Advanced Corporate Finance

• Financing decisions

  A Financing decision is the anticipation of the company's future needs in funds and the possibility to put in place the tools and actions that will ensure that these needs are:

  • Fully covered

  • Risks managed

  • Costs minimized

  • Profitability maximized
• The funding of a firm refers to the way it is financed, by debt and equity (unlevered if it has no debt, levered if there is a debt).

  Capital Structure is the specific mixture of long-term debt and equity the firm uses to finance its operations.
• The leverage is the ratio of the debt to the equity. It is calculated by the sum of the weighted average of the debt and the equity.
• Suppose the firm has issued:

  • an amount E of equity, with return r(e)
  • an amount D of debt, paying an interest r(d)

  The firm’s expected return, often called weighted average cost of capital (WACC), is given by:

  𝑟(firm) = 𝑾𝑨𝑪𝑪 = 𝐸/(𝐸 + 𝐷) * 𝑟(e) + 𝐷/(𝐸 + 𝐷) * 𝑟(d)

  WACC is the rate of return that the firm has to provide, thanks to its activity, to pay interest to the debt and give the return required by the shareholders.
• How can we explain that the return on equity increases when the proportion of debt increases?

  1. Let us start from a firm without any debt: all the free cash-flows go to the shareholder.
  2. The firm issues a debt: it increases the risk for the shareholder; indeed, the bondholder is paid in first rank, so the shareholder is not sure to get money from the free cash-flows.

  ➔The shareholder will require a higher rate of return for his investment.

  Pursuing the reasoning shows that the higher the proportion of debt, the higher the required rate of return for the equity.
• Financing a firm with equity alone :

  Equity in a firm with no debt is called unlevered equity.

  Because there is no debt, the cash flows of the unlevered equity are equal to those of the project.
• Financing a firm with debt and equity :

  Financing the firm exclusively with equity is not the entrepreneur’s only option. He can also raise part of the initial capital using debt.

  Promised payments to debt holders must be made before any payments to equity holders are distributed.
• MODIGLIANI & MILLER’S THEORY

  The firm’s total cash flows still equal the cash flows of the project, and therefore have the same present value of 1000 € calculated earlier.

  Because the cash flows of the debt and equity sum to the cash flows of the project, by the Law of One Price the combined values of debt and equity must be 1000 €.

  Therefore, if the value of the debt is 500 €, the value of the levered equity must be E = 1000 € - 500 € = 500 €.
• MODIGLIANI & MILLER’S THEORY

  Therefore, if the value of the debt is 500 €, the value of the levered equity must be E = 1000 € - 500 € = 500 €.

  What is the new return of the equity?

  • Initial value = 500
  • Value in one year is on average: (875 + 375) / 2 = 625
  • r(e) = (625 – 500) / 500 = 25%
• Leverage impact on rE

  With some mathematical manipulations, the WACC formula can be rewritten in terms of

  𝐫(e) = 𝐖𝐀𝐂𝐂 + 𝐃/𝐄 * (𝐖𝐀𝐂𝐂 − 𝐫(d))

  Expected return on the equity, r(e) , increases in proportion to the debt/equity ratio.
• MODIGLIANI & MILLER’S THEORY – IMPACT ON BETA

  The coefficient β (beta) measures the systematic risk of assets A.

  Similarly, the formula: r = WACC + D/E * (WACC − r(d))

  leads to: Beta(e) = Beta(Cy) +D/E * (Beta(Cy)− Beta(d))

  if we denote by Beta(Cy) the beta of the company.
• Modigliani-Miller theory must be adapted when there are taxes.

  Indeed, interest are paid before computation of the taxes, while dividend (and retained earnings) are what remains after payment of the taxes.

  • Interest payments are tax deductible
  • Dividends and retained earnings are not tax deductible
• Tax shield

  A part of the interest on the debt is paid by the Government, as reduction of taxes.

  With tax shield, the interest paid on the debt is finally not D x r(d) but D x r(d) x (1 – Tax).

  We can also say that the interest rate of the debt is not r(d),

  but r(d) x (1 – Tax).

  • The higher the taxation rate, the higher the potential tax shield by increasing debt.
• Considering Taxes - Impact on value of the company

  The free cash flows of year t are higher for the levered company, by a term Tax x D x r(d).

  As the value of a firm is the present value of the future cash flows, the levered company has a higher value:

  Value(levered) = Value(unlevered) + PV(tax shield)

  • By increasing the debt, we can increase the value of the company (the higher the taxation rate, the higher the increase).
• Risk on the debt

  If the debt increases again, things are not so simple; bankruptcy risk increases and:

  • If the firm has solid assets (ex: Airlines Company), these can always be sold in case of bankruptcy: the debt can increase till moderate levels with few difficulties.
  • Conversely, if the assets are reduced (ex: publishing company) or fragile (ex: food company), their sale in case of bankruptcy will provide too few money to reimburse fully the debt.

  Debt becomes risky, has a beta, and its return increases (as given by the CPAM formula).
• Furthermore, the risk of bankruptcy needs to take additional

  costs into consideration.

  Indeed, a liquidation engenders a series of costs:

  • Administrative costs (lawyers, auditors…). Even if the activities can restart,

  These distress costs must be taken into account.
• Conclusion

  • In a world without taxes, the value of a firm does not depend on the capital structure (i.e., the relative proportion of debt and equity).
  • When there are taxes, they produce an advantage on the debt; the value of the firm increases with the level of the debt (and with the taxation rate).
  • However, increasing the debt generates risk of bankruptcy: costs of distress must be included.
  • The optimal capital structure is a trade-off between this benefit and this cost. It varies according to the assets of the company and the taxation rate.