Summary : Corporate Finance (5th edition)
Chapter 14 - Capital Structure in a Perfect Market
14.1 - Equity Versus Debt Financing
Capital structure = the relative proportions of debt, equity, and other securities
that a firm has outstanding
Two ways to finance a firm/project:
Option 1: financing a firm with only equity (= unlevered equity)
Initial investment = $800
Projected cashflow in 1 year: either $1400 (50%) or $900 (50%) -> estimated:
$1150
Risk free interest rate = 5%
Risk premium = 10%
Cost of capital for this project = 15%
NPV = -$800 + $.15 = $200
-> entrepreneur can either complete the project and keep the projected cash flow
or cash out right now and earn $200 (this is because investors are willing to ‘buy’
the project for the discounted projected cash flow: .15 = 1000)
Option 2: financing a firm with debt and equity (= levered equity)
Borrowed amount = $500
Amount owed in one year: $525 (because of 5% risk free interest rate)
Projected cashflow in 1 year: either $1400 (50%) or $900 (50%)
Since debt holders get paid first, projected profit: either $875 (50%) or $375
(50%)
-> by the law of one price, the combined values of debt and equity must be equal
to the NPV of future cash flows (which is still $1000)
So: levered equity = $500
* Leverage increases the risk of equity even when there is no risk that the firm
will default
14.2 - Modigliani-Miller I: Leverage, Arbitrage, and Firm Value
Perfect capital markets conditions:
1. Investors and firms can trade the same set of securities at competitive market
prices equal to the present value of their future cash flows
2. There are no taxes, transaction costs, or issuance costs associated with
security trading
3. A firm’s financing decisions do not change the cash flows generated by its
investments, nor do they reveal new information about them
MM-proposition 1:
In a perfect capital market, the total value of a firm’s securities is equal to the
market value of the total cash flows generated by its assets and is not affected
by its choice of capital structure
Homemade leverage = when investors use leverage in their own portfolios to
adjust the leverage choice made by the firm
, Market value balance sheet = accounting balance sheet with 2 exceptions:
1. All assets and liabilities of the firm are included, even intangible assets which
are normally excluded from accounting balance sheets
2. All values are current market values rather than historical costs
Market value of equity = Market value of assets – Market value of debt(or
other liabilities)
Leveraged recapitalization = when a firm repurchases a significant
percentage of its outstanding shares by borrowing money
14.3 - Modigliani-Miller II: Leverage, Risk, and the Cost of Capital
MM-proposition 1:
E+D=U=A
E = market value of equity
D = market value of debt
U = market value of equity if the firm is unlevered
A = market value of the firm’s assets
This equality implies the following relationship:
E D
∗R E + ∗R D=RU RE = returns of levered equity
E+ D E +D
RD = returns of debt
RU = returns of unlevered equity
This can be rearranged into:
D
R E=R U + ( R −R D )
E U
MM-proposition 2:
The cost of capital of levered equity increases with the firm’s market value debt-
equity ratio
In the preceding two formulas you can replace R with ꟗ, with ꟗ representing risk
14.4 - Capital Structure Fallacies
Two incorrect arguments made in favour of leverage:
1. Leverage can increase a firm’s expected earnings per share
-> its true that repurchasing shares with borrowed money can increase EPS but
that happens because the risk also increases because of the leverage. Therefore
its consistent with MM-proposition 1
2. Issuing equity will dilute existing shareholders’ ownership, so debt financing
should be used instead
-> this statement ignores that the cash raised by issuing new shares will increase
the firm’s assets. As long as the firm issues the new shares at fair price, there will
be no loss or gain to the shareholders. Any gain or loss associated with the
transaction will result from the NPV of the investments the firm makes with the
raised funds
, 14.5 - MM: Beyond the Propositions
Conclusive note:
With perfect capital markets, financial transactions neither add nor destroy value,
but instead represent a repackaging of risk
Chapter 15 - Debt and Taxes
15.1 - The Interest Tax Deduction
Corporations pay taxes on their profits after interest payments are deducted
-> this means that interest expenses reduce the amount of corporate tax firms
must pay
Example:
With leverage Without leverage
EBIT $2800 $2800
Interest Expense -400 0
Income before tax 2400 2800
Taxes (35%) -840 -980
Net Income $1560 $1820
Without leverage, the firm is left with more net income but there is less
total amount available to all investors. Debt holders and equity holders are
both financiers of the firm. Without leverage: only the 1820 net income is
available (to equity holders)
With leverage: 1560 net income is available (to equity holders) AND 400 is
available (to debt holders) which amounts to 1960 total
Interest tax shield = the additional amount that a firm would pay in taxes if it
did not have leverage
FORMULA: Interest tax shield = Corporate tax rate * Interest payments
15.2 - Valuing the Interest Tax Shield
In the presence of taxes, MM-proposition I is changed:
The total value of the levered firm exceeds the value of the firm without leverage
due to the present value of the tax savings from debt
FORMULA: Value levered firm = Value unlevered firm + Present Value Interest
Tax Shield
τ c∗Interest τ c∗( r f ∗D )
PV ( Interest Tax Shield ) = = =τ c∗D
rf rf
τ c =fir m' s marginal tax rate D=amount of debt r f =risk free interest rate
With tax-deductible interest, the effective after-tax borrowing rate is r *(1 - t c)
Weighted Average Cost of Capital (After Tax):
E D
r wacc = r E+ r (1−τ c ) 15.3 - Recapitalizing to Capture the Tax Shield
E+D E+ D D
When securities are fairly priced, the original shareholders of a firm capture the
full benefit of the interest tax shield from an increase in leverage
Chapter 14 - Capital Structure in a Perfect Market
14.1 - Equity Versus Debt Financing
Capital structure = the relative proportions of debt, equity, and other securities
that a firm has outstanding
Two ways to finance a firm/project:
Option 1: financing a firm with only equity (= unlevered equity)
Initial investment = $800
Projected cashflow in 1 year: either $1400 (50%) or $900 (50%) -> estimated:
$1150
Risk free interest rate = 5%
Risk premium = 10%
Cost of capital for this project = 15%
NPV = -$800 + $.15 = $200
-> entrepreneur can either complete the project and keep the projected cash flow
or cash out right now and earn $200 (this is because investors are willing to ‘buy’
the project for the discounted projected cash flow: .15 = 1000)
Option 2: financing a firm with debt and equity (= levered equity)
Borrowed amount = $500
Amount owed in one year: $525 (because of 5% risk free interest rate)
Projected cashflow in 1 year: either $1400 (50%) or $900 (50%)
Since debt holders get paid first, projected profit: either $875 (50%) or $375
(50%)
-> by the law of one price, the combined values of debt and equity must be equal
to the NPV of future cash flows (which is still $1000)
So: levered equity = $500
* Leverage increases the risk of equity even when there is no risk that the firm
will default
14.2 - Modigliani-Miller I: Leverage, Arbitrage, and Firm Value
Perfect capital markets conditions:
1. Investors and firms can trade the same set of securities at competitive market
prices equal to the present value of their future cash flows
2. There are no taxes, transaction costs, or issuance costs associated with
security trading
3. A firm’s financing decisions do not change the cash flows generated by its
investments, nor do they reveal new information about them
MM-proposition 1:
In a perfect capital market, the total value of a firm’s securities is equal to the
market value of the total cash flows generated by its assets and is not affected
by its choice of capital structure
Homemade leverage = when investors use leverage in their own portfolios to
adjust the leverage choice made by the firm
, Market value balance sheet = accounting balance sheet with 2 exceptions:
1. All assets and liabilities of the firm are included, even intangible assets which
are normally excluded from accounting balance sheets
2. All values are current market values rather than historical costs
Market value of equity = Market value of assets – Market value of debt(or
other liabilities)
Leveraged recapitalization = when a firm repurchases a significant
percentage of its outstanding shares by borrowing money
14.3 - Modigliani-Miller II: Leverage, Risk, and the Cost of Capital
MM-proposition 1:
E+D=U=A
E = market value of equity
D = market value of debt
U = market value of equity if the firm is unlevered
A = market value of the firm’s assets
This equality implies the following relationship:
E D
∗R E + ∗R D=RU RE = returns of levered equity
E+ D E +D
RD = returns of debt
RU = returns of unlevered equity
This can be rearranged into:
D
R E=R U + ( R −R D )
E U
MM-proposition 2:
The cost of capital of levered equity increases with the firm’s market value debt-
equity ratio
In the preceding two formulas you can replace R with ꟗ, with ꟗ representing risk
14.4 - Capital Structure Fallacies
Two incorrect arguments made in favour of leverage:
1. Leverage can increase a firm’s expected earnings per share
-> its true that repurchasing shares with borrowed money can increase EPS but
that happens because the risk also increases because of the leverage. Therefore
its consistent with MM-proposition 1
2. Issuing equity will dilute existing shareholders’ ownership, so debt financing
should be used instead
-> this statement ignores that the cash raised by issuing new shares will increase
the firm’s assets. As long as the firm issues the new shares at fair price, there will
be no loss or gain to the shareholders. Any gain or loss associated with the
transaction will result from the NPV of the investments the firm makes with the
raised funds
, 14.5 - MM: Beyond the Propositions
Conclusive note:
With perfect capital markets, financial transactions neither add nor destroy value,
but instead represent a repackaging of risk
Chapter 15 - Debt and Taxes
15.1 - The Interest Tax Deduction
Corporations pay taxes on their profits after interest payments are deducted
-> this means that interest expenses reduce the amount of corporate tax firms
must pay
Example:
With leverage Without leverage
EBIT $2800 $2800
Interest Expense -400 0
Income before tax 2400 2800
Taxes (35%) -840 -980
Net Income $1560 $1820
Without leverage, the firm is left with more net income but there is less
total amount available to all investors. Debt holders and equity holders are
both financiers of the firm. Without leverage: only the 1820 net income is
available (to equity holders)
With leverage: 1560 net income is available (to equity holders) AND 400 is
available (to debt holders) which amounts to 1960 total
Interest tax shield = the additional amount that a firm would pay in taxes if it
did not have leverage
FORMULA: Interest tax shield = Corporate tax rate * Interest payments
15.2 - Valuing the Interest Tax Shield
In the presence of taxes, MM-proposition I is changed:
The total value of the levered firm exceeds the value of the firm without leverage
due to the present value of the tax savings from debt
FORMULA: Value levered firm = Value unlevered firm + Present Value Interest
Tax Shield
τ c∗Interest τ c∗( r f ∗D )
PV ( Interest Tax Shield ) = = =τ c∗D
rf rf
τ c =fir m' s marginal tax rate D=amount of debt r f =risk free interest rate
With tax-deductible interest, the effective after-tax borrowing rate is r *(1 - t c)
Weighted Average Cost of Capital (After Tax):
E D
r wacc = r E+ r (1−τ c ) 15.3 - Recapitalizing to Capture the Tax Shield
E+D E+ D D
When securities are fairly priced, the original shareholders of a firm capture the
full benefit of the interest tax shield from an increase in leverage
