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Capital Structure Case Solution

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The term arbitrage refers to the notion of ‘riskless profit’. In the field of finance and economics, arbitrage represents the purchase of an asset/commodity at a certain price and its immediate sale at a higher price. Usually, the differences in the purchase and sale price arise due to several reasons. However, the two strongest reasons in favor of arbitrage principle are the market inefficiencies and the information asymmetry in the market. Either the markets are not aligned, or the market participants are not aware of the true fair value of the underlying asset/stock. At the same time, it should be noted that in finance, arbitrage can only be carried out in the short term. In the long run, every investor tries to gain riskless profit. As a result of increased purchases and sales of an asset/stock, the market redefines its price in such a way that the market inefficiencies and information asymmetry are removed, and the price of the good in different markets becomes equal. This identical price of the asset/stock in different markets is the actual fair value. In economics, this concept of having no arbitrage, in the long run, was termed by Adam Smith as ‘the invisible hand’. Arbitrage borrows its central theme from the notion of a law of one price that states that the price of a good will be same in all markets, and hence any mismatch in the pricing is either impossible or temporary.

Following questions are answered in this case study solution

  1. In finance, what does one mean by the term arbitrage?

  2. Describe how Miller explains the proof of MM I using the no-arbitrage principle in this article.

  3. Miller lists many objections people have raised since 1958 on his work with Modigliani and answers them each with counter-arguments.

  4. Similarly, in your own words, describe the criticism of MMs Dividend Irrelevance Theory and Millers response as discussed in this paper.

Case Analysis for Capital Structure

2. Describe how Miller explains the proof of MM I using the no-arbitrage principal in this article.

The first preposition of Modigliani and Miller state that the value of the firm is calculated by the present value of the cash flow streams that its asset generate. Hence, this value is not affected by the choice of capital structure. In other words, the values of identical levered and unlevered firms are equal. Miller points out that the concept of homemade leverage can be used as a tool to attain equal payoffs for both the levered and unlevered firms. For example, let's suppose an investor can invest in both unlevered (U) and levered (L) firms.

X = Identical cash flow steams of U and L

S(u,l) = Equity

D(l) = Debt

If the investors hold A% shares of U, then the investment can be calculated as follows:

Investment in Equity Only


A * S (u) = A * V (u)

A * X

This investment will yield a return of A * X.

On the other hand, an investor can replicate the exact payoff by investing in the equity and debt of levered firm L.





A * S (l) = A * {V (l) - D (l)}

A * {X - rD (l)}


A * D (l)

A * r * D (l)



A * X

The total return in this case again comes out to be A times X. Hence, the investor can buy both the stock and the bonds of the levered firm in order to replicate the returns unlevered firms. This step will provide the investor with an equivalent of all equity-type investment. In this scenario, the value of both the levered and unlevered firms should be equal because no one would buy a share if the value of levered and unlevered firms are not equal.

3. Miller lists many objections people have raised since 1958 on his work with Modigliani and answers them each with counter-arguments.

The points of criticism along with the counter-arguments are listed in the following table:

S no

Point of Criticism



When the dividends of the firm and the cash flows are different, the value invariance preposition will not hold sound empirical evidence.

A second preposition named as dividend irrelevance was formulated in order to tackle this objection. According to this preposition, the value of the firm is independent of its dividend policy.


The announcement of dividend invokes a high stock price reaction.

This price reaction is a failure of one of the assumptions of MM1 and MM2 and not the prepositions themselves. The price adjusts to the ‘new information’ about future cash flows.


Cutting the investment and paying them as dividends also cause price shocks  

Voting rights are allocated the commons shareholders, and there is a separation between management and ownership.


Individuals cannot duplicate the corporate form of structure in which the firms possess limited liability, and the arbitrage proof assumed that individual could do that.

Individual investors can duplicate the form by including a riskless asset as debt in their portfolio. This riskless investment in the government bonds can be taken as a synonymous to the riskless bond.  


Firms can use financial innovation to create more value via high leveraged and limited liability securities. 

The financial innovation via high leveraged securities is very difficult to attain. Moreover, the main source of financial innovation is commodity and securities exchange rather than corporations.

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