Optimal Capital Structure: Impact on Firm Value and Cost of Capital

Posted on Jan 17, 2025 in Business Administration and Management (BAM)

RA-RP Combination for Maximizing Firm Value and Minimizing Cost of Capital

The RA-RP combination aims to maximize the market value of the firm (V) and minimize the weighted average cost of capital (Ko). Several theories attempt to find the optimal capital structure. Two main groups of thought exist:

• Those that defend the existence of an optimal capital structure.
• Those that consider that there is no optimal capital structure.

Modigliani-Miller Theorem

Modigliani and Miller (MM) found that the optimal capital structure of a company seeks its explanation in arbitrage.

Departure Hypothesis

1. We are in perfect capital markets with no transaction costs, equal information for all investors, and no influence of divisible values on the price of securities.
2. Absence of income tax.
3. Rational behavior of investors (preferring more wealth to less wealth).
4. Homogeneous expectations: expected value and risk profit are the same for all companies and buyers of shares that are in the same class.
5. Future expected Ktbf (cash flow) by all investors are assumed to be similar.

MM argue that considering this optimal capital structure, the debt level does not affect V or Ko. What is important is the ability of the company’s assets to generate benefits, regardless of how it is financed. Therefore, two companies with the same expected benefits and risk will have the same value.

Proposition 1

Starting hypothesis: No effect of the company’s capital structure on making investment decisions.

Let’s assume that V is obtained by capitalizing the benefits before interest and taxes for all Ko rates. Ko is the same for equivalent risk, regardless of how the company is financed.

Whenever two companies with the same expected benefits have different values, arbitrage comes into play.

We believe that we have two companies (A and B). A is funded only with equity, and B is funded with equity and debt.

Two situations:

1. The company with debt (B) has a higher value.
2. The company without debt (A) has a higher or equal value.

Case 1: Company with Debt (B) Has a Higher Value

There are two shareholders. The first shareholder has:

shares of Company A, while the second has:

shares of Company B. The income on the shares will be:

The shareholder of company B decides to sell its stake, believing that A yields a higher return. The shareholder sells its shares in B and requests a loan to purchase more shares of A. It acquires the equivalent of what it had in B plus a percentage of debt.

It sells:

and borrows:

So that:

The shareholder’s income after the operation is:

The shareholder is still paying interest on the loan. Clearing:

As initially:

and we see that:

the shareholders will continue to sell their shares in the company with debt. This will decrease the price of the shares of the company with debt. On the other hand, they will continue to buy shares of A, increasing its quote. The arbitrage function will make VA = VB. Then, they will stop selling shares of B and buying shares of A.

Case 2: Company without Debt (A) Has a Higher or Equal Value

Then, the shareholder of A will sell its shares and buy shares of B.

It buys:

of shares of Company B and:

debt of Company B. The income will be:

Substituting:

As we believe that:

the returns that are obtained at B are greater than the returns at A. The shareholder will sell shares of A to buy shares of B. This will decrease the value of A and increase the quote of B until they are equal.

Proposition 2

MM believe that the return on equity is constant in proportion to the ratio of debt to equity. A company with debt requires a higher return on equity because as the debt increases, the risk increases.

Proposition 3

MM considered the optimal capital structure of the company independent of making investment decisions. They will always invest if the return rate is at least equal to the weighted average cost of capital.