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Samenvatting Alle formules voor ondernemingsfinanciering en vermogensmarkten
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Chapter 17 Payout policyChapter 14 Captial structure in perfect market • 𝑃𝑐𝑢𝑚 = Current Dividend + PV (Future Dividends)
• MMII, the cost of capital for levered equity is 𝑃𝑒𝑥 = PV (Future Dividends)
𝐷
𝑟𝐸 = 𝑟𝑈 + (𝑟𝑈 − 𝑟𝐷 ) • The effective dividend tax rate 𝜏𝑑∗ , measures the
𝐸
• Firm’s WACC in perfect capital market net tax cost to the investor per dollar of dividend
𝐸 𝐷 income received:
𝑟𝑤𝑎𝑐𝑐 = 𝑟𝐴 = 𝑟𝑈 = 𝑟𝐸 + 𝑟𝐷 (𝜏𝑑 −𝜏𝑔 )
𝐸+𝐷 𝐸+𝐷
• The market risk of a firm’s assets can be estimated 𝜏𝑑∗ =
(1−𝜏𝑔 )
by its unlevered beta: 𝜏𝑔 : tax on capital gains
𝐸 𝐷
𝛽𝑈 = 𝛽𝐸 + 𝛽𝐷 𝜏𝑑 : tax on dividend
𝐸+𝐷 𝐸+𝐷
• Leverage increases the beta of a firm’s equity: • The effective tax disadvantage of retaining cash is
𝐷 given by
𝛽𝐸 = 𝛽𝑈 + (𝛽𝑈 − 𝛽𝐷 ) (1−𝜏𝑐 )(1−𝜏𝑔 )
𝐸 ∗
𝜏𝑟𝑒𝑡𝑎𝑖𝑛 = (1 − (1−𝜏𝑖 )
)
Chapter 15 Dept and taxes
• The gain to investors from the tax deductibility of Chapter 18 Capital budgeting and Valuation with leverage
interest payments is called the interest tax shield. • The key steps in the WACC valuation method are
Interest Tax Shield = Corporate Tax Rate x Interest as follows:
Payments 1. Determine the unlevered free cash flows
• Value unlevered firm of the investment.
𝑉𝐿 = 𝑉𝑈 + PV(Interest Tax Shield) 2. Compute the weighted average cost of
• Present value of permanent dept tax shield capital:
𝐸 𝐷
PV (interest Tax Shield) = 𝜏𝑐 x D 𝑟𝑤𝑎𝑐𝑐 = 𝑟 + 𝑟 (1 − 𝜏𝑐 )
𝐸+𝐷 𝐸 𝐸+𝐷 𝐷
• Effective after-tax WACC 3. Compute the value with leverage, 𝑉0𝐿 , by
𝐸 𝐷
𝑟𝑤𝑎𝑐𝑐 = 𝑟𝐸 + 𝑟𝐷 (1 − 𝜏𝑐 ) discounting the free cash flows of the
𝐸+𝐷 𝐸+𝐷
investment using the WACC.
𝐸 𝐷 𝐷 𝐹𝐶𝐹
= 𝑟 + 𝑟 - 𝑟 𝜏 𝑉𝐿 =
𝐸+𝐷 𝐸 𝐸+𝐷 𝐷 𝐸+𝐷 𝐷 𝑐 𝑟𝑤𝑎𝑐𝑐
• To determine the value of a levered investment
Pre-tax WACC Reduction due to interest tax using the APV method, proceed as follows:
1. Determine the investment’s value
• effective tax advantage of dept without leverage, 𝑉𝑈 , by discounting
(1−𝜏𝑐 )(1−𝜏𝑒 )
𝜏* = 1 - its free cash flows at the unlevered
(1−𝜏𝑖 )
cost of capital 𝑟𝑈
𝐸 𝐷
𝜏𝑐 : corporate tax 𝑟𝑈 = 𝑟 + 𝑟 =
𝐸+𝐷 𝐸 𝐸+𝐷 𝐷
𝜏𝑒 : tax on equity income 𝑝𝑟𝑒𝑡𝑎𝑥 𝑊𝐴𝐶𝐶
𝜏𝑖 : tax on interest income 2. Determine the present value of the
interest tax shield:
• We can quantify the tax disadvantage for excess a. Given debt 𝐷𝑡 on date t, the tax
interest payments by setting 𝜏𝑐 = 0 (assuming shield on date t + 1 is 𝜏𝑐 𝑟𝐷 𝐷𝑡
there is no reduction in the corporate tax for b. If the debt level varies with the
excess interest payments) investment’s value or free cash flow,
∗ (1−𝜏 ) 𝜏 −𝜏 use the discount rate 𝑟𝑈 . (If the debt
𝜏𝑒𝑥 = 1 − (1−𝜏𝑒) = (1−𝜏
𝑒 𝑖
)
<0
𝑖 𝑖 is predetermined, discount the tax
shield at rate 𝑟𝐷 .
Chapter 16 Financial distress, Managerial incentives and
3. Add the unlevered value 𝑉𝑈 to the
information
present value of the interest tax
• Value unlevered firm shield to determine the value of the
𝑉𝐿 = 𝑉𝑈 + PV(Interest Tax Shield) – PV(financial investment with leverage, 𝑉𝐿
distress Costs) 𝑉𝐿 = 𝐴𝑃𝑉 = 𝑉𝑈 + 𝑃𝑉(𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑇𝑎𝑥 𝑆ℎ𝑖𝑒𝑙𝑑)
→ Optimal leverage is the level of debt that • The key steps in the flow-to-equity method for
maximizes 𝑉𝐿 valuing a levered investment are as follows:
• With debt overhang, equity holders will benefit 1. Determine the free cash flow to equity of
from new investment only if the investment:
𝑁𝑃𝑉 𝛽𝐷 𝐷
> FCFE = FCF - (1 - 𝜏𝑐 ) x (Interest Payments)
𝐼 𝛽𝐸 𝐸
I: investment from equity holders in the project + (Net Borrowing)
with similar risk as the rest of the firm 2. Determine the equity cost of capital 𝑟𝐸
• The value of a firm, including agency costs and 3. Compute the contribution to equity value,
benefits, is: E, by discounting the free cash flow to
𝑉𝐿 = 𝑉𝑈 + PV(Interest Tax Shield) – PV(financial equity using the equity cost of capital.
distress Costs) – PV(Agency Costs of Dept) + • Dept capacity is the amount of dept at date t that
PV(Agency Benefits of Dept) is required to maintain firms target dept-to-value
ratio, d. If 𝑉𝑡𝐿 , is the project’s levered continuation
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