% This is lecture no. 10 of BU8201/: Business Finance.

\chapter{Capital Structure \& Leverage}%
\label{cha:capital_structure_&_leverage}

In capital structure there are two main sources of capital:
\begin{enumerate}
	\item Debt: The firm promises to make fixed payments regularly. However, when the firm defaults on payment, bankruptcy may occur.
	\item Equity: Equity holders receive whatever cash flows that is left over in the firm after paying the debt holders.
\end{enumerate}

Capital structure refers to the percentage of debt, preferred stock, and common equity that is used to finance a firm's assets.

\section{Business vs. Financial Risk}%
\label{sec:business_vs_financial_risk}

\subsection{Business Risk}%
\label{sub:business_risk}

\begin{definition}
	Business Risk.
	Business risk is the risk inherent in a firm's operations, surrounding uncertainty about the future operating income (EBIT).
\end{definition}
Business risk is measured using standard deviation of the EBIT.
We know that the EBIT is calculated as follows:
\begin{align*}
	\text{EBIT} & = \text{Sales} - \text{Operating Cost}\\
		    & = \text{Quantity} \times \text{Price} - \text{Operating Cost}
\end{align*}

\noindent
The following factors determine business risk:
\begin{enumerate}
	\item Uncertainty about demand (sales)
	\item Uncertainty about output prices
	\item Uncertainty about costs
	\item Operating leverage
\end{enumerate}

Operating leverage is the use of fixed costs rather than variable costs.
In general, more fixed costs lead to more operating leverage, which leads to more business risk.
This means that a small sales decline causes a big decline in the EBIT.

Although operating leverage comes with higher business risk, it is also accompanied by a higher expected EBIT.

\subsection{Financial Risk}%
\label{sub:financial_risk}

\begin{definition}
	Financial Leverage.
	Financial leverage is the use of debt and preferred stock which incurs fixed financial charges.
\end{definition}

Financial risk is the additional risk concentrated on common stockholders as a result of financial leverage.
The more debt there is, the more financial risk is associated with the firm.

\section{Optimal Capital Structure}%
\label{sec:optimal_capital_structure}

\begin{definition}
	Optimal Capital Structure.
	Optimal Capital Structure is the capital structure at which the stock price is maximised.
\end{definition}

\subsection{How to Determine the Impact of Changing Capital Structure on Stock Price}%
\label{sub:how_to_determine_the_impact_of_changing_capital_structure_on_stock_price}

To calculate the stock price, we must assume that all earnings are paid out as dividends, making the growth rate, $g=0$.
This means that:
\[
	\text{EPS} = \text{DPS}
.\]
And therefore the stock price is as follows:
\[
	\hat{P}_0 = \frac{D_1}{r_s - g} = \frac{\text{DPS}}{r_s} = \frac{\text{EPS}}{r_s}
.\]
To find the expected stock price, $\hat{P}_0$ at each debt level, we must find the EPS and appropriate $r_s$ at each debt level.

In practice, when a firm decides to change it's capital structure, it undergoes a process known as recapitalisation.

When a firm decides to take on more debt as part of it's capital structure, it borrows money from debt holders, and uses that money to purchase stock from stockholders.

In the opposite case, new shares are issued, the equity of which are used to pay of debt holders.

Taking in more debt increases financial risk.
To reflect this increase in risk, the Hamada equation shows how the beta in $r_s$ is affected by a change in the debt to equity ratio:
\[
	b_l = b_u\left[1 + (1-T)\left(\frac{D}{E}\right)\right]
.\]
Where $b_l$ is the levered beta that is determined by both business risk and financial risk, $b_u$ is the unlevered beta determined by business risk only, and $\frac{D}{E}$ is the debt to equity ratio.
