Chapter 14 Capital structure in a perfect market
14.1 Equity versus debt financing
Unlevered firm: firm with only equity
Levered firm: firm with equity and debt. The amount of debt determines the degree of
leverage.
Levered equity: equity in a firm that also has debt outstanding
More leverage leads to higher risk for shareholders and higher expected returns for
shareholders
But return on assets remains constant and cashflows do not change.
14.2 Modigliani and Miller I: Leverage, arbitrage and firm value
Perfect capital market:
1. Investors and firms can trade the same set of securities at competitive market prices
equal to the present value of their future cashflows.
2. There are no taxes, transaction cost, issuance costs associated with security trading
3. A firm’s financing decisions do not change the cashflows generated by its
investments nor do they reveal new information about them
MM proposition 1
In a PCM the total value of a firm is equal to the market value of the total cashflows
generated by its assets and is not affected by its choice of capital structure.
In PCM the total cashflow paid out to all of a firm’s security holders is equal to the total
cashflow generated by the firm’s assets. As long as the firm’s choice of securities does not
change the cash flows generated by its assets, this decision will not change the total value of
the firm or the amount of capital it can raise.
Even if investors prefer alternative capital structure, the capital structure is still irrelevant.
Investors can borrow or lend on their own and achieve the same result. We call this
homemade leverage. As long as the investors can borrow or lend at the same interest rates
as the firm, homemade leverage is a perfect substitute for the use of leverage by the firm.
Sometimes firms balance sheet includes cash or other risk-free assets
- These securities reduce the risk of firm assets
- Then, they have the opposite effect as leverage
- Thus, we consider them as negative debt that is, what we call debt is actually netto
debt
Net debt = Debt - cash
Market value of equity: market value of assets – market value of debt and other liabilities
1
,14.3 Modigliani-Miller II: leverage, risk, and the cost of capital.
By holding a portfolio of the firm’s equity and debt, you can replicate the cashflows from
holding unlevered equity. Because the return of a portfolio is equal to the weighted average
of the returns of the securities in it. This equality implies the following relationship
RE = Return on levered equity
RU = Return on unlevered equity
RD= Return on debt
D= debt
E = equity
E+D = total assets
So, levered equity return is equal to the unlevered return, plus an additional effect due to
leverage.
The amount of additional risk depends on the amount of leverage. This is measured by the
firms’ market value debt-equity ratio (D/E).
r = expected returns
R = realized returns.
MM proposition II
The costs of levered equity are equal to the cost of unlevered equity plus a premium that is
proportional to the market value debt-equity ratio as provided in the equation.
Weighted average cost of capital WACC
- The cost of capital of the firm’s assets should equal
the return that is available on other investments with
similar risk.
- With PCM, a firm’s WACC is independent of its capital structure and WACC equal to
its unlevered equity cost of capital. Although RD is cheaper, the risk of RE will rise
and so on the RE will rise so the WACC stays the same.
Beta
The effect of leverage on the risk of a firm’s securities can also be expressed in terms of
beta. Unlevered equity is equivalent to a portfolio of debt and levered equity, and because
the beta of a portfolio is the weighted average of the beta of the securities:
βU= Unlevered beta. D = debt
E = equity. βE= levered beta
βD = debt beta
it is often assumed that the debt beta is zero:
2
,Holding cash has the opposite effect of leverage. Leverage of the firm should be measured
in terms of its net debt: debt – cash and risk-free securities.
- The unlevered equity beta is always higher than the debt beta.
- The leveraged Equity beta is always higher than the unlevered equity beta.
- As we increase debt, the beta of the equity increases.
o This happens because as we increase debt, debt holders are getting the
money in the bad states of the economy and therefore equity holders are
losing more money in these states and they are compensated by receiving
more money in good states which creates a higher systematic risk.
- And there for expected return must be higher and also de beta must be higher.
Initial market value/market capitalization of unlevered firm (the value of the firm's equity):
o PV (equity) = cashflow / CoC
o Estimated cashflow = - investment costs + (cashflow/1+CoC)
A leveraged recap does NOT increase/decreases the value of equity
In PCM, capital structure does not affect firm value. A leveraged recap changes the capital structure
but it does not change the assets of the firm (same pizza, different cuts); hence, the firm value is the
same.
14.4 Capital structure fallacies
Two incorrect arguments:
- When leverage increases a firm’s expected earnings per share (EPS) increases, it will
cause the firm’s stock price to increase, however, with PCM an increase in EPS is
accompanied by an increase risk the shareholders are exposed to and MM
proposition I holds.
- Issuing equity will dilute existing shareholders’ ownership, so debt financing should
be used instead. In this context, earnings dilution refers to the idea that if the firm
issues new shares, the cashflows generated by the firms must be divided among a
larger number of shares, thereby reducing the value of each individual share. The
problem with this line of reasoning is that it ignores the fact that the cash raised by
issuing new shares will increase the firm’s assets. As long as the capital raised is
invested in zero NPV investments, the value per share will not change.
In short:
- More leverage increases Earnings per Share (EPS) then stock price should increase.
- issuing capital increases the number of shares, therefore share prices should decrease
14.5 MM: beyond the proposition
Proposition I was one of the first arguments to show that the law of one price could have
strong implications for securities prices and firm values in a competitive market.
Conservation of value principle
With PCM, financial transactions neither add nor destroy value, but instead represent a
repackaging of risk. It implies that any financial transaction that appears to be a good deal in
3
, terms of adding value either is likely too good to be true or is exploiting some type of
market imperfection.
Concept chapter 14:
- Debt is senior to equity; hence leverage increases the risk of equity
- In PCM, capital structure does not affect firm value
4
14.1 Equity versus debt financing
Unlevered firm: firm with only equity
Levered firm: firm with equity and debt. The amount of debt determines the degree of
leverage.
Levered equity: equity in a firm that also has debt outstanding
More leverage leads to higher risk for shareholders and higher expected returns for
shareholders
But return on assets remains constant and cashflows do not change.
14.2 Modigliani and Miller I: Leverage, arbitrage and firm value
Perfect capital market:
1. Investors and firms can trade the same set of securities at competitive market prices
equal to the present value of their future cashflows.
2. There are no taxes, transaction cost, issuance costs associated with security trading
3. A firm’s financing decisions do not change the cashflows generated by its
investments nor do they reveal new information about them
MM proposition 1
In a PCM the total value of a firm is equal to the market value of the total cashflows
generated by its assets and is not affected by its choice of capital structure.
In PCM the total cashflow paid out to all of a firm’s security holders is equal to the total
cashflow generated by the firm’s assets. As long as the firm’s choice of securities does not
change the cash flows generated by its assets, this decision will not change the total value of
the firm or the amount of capital it can raise.
Even if investors prefer alternative capital structure, the capital structure is still irrelevant.
Investors can borrow or lend on their own and achieve the same result. We call this
homemade leverage. As long as the investors can borrow or lend at the same interest rates
as the firm, homemade leverage is a perfect substitute for the use of leverage by the firm.
Sometimes firms balance sheet includes cash or other risk-free assets
- These securities reduce the risk of firm assets
- Then, they have the opposite effect as leverage
- Thus, we consider them as negative debt that is, what we call debt is actually netto
debt
Net debt = Debt - cash
Market value of equity: market value of assets – market value of debt and other liabilities
1
,14.3 Modigliani-Miller II: leverage, risk, and the cost of capital.
By holding a portfolio of the firm’s equity and debt, you can replicate the cashflows from
holding unlevered equity. Because the return of a portfolio is equal to the weighted average
of the returns of the securities in it. This equality implies the following relationship
RE = Return on levered equity
RU = Return on unlevered equity
RD= Return on debt
D= debt
E = equity
E+D = total assets
So, levered equity return is equal to the unlevered return, plus an additional effect due to
leverage.
The amount of additional risk depends on the amount of leverage. This is measured by the
firms’ market value debt-equity ratio (D/E).
r = expected returns
R = realized returns.
MM proposition II
The costs of levered equity are equal to the cost of unlevered equity plus a premium that is
proportional to the market value debt-equity ratio as provided in the equation.
Weighted average cost of capital WACC
- The cost of capital of the firm’s assets should equal
the return that is available on other investments with
similar risk.
- With PCM, a firm’s WACC is independent of its capital structure and WACC equal to
its unlevered equity cost of capital. Although RD is cheaper, the risk of RE will rise
and so on the RE will rise so the WACC stays the same.
Beta
The effect of leverage on the risk of a firm’s securities can also be expressed in terms of
beta. Unlevered equity is equivalent to a portfolio of debt and levered equity, and because
the beta of a portfolio is the weighted average of the beta of the securities:
βU= Unlevered beta. D = debt
E = equity. βE= levered beta
βD = debt beta
it is often assumed that the debt beta is zero:
2
,Holding cash has the opposite effect of leverage. Leverage of the firm should be measured
in terms of its net debt: debt – cash and risk-free securities.
- The unlevered equity beta is always higher than the debt beta.
- The leveraged Equity beta is always higher than the unlevered equity beta.
- As we increase debt, the beta of the equity increases.
o This happens because as we increase debt, debt holders are getting the
money in the bad states of the economy and therefore equity holders are
losing more money in these states and they are compensated by receiving
more money in good states which creates a higher systematic risk.
- And there for expected return must be higher and also de beta must be higher.
Initial market value/market capitalization of unlevered firm (the value of the firm's equity):
o PV (equity) = cashflow / CoC
o Estimated cashflow = - investment costs + (cashflow/1+CoC)
A leveraged recap does NOT increase/decreases the value of equity
In PCM, capital structure does not affect firm value. A leveraged recap changes the capital structure
but it does not change the assets of the firm (same pizza, different cuts); hence, the firm value is the
same.
14.4 Capital structure fallacies
Two incorrect arguments:
- When leverage increases a firm’s expected earnings per share (EPS) increases, it will
cause the firm’s stock price to increase, however, with PCM an increase in EPS is
accompanied by an increase risk the shareholders are exposed to and MM
proposition I holds.
- Issuing equity will dilute existing shareholders’ ownership, so debt financing should
be used instead. In this context, earnings dilution refers to the idea that if the firm
issues new shares, the cashflows generated by the firms must be divided among a
larger number of shares, thereby reducing the value of each individual share. The
problem with this line of reasoning is that it ignores the fact that the cash raised by
issuing new shares will increase the firm’s assets. As long as the capital raised is
invested in zero NPV investments, the value per share will not change.
In short:
- More leverage increases Earnings per Share (EPS) then stock price should increase.
- issuing capital increases the number of shares, therefore share prices should decrease
14.5 MM: beyond the proposition
Proposition I was one of the first arguments to show that the law of one price could have
strong implications for securities prices and firm values in a competitive market.
Conservation of value principle
With PCM, financial transactions neither add nor destroy value, but instead represent a
repackaging of risk. It implies that any financial transaction that appears to be a good deal in
3
, terms of adding value either is likely too good to be true or is exploiting some type of
market imperfection.
Concept chapter 14:
- Debt is senior to equity; hence leverage increases the risk of equity
- In PCM, capital structure does not affect firm value
4
