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Notities hoorcolleges O&V
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College 1. HerhalingInvestment project within a firm
- Investment outlay (uitgave) 𝐼0 = 𝐶𝑎𝑝𝐸𝑋 + Δ𝑁𝑊𝐶
- Projected cash flows E(CFt), using all-equity fiction
- Cost of capital, applicable to the project (rP)
𝐸(𝐶𝐹 )
Project value= 𝑃𝑉 = ∑𝑇𝑡=1 (1+𝑟 𝑡)𝑡 = current market value of additional cash flow stream for
𝑃
the firm but this is only obtainable after paying the investment outlay I 0.
Net present value= NPV=PV-I0.
NPV is identical to the increase in the firm market value
The project discount 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 𝑟𝑃 = 𝑟𝑓 + [𝐸(𝑅𝑚𝑘𝑡 ) − 𝑟𝑓 ] 𝛽𝑃
Market risk premium= 𝐸(𝑅𝑚𝑘𝑡 ) − 𝑟𝑓
However, 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→rwacc
𝐸 𝐷
𝑟𝑤𝑎𝑐𝑐 = 𝐸+𝐷 𝑟𝐸 + 𝐸+𝐷 𝑟𝐷 → E,D= (market value) amounts of equity and debt used to finance
the investment project.
rE and rD are the required returns by outside investors on equity and debt in the company.
Chapter 14. Capital structure in a perfect market
Unlevered equity: equity in a firm with no debt
Levered equity: equity in a firm that also has debt outstanding
Levered equity cash flower 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.
Proposition 1 of Modigliani and Miller (MM I): there is not present value to be created by
choosing whatever financing package
MM I holders 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: when a company uses borrowed funds to pay a large special
dividend or to repurchase a significant amount of outstanding shares.
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 and rD= market value returns on levered equity and debt
𝐸 𝐷
- 𝐸+𝐷 𝑟𝐸 + 𝐸+𝐷 𝑟𝐷 = 𝑟𝑈
𝐷
- Rewriting this gives 𝑟𝐸 = 𝑟𝑈 + (𝑟𝑈 − 𝑟𝐷 ) 𝐸 = MM Proposition II
In an unlevered firm:
- All of the free cash flows generated by the firm’s assets are paid out to its
equityholders
- Market value, risk and cost of capital for the firm’s assets and its equity coincide→
rU=rA
In a levered firm:
- There is no change in asset free cash flows, so r U is still equal to rA
- MM I states that rwacc continues to be equal to rU, since increased leverage adjusts rE
𝐸 𝐷
accordingly→ 𝑟𝑤𝑎𝑐𝑐 = 𝐸+𝐷 𝑟𝐸 + 𝐸+𝐷 𝑟𝐷
If debt is risky, it means that it is not sure that debt providers receive their promised
payments in full. With the MM assumptions, debtholders know in advance that:
- The firm will default in the weak state
- They will only receive the firm’s cash flow
→ 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. This risk premium is determined by the market price of risk
Equity issue and dilution
As long as shares are sold to investors at a fair price, there is no cost of dilution
(value dilution describes the reduction in the current price of a stock due to the increase in
the number of shares) associated with issuing equity. While the number of shares increases
when equity is issued, the firm’s assets also increase because of the cash raised, and the
per-share value of equity remains unchanged (see page 540).
Real value of MM analysis
,With perfect capital markets, financial transactions are a zero-NPV activity that neither add
nor destroy value on their own, but rather repackage the firm’s risk and return. Capital
structure- and financial transactions more generally- affect a firm’s value only because of its
impact on some type of market imperfection.
Chapter 15. Debt and taxes
Dutch corporate tax regime
Corporate taxation= vennootschapsbelasting (VPB). Interest payments are tax deductable.
Delnemingsvrijstelling is a provision/exemption to avoid double taxation, it is heavily used
by multinational companies and artists.
Incentive to use debt
Net income (available to equityholders) is lower with leverage, so levered equity value is
lower than unlevered equity value. Although debt obligations reduce equity value, the total
amount available to all investors (so equityholders and debtholders) is higher with leverage.
Interest tax shield= (Corporate tax rate) x (Interest payments).
The interest tax shield is a debt-related cash flow. It arises by the very existence of debt in
the firm. This 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 by the present value of the interest tax shield,
discounted using the cost of debt capital, so we get:
VL = VU + PV(interest tax shield) = MM proposition I with taxes
After-tax cost of debt capital
With tax-deductible interest, the firm effectively borrows at 𝑟𝐷 (1 − 𝜏𝑐 )= cost of debt capital
after tax→ the weighted average after-tax cost of capital becomes:
𝐸 𝐷 𝐷
𝑟𝑤𝑎𝑐𝑐 = 𝐸+𝐷 𝑟𝐸 + 𝐸+𝐷 𝑟𝐷 − 𝐸+𝐷 𝑟𝐷 𝜏𝑐 = Pretax WACC – Reduction due to interest tax shield.
Leveraged recapitalization
There is tax-related value to be gained from using debt. So firms should exploit this by
switching to a higher debt ratio: recapitalization. Why firms should do this: management
acts in the interest of all investors in the firm (equityholders, debtholders). The decision to
use more debt does not affect asset cash flows (at least under the current assumptions).
With fair pricing, debtholder are never worse off (want die wordt niets afgenomen). The
interest tax shield makes equityholders better off. So employing more debt is Pareto
optimal.
Equilibrium repurchase price P’
𝐷
- R= number of shares repurchased = 𝑃′ → P’ is de prijs waartegen we gaan kopen
- N= number of remaining shares = 𝑁0 − 𝑅; 𝑁0 = pre-repurchase number of shares
𝐸
- 𝑃′ = 𝑁𝐿, where 𝐸𝐿 follows from 𝑉𝐿 = 𝑉𝑈 + 𝑇𝐷 ;
𝑇 𝑖𝑠 𝑝𝑟𝑒𝑠𝑒𝑛𝑡 𝑣𝑎𝑙𝑢𝑒 𝑡𝑎𝑥 𝑠ℎ𝑖𝑒𝑙𝑑 𝑎𝑛𝑑 𝐷 𝑖𝑠 𝑑𝑒𝑏𝑡, and 𝐸𝐿 = 𝑉𝐿 − 𝐷
- Equilibrium pricing requires that 𝐸𝐿 + 𝐷 = 𝑉𝐿 = (𝑁 + 𝑅) 𝑃′ , so
𝑉𝐿 𝑉
𝑃′ = 𝑁+𝑅 = 𝑁𝐿 (dit is hetzelfde als wat bij puntje 3 staat)
0
, - 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’
Personal taxes
The Dutch and US income tax systems are both based on the double taxation principle:
- Cash flows to investors are typically taxed twice: once when earned at the corporate
level and again at the personal level when investors receive interest or dividend
income, and when they realize capital gains. The Dutch Income Tax code taxes
personal wealth in Box 3 and Box 2 (“Aanmerkelijk Belang”). However, interest
payments are tax deductible, also at the personal level. There are some important
exemptions, such as the Dutch “Vrijstelling voor beleggingsinstellingen”
Economically, this implies:
- 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 differential tax treatment between debt- and equity-related income
US personal tax system
- 𝜏𝑐 = corporate tax
- 𝜏𝑖 = income tax rate on interest income
- 𝜏𝑒 = income tax rate on equity income (dividenden
en koerswinsten)
Differential treatment
- Interest income is tax deductible for the firm, but
(highly) taxed at the investor level
- Equity income is taxed both at firm level and at
investor level
Cash flows and value
(1−𝜏𝑐 )(1−𝜏𝑒)
: 𝜏∗ = 1 − (1−𝜏𝑖 )
Personal taxes and the WACC
𝐸 𝐷 𝐷
The WACC for the firm is still given by: 𝑟𝑤𝑎𝑐𝑐 = 𝐸+𝐷 𝑟𝐸 + 𝐸+𝐷 𝑟𝐷 − 𝐸+𝐷 𝑟𝐷 (1 − 𝜏𝑐 )
- With personal taxes, the firm’s equity (𝑟𝐸 ) and debt (𝑟𝐷 ) costs of capital will adjust to
compensate for their tax burdens
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