WACC) is

independent of its debt-equity ratio and equal to the cost of capital that the firm would have

with no gearing in its capital structure. In other words, the appropriate capitalization rate for a

firm is the rate applied by the market to an ungeared company in the relevant risk category, i.e.

that companys cost of equity.

This proposition as we have stated above is also known as the Pie Model in the book

Essentials ofCorporate Finance. Under this, one way to illustrate the M&M proposition is to

imagine any two firms that are identical on the left hand side of the balance sheet. Their assets

and operations are exactly the same. The right hand sides are different because the two firms

financed their operations differently. In this case we can view the capital structure question in

terms of a pie model. Consider two firms A and B. According to proposition I, the value of the

two firms should be the same irrespective of their capital structure. Firm A has 40% stock and

60% bonds in its capital structure. Firm B has 60% stock and 40% bonds in their capital

structure. Even though the two firms have different sizes of bonds and stocks, or have their pie

slices differently, the value of their assets is the same. This is precisely what Proposition I states:

the size of the pie doesnt depend on how it is sliced.

Firm A Firm

B

However, the arbitrage mechanism will operate to equalize the values of any two companies

whose values are temporarily out of line with each other.

Stocks

40% Bonds

60%

Stocks

60%

Bonds

40%

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If we have determined that any two firms A and B, as in our example, have the same value

irrespective of their capital structure, their returns of equity may differ as well as their return on

debt. Even though their values are the same, the two firms experience different values on their

returns of their equity and their debt, hence the need for the next proposition made by Miller and

Modigliani.

Proposition II:

This proposition talks about the behavior of the relevant cost of capital concepts, in

particular, the rate of return required by shareholders. This is expressed in a statement the

expected yield of a share of equity is equal to the appropriate capitalization rate,K.e,for a pure

equity stream in the class, plus a premium related to the financial risk equal to the debt-equity

ratio times the spread between K.e andK.d.

This same statement is rephrased from another book previously mentioned, Essentials

ofCorporate Finance.According to it, although changing the capital structure of the firm may

not change the firms total value, it does cause important changes in the firms debt and equity.

The book states the proposition II as follows: a firms cost of equity capital is a positive linear

function of its capital structure.

We consider the example of a form that is both debt financed and equity financed and

see the effects when the debt/equity ratio is changed. Since we made the assumption that there

are neither personal nor corporate income taxes, the assumption is used for this analysis. The

Weighted Average Cost of Capital (WACC)is the average return on a firms assets and has the

following formula:

WACC(K.o) = (E/V) * K.e + (D/V) * K.d

where V=D+E. Since the WACC is a rate, we have also represented it by the variable K.o.

If we rearrange the above equation to make K.e the subject, the following formula arises:

K.e = K.o + (K.o K.d) * (D/E) ----------- (1)

The equation above emphasizes the M&M proposition II and shows that the cost of equity

depends on three things: the required rate of return on the firms assets, K.o, the firms cost of

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debt, K.d. and the firms debt-equity ratio (D/E). From the above equation, the firms cost of

equity is a positive linear function of the capital structure of the firm, i.e. the debt-equity ratio.

This formula is reaffirmed by the use of figures. Our example is that Firm A, as mentioned

earlier, has a weighted average cost of capital (K.o), ignoring taxes, of 12% and can borrow at

8%. Assuming that firm A has a target capital structure of 80% equity and 20% debt, the cost of

equity (K.e) is calculated as 0.12+ (0.12 0.08) * (0.02/0.08) = 0.13 or 13%. If the firm changes

its capital structure by raising the debt proportion to 50%, the debt-equity ratio becomes

0.5/0.5=1. Hence the return on equity/ cost of equity is calculated as 0.12 + (0.12 0.08) * (1) =

0.16 or 16 %.

Now the weighted average cost of capital (K.o) is calculated using its formula and referring

to the capital structure of 80% equity and 20% debt. The K.e of 13% and the K.d of 8% is used

to get the K.o of 0.12 or 12% under the capital structure of 80% equity and 20% debt. Also,

when the debt-equity ratio is changed to 50% debt and 50% equity, the weighted average cost of

capital (K.o) is calculated, using K.e of 16% and K.d of 8%, to give the same answer to be 0.12

or 12%.

The proposition II is established by K.e adjusting from 13% to 16% when the debt-equity

ratio moved from 0.2/0.8 to 0.5/0.5. This shows the positive relationship between the cost of

equity and the debt-equity ratio.

However, the firms return on assets remains unchanged by the K.o remaining at 12% even

when the capital structure (debt-equity ratio) and the return on equity (K.e) were changed. This

also re-emphasizes the M&M proposition I since the return on the companys assets, which is a

measure of the value of the firm, remains unchanged. A graph of this relationship is shown on

the next page. That means that the return/ cost on equity (K.e) will always adjust positively to the

debt-equity ratio (D/E) so that the return/cost on all the firms assets (K.o) will remain the same,

as long as all the assumptions hold.

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PROPOSTION III:

We conclude our work by considering the last proposition made by Miller and Modigliani.

Here, the cut-off rate for new investment will in all cases be K.o and will be unaffected by the

type of security used to finance the investment. Proposition I states that the WACC, Ko, is

constant and equal to the cost of equity in an equivalent ungeared company. Since Ko is

invariant to capital structure, it follows that however a project is financed, it must yield a returnof at least Ko, the overall minimum return required to satisfy stake holders as a whole

References:

Corporate Finance and Investment Decisions and Strategies, Richard Pilke and Bill Naele,

p. 523-526

Essentials of Corporate Finance, Stephen A. Ross, Randolph Westerfield, Bradford Jordan,

p. 361-363