Funding firm--> the way it is financed, by debt and equity

Unlevered = no debt

Levered = debt

Capital Structure --> mixture of long term debt and equity

Leverage = D/E where D can be change as E

Return of the portfolio : wA x rA + wB x rB

With weight =

The WACC is given by :

Blended rate : ((debt₀ / debt₀₊₁₎ x r₁) x ((debt₁ / debt₀₊₁) x r₂) = y

After tax-rate : y x 1 - T_c = X

X is the new r_d needed for the new WACC. §

NPV (Net Present Value) = -initial investment + expected CF / (1 + cost of capital)^

With expected CF = amount x % + amount x % + ...

And cost of capital = risk free + risk premium

If NPV > 0 then it's a good investment bc you'll expect to generate a return that exceed the required return.

NPV can be equity as we saw in Part III Exercise 1 of TD1.

• Financing a firm with equity alone :

It's called unlevered equity.

Unlevered equity = expected CF / (1+cost of capital)^t

This will give the amount that the investor are willing to pay today for the futur CF of the project and the maximum amount that can be raised by selling equity.

CF of unlevered equity = CF of the project which means risk of unlevered E = risk of the project.

Bc both of the risk are equal, shareholders are learning an appropriate return for the risk they are taking

• Financing a firm with equity & debt:

Can be use to raise part of the initial capital using debt.

Bc the CF will always be enough to repay the debt, the debt is risk-free.

Equity in a firm that also had debt is called levered equity.

CF for levered equity = (CF - debt repayment) x % + ...

And add the sum of all the CF to equity that you have.

Then r_e (return on equity) = (CF for levered on equity - NPV) / NPV

• First Form : In the absences of taxes, the value of the firm does not depend on its financing. -> There is no optimal capital structure.

• Second form : In the absences of taxes, the WACC does not depend on its financing.

CAPM Theory =

With B the coefficient which measures the systematic risk of assets A and (r_m - r_f)

With the WACC formula, it leads to :

M&M theory must be adapted bc interest is paid before computation of taxes while dividends ( and retained earning ) are what remains after payment.

• Interest are tax deductible
• Div and retained earning are not

In a world without taxes :

• Inv decision fully determine the firm's CF
• The way the firm is financed has no impact on CF

In a world with taxes :

• Inv decision fully determine the firm's pre tax CF
• The way it's financed has no impact on the pre tax CF

Tax shield = tax rate x interest paid

But tax shields bc company pay less taxes is :

Explanation : A part of the r_d is paid by the government, as reduction of taxes.

Value_levered = Value_unlevered + PV (tax shield)

By increasing the debt, we increase the value of the company

With Value_firm = Value_D + Value_E