ONDERNEMINGSFINANCIERING
& VERMOGENSMARKTEN
H14 CAPITAL STRUCTURE IN A PERFECT MARKET
NPV and Market Value
Investment project within a firm:
• Investment outlay I0 = CapEx + ΔNWC
• Projected cash flows E(CFt), using all-equity fiction
• Cost of capital, applicable to the project (rp)
Project value = PV =
This is the current market value of additional cash flow stream for the firm, but this is only obtainable
after paying the investment outlay I0.
Net Present Value = NPV = PV − I0
NPV is identical to the increase in firm market value: NPV = ΔV
Project discount rate (rp)
This rate reflects the risk embedded in the project cash flows, as perceived by the capital market.
Only the systematic part of the risk is relevant (CAPM), which is measured by the project’s beta-
coefficient (β).
The project’s risk (βp) is not necessarily equal to that of the existing projects in the firm (β).
Therefore CAPM: rp = rf + [E(Rmkt) − rf] βp
market risk premium = E(Rmkt) − rf
In determining expected cash flows, we continue to use the all-equity assumption. But firms are
usually financed with equity and debt. This should be included in the (N)PV calculation.
Not in the expected cash flows, but in the relevant cost of capital.
Think of: rwacc = weighted average cost of capital =
rE = equity cost of capital
rD = cost of debt capital
βd = beta of debt
βE = equity beta
This rwacc is used to discount the expected cash flows.
Expected cash flows and all-equity fiction
Why do we determine expected cash flows using this all-equity fiction?
Voor de berekening van de expected cash flows moet je doen alsof er alleen eigen vermogen is. Zelfs
al is er vreemd vermogen aanwezig in de onderneming.
This is a profound question, which relates to: Should a company be assessed at its ability to undertake
excellent real projects, or at its qualities to make smart financial decisions?
The relevant expected cash flow definition should not include financial items such as interest costs.
Therefore the all-equity fiction.
, ONDERNEMINGSFINANCIERING
& VERMOGENSMARKTEN
Finance gebruikt een condensed balance sheet, een verkorte versie van de normale balans.
De adjusted balance sheet is de condensed balance sheet
nog verder vereenvoudigd. →
This defines (net) productive assets as closely as possible
(worden benadrukt). This asset total is financed by capital
market investors. → expliciete financieringsovereenkomst
Using explicit financing agreements or securities:
◦ Equity, i.e. shares of stock
◦ Bonds, loans (long term)
◦ Bank credit, short term loans
Net working capital = operationeel werkkapitaal = Voorraden + vorderingen – crediteuren – overige
kortlopende passiva
Start up a new firm: steps
• Strategy, management team (MT)
• Business plan is ready, which includes current investment:
◦ Capital expenditures in fixed assets, i.e. CapEx
◦ Operational net working capital, i.e. ΔNWC
• It also includes expected cash flows, resulting from investing and pursuing the strategy
However: MT-members are not able to fund the investment outlay themselves, so they have to attract
external capital and issue securities on the capital market.
The fundamental question is:
What capital structure should the MT choose? So, what relative proportions (or “package”) of debt,
equity and other securities should they issue in order to finance the firm’s initial investment?
Relevant because maybe different packages have different (net) present values (!) It is not just money
that is needed, so not just any package will do.
Unlevered firm: bedrijf met alleen eigen vermogen
Unlevered equity: equity in een onderneming waar slechts equity is, géén debt, vreemd
vermogen.
Levered equity: equity in a firm that also has debt outstanding.
, ONDERNEMINGSFINANCIERING
& VERMOGENSMARKTEN
Law of One Price: als iets hetzelfde is, heeft het ook dezelfde prijs.
The cash flows of both debt and levered equity sum to the firm’s cash flow.
When using both debt and equity:
The issue amount of levered equity is lower than with unlevered equity, but the total financing
package still yields the same amount. Therefore 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. So levered equity cash flows may not be discounted at the same
(unlevered) discount rate.
Hefboomeffect: vergroting van risico.
Debt is riskfree, met rf als disconteringsvoet.
! Cash flows kunnen niet veranderen door de toevoeging van debt, die berekenen we altijd onder de
all-equity assumption.
Cost of capital and leverage
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 is:
EU = V U = V L = E L + D
EU = unlevered eigen vermogen
EL = levered eigen vermogen
VU = marktwaarde onderneming die unlevered is.
VL = marktwaarde onderneming die levered is.
D = debt
There is no net present value to be created by choosing whatever financing package
→ This is the famous Proposition I of Modigliani and Miller (MM I): VU = V L
Waarde creëer je door investeringsprojecten te doen met een positieve netto contante waarde, maar
denk niet dat je daar bovenop door slim te financieren nog iets kunt bedenken. Je voegt geen waarde
toe aan datgene wat je ook unlevered zou kunnen bereiken.
This holds also for other
debt/equity packages. rwacc does
not change for different values of
debt.
Cost of levered equity rises
sharply for higher debt levels.
, ONDERNEMINGSFINANCIERING
& VERMOGENSMARKTEN
Modigliani-Miller 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: herkapitalisatie, andere verhouding vreemd vermogen en eigen
vermogen. Je leent om vervolgens met dat geld aandelen in de markt op te kopen, en dus grijp je
direct in in het aantal aandelen dat uitstaat en krijg je een andere capital structure.
This happens when a company uses borrowed funds:
• to pay a large special dividend
• or to repurchase a significant amount of outstanding shares
LEVERAGE, RISK AND THE COST OF CAPITAL MODIGLIANI-MILLER’S PROPOSITION II
Symbols and terminology
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
MM Proposition II
rU = market value return on unlevered equity
rE = market value returns on levered equity
rD = market value returns on debt
Linear relationship between rE and D/E →
& VERMOGENSMARKTEN
H14 CAPITAL STRUCTURE IN A PERFECT MARKET
NPV and Market Value
Investment project within a firm:
• Investment outlay I0 = CapEx + ΔNWC
• Projected cash flows E(CFt), using all-equity fiction
• Cost of capital, applicable to the project (rp)
Project value = PV =
This is the current market value of additional cash flow stream for the firm, but this is only obtainable
after paying the investment outlay I0.
Net Present Value = NPV = PV − I0
NPV is identical to the increase in firm market value: NPV = ΔV
Project discount rate (rp)
This rate reflects the risk embedded in the project cash flows, as perceived by the capital market.
Only the systematic part of the risk is relevant (CAPM), which is measured by the project’s beta-
coefficient (β).
The project’s risk (βp) is not necessarily equal to that of the existing projects in the firm (β).
Therefore CAPM: rp = rf + [E(Rmkt) − rf] βp
market risk premium = E(Rmkt) − rf
In determining expected cash flows, we continue to use the all-equity assumption. But firms are
usually financed with equity and debt. This should be included in the (N)PV calculation.
Not in the expected cash flows, but in the relevant cost of capital.
Think of: rwacc = weighted average cost of capital =
rE = equity cost of capital
rD = cost of debt capital
βd = beta of debt
βE = equity beta
This rwacc is used to discount the expected cash flows.
Expected cash flows and all-equity fiction
Why do we determine expected cash flows using this all-equity fiction?
Voor de berekening van de expected cash flows moet je doen alsof er alleen eigen vermogen is. Zelfs
al is er vreemd vermogen aanwezig in de onderneming.
This is a profound question, which relates to: Should a company be assessed at its ability to undertake
excellent real projects, or at its qualities to make smart financial decisions?
The relevant expected cash flow definition should not include financial items such as interest costs.
Therefore the all-equity fiction.
, ONDERNEMINGSFINANCIERING
& VERMOGENSMARKTEN
Finance gebruikt een condensed balance sheet, een verkorte versie van de normale balans.
De adjusted balance sheet is de condensed balance sheet
nog verder vereenvoudigd. →
This defines (net) productive assets as closely as possible
(worden benadrukt). This asset total is financed by capital
market investors. → expliciete financieringsovereenkomst
Using explicit financing agreements or securities:
◦ Equity, i.e. shares of stock
◦ Bonds, loans (long term)
◦ Bank credit, short term loans
Net working capital = operationeel werkkapitaal = Voorraden + vorderingen – crediteuren – overige
kortlopende passiva
Start up a new firm: steps
• Strategy, management team (MT)
• Business plan is ready, which includes current investment:
◦ Capital expenditures in fixed assets, i.e. CapEx
◦ Operational net working capital, i.e. ΔNWC
• It also includes expected cash flows, resulting from investing and pursuing the strategy
However: MT-members are not able to fund the investment outlay themselves, so they have to attract
external capital and issue securities on the capital market.
The fundamental question is:
What capital structure should the MT choose? So, what relative proportions (or “package”) of debt,
equity and other securities should they issue in order to finance the firm’s initial investment?
Relevant because maybe different packages have different (net) present values (!) It is not just money
that is needed, so not just any package will do.
Unlevered firm: bedrijf met alleen eigen vermogen
Unlevered equity: equity in een onderneming waar slechts equity is, géén debt, vreemd
vermogen.
Levered equity: equity in a firm that also has debt outstanding.
, ONDERNEMINGSFINANCIERING
& VERMOGENSMARKTEN
Law of One Price: als iets hetzelfde is, heeft het ook dezelfde prijs.
The cash flows of both debt and levered equity sum to the firm’s cash flow.
When using both debt and equity:
The issue amount of levered equity is lower than with unlevered equity, but the total financing
package still yields the same amount. Therefore 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. So levered equity cash flows may not be discounted at the same
(unlevered) discount rate.
Hefboomeffect: vergroting van risico.
Debt is riskfree, met rf als disconteringsvoet.
! Cash flows kunnen niet veranderen door de toevoeging van debt, die berekenen we altijd onder de
all-equity assumption.
Cost of capital and leverage
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 is:
EU = V U = V L = E L + D
EU = unlevered eigen vermogen
EL = levered eigen vermogen
VU = marktwaarde onderneming die unlevered is.
VL = marktwaarde onderneming die levered is.
D = debt
There is no net present value to be created by choosing whatever financing package
→ This is the famous Proposition I of Modigliani and Miller (MM I): VU = V L
Waarde creëer je door investeringsprojecten te doen met een positieve netto contante waarde, maar
denk niet dat je daar bovenop door slim te financieren nog iets kunt bedenken. Je voegt geen waarde
toe aan datgene wat je ook unlevered zou kunnen bereiken.
This holds also for other
debt/equity packages. rwacc does
not change for different values of
debt.
Cost of levered equity rises
sharply for higher debt levels.
, ONDERNEMINGSFINANCIERING
& VERMOGENSMARKTEN
Modigliani-Miller 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: herkapitalisatie, andere verhouding vreemd vermogen en eigen
vermogen. Je leent om vervolgens met dat geld aandelen in de markt op te kopen, en dus grijp je
direct in in het aantal aandelen dat uitstaat en krijg je een andere capital structure.
This happens when a company uses borrowed funds:
• to pay a large special dividend
• or to repurchase a significant amount of outstanding shares
LEVERAGE, RISK AND THE COST OF CAPITAL MODIGLIANI-MILLER’S PROPOSITION II
Symbols and terminology
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
MM Proposition II
rU = market value return on unlevered equity
rE = market value returns on levered equity
rD = market value returns on debt
Linear relationship between rE and D/E →
