Samenvatting
Ondernemingsfinanciering & vermogensmarkten
Hoofdstuk 14
Expected unlevered equity return = verwachte opbrengst op basis van de kans op winst of
verlies. Geen vreemd vermogen aanwezig.
Levered equity alternative = ook vreemd vermogen aanwezig.
The cash flow of the company will now be divided between debt and equity providers:
debtholders have a priority claim paid first.
Equityholders receive the residual of the cash flow = residual claimholders.
The cash flows of both debt and levered equity sum to the firm’s cash flow
By the law of one price, the combined debt and equity package value must be equal to the
total firm value (1000 in het voorbeeld). So the levered equity is equal to the total firm value
– debt = 500 in het voorbeeld.
The cash flows of levered equity are smaller than those of unlevered equity. So the issue
amount of levered equity is lower than with unlevered equity. But the total financing
package still yields 1000 and the MT will be indifferent between both packages.
Levered equity cash flows are not only smaller, but the spread in levered equity returns is
also higher: levered equity is more risky levered equity may not be discounted at the
same (unlevered) discount rate.
Levered equityholders require a higher return in order to compensate them for the
increased risk.
Leverage increases the risk of equity even when ther is a zero probability that the firm will
default!
Levered cost of capital = rwacc is equal in both financing packages.
The suggested advantage of cheaper debt is annihilated by a compensating rise in the cost of
levered equity, such that for the market value of the firm: Eu= Vu=Vl=El + D
There is no net present value to be created by choosing whatever financing package =
Proposition I of Modigliani and Miller (MM I)
MM I holds under a set of conditions that defines a perfect capital market:
Investors and firms can trade the same set of securities at competitive market prices
equal to the present value of their future cash flows
There are no taxes, transaction costs or issuance costs associated with security
trading
A firm’s financing decisions do not change the cash flows generated by its
investments, nor do they reveal new information about them
In such a setting the law of one price implies that leverage will not affect the total value of
the firm total firm value is equal to the market value generated by its assets and is not
,affected by its choice of capital structure. Leverage only changes the allocation of cash flows
between debt and equity, without altering the total cash flows of the firm.
Leveraged recapitalization (recap) = when a company uses borrowed funds to pay a large
special dividend or to repurchase a significant number of outstanding shares.
Recap = choosing a completely different capital structure.
E = market value of equity in a levered firm
D = market value of debt (in a levered firm)
U = market value of unlevered equity
A = market value of the firm’s assets
MM I states: A = U = E + D
Ru = market value return on unlevered equity
Re and Rd = market value returns on levered equity and debt
Identity relationship = E/(E+D)*Re + D/(E+D)*Rd = Ru
Rewritten = Re = Ru+(Ru-Rd)*D/E
Cost of levered equity = cost of unlevered equity + premium due to leverage (MM
proposition II)
Cost of capital for capital budgeting
For unlevered firm: Ru = Ra
For a levered firm: there is no change in asset free cash flows, so Ru is still equal to Ra
MM I states that Rwacc continues to be equal to Ru since increased leverage adjusts Re
accordingly: Rwacc = E/(E+D)*Re + D/(E+D)*Rd
What if there is so much leverage that debt is risky?
It is not sure that debt providers receive their promised payments in full
The company is not able to pay debtholders fully when the weak state materializes at time 1:
the company will default.
The debtholders know in advance that
The firm will default in the weak state
They will only receive the firm’s cash flow of 900 which is less than face value +
interest
Fair pricing implies that debtholders want to be compensated for this default risk they
require a promised yield which includes a risk premium over the riskless interest rate. The
risk premium is determined by the market price of risk.
Equity issue and dilution (verwatering)
As long as the firm sells the new shares of equity at the fair market price = no gain or loss for
current shareholders
But investment project may involve a positive NPV which is likely to rise due to this good
investment. So any dilution argument is overly fallacious: it suggest that investments
financed by equity issues are always bad investments.
, Hoofdstuk 15
Corporate taxation = vennootschapsbelasting
Interest payments are tax deductible
Vreemd vermogen je betaalt interest
Eigen vermogen dividend aan aandeelhouders (dit is niet aftrekbaar)
Although debt obligations reduce equity value, the total amount available to all investors is
higher with leverage. Difference between levered and unlevered = interest tax shield.
Interest tax shield = interest rate x market value of debt
Interest tax shield arises by the very existence of debt in the firm
The cash flow carries the same risk as the debt cash flow
Its value should therefore be obtained using the cost of debt capital
The value of the levered firm is higher due to the present value of the interest tax shield
discounted using the cost of debt capital: Vl = Vu+PV(interest tax shield)
= MM Proposition I with taxes
With tax-deductible interest, the firm effectively borrows at Rd(1-taxrate)
This is the firm’s cost of debt capital after tax
Rwacc after-tax becomes: Rwacc= E/(E+D)*rE+ D/(E+D)*rD * (1-taxrate)
Leveraged recapitalization tax-related value to be gained from using debt, firms could
exploit this by switching to a higher debt ratio.
Equilibrium repurchase price P’
R = number of shares repurchased= D/P’
N = number of remaining shares = N0 – R (N0 = pre-repurchase number of shares)
P’= EL/N (EL follows from VL = Vu + TD and EL = VL – D)
Equilibrium pricing requires that EL + D = VL = (N+R)*P’ dus
P’= VL/(N+R) = VL/N0
from finance theory thus far, we know that the interest tax shield will be claimed by
existing shareholders, so this is consistent with the equilibrium relationship for P’.
Dutch and US income tax systems are both based on the double taxation principle
Typically taxed twice: once when earned at corporate level and again on personal
level
Debt and equity investors pay income taxes on their share of the after-tax corporate
cash flow, reducing the net cash flow received
There might be a differential tax treatment between debt- and equity-related income
Symbols used:
Tau c = corporate tax rate
Tau I = income tax rate on interest income
Tau e = income tax rate on equity income (average of dividend tax and capital gains
tax rate)
Market capitalization = waarde van het eigen vermogen
Ondernemingsfinanciering & vermogensmarkten
Hoofdstuk 14
Expected unlevered equity return = verwachte opbrengst op basis van de kans op winst of
verlies. Geen vreemd vermogen aanwezig.
Levered equity alternative = ook vreemd vermogen aanwezig.
The cash flow of the company will now be divided between debt and equity providers:
debtholders have a priority claim paid first.
Equityholders receive the residual of the cash flow = residual claimholders.
The cash flows of both debt and levered equity sum to the firm’s cash flow
By the law of one price, the combined debt and equity package value must be equal to the
total firm value (1000 in het voorbeeld). So the levered equity is equal to the total firm value
– debt = 500 in het voorbeeld.
The cash flows of levered equity are smaller than those of unlevered equity. So the issue
amount of levered equity is lower than with unlevered equity. But the total financing
package still yields 1000 and the MT will be indifferent between both packages.
Levered equity cash flows are not only smaller, but the spread in levered equity returns is
also higher: levered equity is more risky levered equity may not be discounted at the
same (unlevered) discount rate.
Levered equityholders require a higher return in order to compensate them for the
increased risk.
Leverage increases the risk of equity even when ther is a zero probability that the firm will
default!
Levered cost of capital = rwacc is equal in both financing packages.
The suggested advantage of cheaper debt is annihilated by a compensating rise in the cost of
levered equity, such that for the market value of the firm: Eu= Vu=Vl=El + D
There is no net present value to be created by choosing whatever financing package =
Proposition I of Modigliani and Miller (MM I)
MM I holds under a set of conditions that defines a perfect capital market:
Investors and firms can trade the same set of securities at competitive market prices
equal to the present value of their future cash flows
There are no taxes, transaction costs or issuance costs associated with security
trading
A firm’s financing decisions do not change the cash flows generated by its
investments, nor do they reveal new information about them
In such a setting the law of one price implies that leverage will not affect the total value of
the firm total firm value is equal to the market value generated by its assets and is not
,affected by its choice of capital structure. Leverage only changes the allocation of cash flows
between debt and equity, without altering the total cash flows of the firm.
Leveraged recapitalization (recap) = when a company uses borrowed funds to pay a large
special dividend or to repurchase a significant number of outstanding shares.
Recap = choosing a completely different capital structure.
E = market value of equity in a levered firm
D = market value of debt (in a levered firm)
U = market value of unlevered equity
A = market value of the firm’s assets
MM I states: A = U = E + D
Ru = market value return on unlevered equity
Re and Rd = market value returns on levered equity and debt
Identity relationship = E/(E+D)*Re + D/(E+D)*Rd = Ru
Rewritten = Re = Ru+(Ru-Rd)*D/E
Cost of levered equity = cost of unlevered equity + premium due to leverage (MM
proposition II)
Cost of capital for capital budgeting
For unlevered firm: Ru = Ra
For a levered firm: there is no change in asset free cash flows, so Ru is still equal to Ra
MM I states that Rwacc continues to be equal to Ru since increased leverage adjusts Re
accordingly: Rwacc = E/(E+D)*Re + D/(E+D)*Rd
What if there is so much leverage that debt is risky?
It is not sure that debt providers receive their promised payments in full
The company is not able to pay debtholders fully when the weak state materializes at time 1:
the company will default.
The debtholders know in advance that
The firm will default in the weak state
They will only receive the firm’s cash flow of 900 which is less than face value +
interest
Fair pricing implies that debtholders want to be compensated for this default risk they
require a promised yield which includes a risk premium over the riskless interest rate. The
risk premium is determined by the market price of risk.
Equity issue and dilution (verwatering)
As long as the firm sells the new shares of equity at the fair market price = no gain or loss for
current shareholders
But investment project may involve a positive NPV which is likely to rise due to this good
investment. So any dilution argument is overly fallacious: it suggest that investments
financed by equity issues are always bad investments.
, Hoofdstuk 15
Corporate taxation = vennootschapsbelasting
Interest payments are tax deductible
Vreemd vermogen je betaalt interest
Eigen vermogen dividend aan aandeelhouders (dit is niet aftrekbaar)
Although debt obligations reduce equity value, the total amount available to all investors is
higher with leverage. Difference between levered and unlevered = interest tax shield.
Interest tax shield = interest rate x market value of debt
Interest tax shield arises by the very existence of debt in the firm
The cash flow carries the same risk as the debt cash flow
Its value should therefore be obtained using the cost of debt capital
The value of the levered firm is higher due to the present value of the interest tax shield
discounted using the cost of debt capital: Vl = Vu+PV(interest tax shield)
= MM Proposition I with taxes
With tax-deductible interest, the firm effectively borrows at Rd(1-taxrate)
This is the firm’s cost of debt capital after tax
Rwacc after-tax becomes: Rwacc= E/(E+D)*rE+ D/(E+D)*rD * (1-taxrate)
Leveraged recapitalization tax-related value to be gained from using debt, firms could
exploit this by switching to a higher debt ratio.
Equilibrium repurchase price P’
R = number of shares repurchased= D/P’
N = number of remaining shares = N0 – R (N0 = pre-repurchase number of shares)
P’= EL/N (EL follows from VL = Vu + TD and EL = VL – D)
Equilibrium pricing requires that EL + D = VL = (N+R)*P’ dus
P’= VL/(N+R) = VL/N0
from finance theory thus far, we know that the interest tax shield will be claimed by
existing shareholders, so this is consistent with the equilibrium relationship for P’.
Dutch and US income tax systems are both based on the double taxation principle
Typically taxed twice: once when earned at corporate level and again on personal
level
Debt and equity investors pay income taxes on their share of the after-tax corporate
cash flow, reducing the net cash flow received
There might be a differential tax treatment between debt- and equity-related income
Symbols used:
Tau c = corporate tax rate
Tau I = income tax rate on interest income
Tau e = income tax rate on equity income (average of dividend tax and capital gains
tax rate)
Market capitalization = waarde van het eigen vermogen
